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Math Handbook 833 I. Symbols 833 Isolating a Variable Square Root Property II. Measurements and Quadratic Equations Significant Digits 833–836 Quadratic Formula Significant Digits Dimensional Calculations Rounding Dimensional Analysis Operations with Significant Digits VII. Graphs of Relations 848–852 III. Fractions, Ratios, The Coordinate Plane Rates, and Proportions 837–838 Graphing Data to Fractions Determine a Relationship Ratios Interpolating and Extrapolating Rates Interpreting Line Graphs Proportions Linear Equations Slope IV. Exponents, Powers, Roots, Direct Variation and Absolute Value 839–841 Inverse Variation Exponents Quadratic Graphs Square and Cube Roots Operations with Exponents VIII. Geometry and Absolute Value Trigonometry 853–856 Perimeter, Area, and Volume V. Scientific Notation 841–843 Area Under a Graph Large Numbers— Right Triangles Using Positive Exponents Trigonometric Ratios Small Numbers— Law of Cosines and Law of Sines Using Negative Exponents Inverses of Sine, Cosine, and Tangent Operations with Scientific Notation Graphs of Trigonometric Functions VI. Equations 843–847 IX. Logarithms 857 Order of Operations Logarithms with Base b Solving Equations Common Logarithms Antilogarithms or Inverse Logarithms
Additional Problems 858
Solutions for Practice Problems 890
Tables 910 Color Conventions 910 Heats of Fusion and Electric Circuit Symbols 910 Vaporization of Some SI Base Units 911 Common Substances 913 SI Derived Units 911 Coefficients of Thermal Useful Conversions 911 Expansion at 20°C 914 Physical Constants 912 Speed of Sound SI Prefixes 912 in Various Media 914 Moments of Inertia for Wavelengths of Visible Light 914 Various Objects 912 Dielectric Constants, K (20°C) 914 Densities of Some The Planets 915 Common Substances 913 The Moon 915 Melting and Boiling Points The Sun 915 of Some Substances 913 Periodic Table of the Elements 916 Specific Heats of Some The Elements 917 Common Substances 913 Safety Symbols 918
919
927
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I. Symbols
change in quantity a b plus or minus a quantity ab } a multiplied by b ∝ is proportional to a(b) is equal to a b is approximately equal to a/badivided by b a } is approximately equal to b is less than or equal to a square root of a is greater than or equal to a absolute value of a is much less than logb x log to the base, b, of x ≡ is defined as
II. Measurements and Significant Digits Connecting Math to Physics Math is the language of physics. Using math, physicists are able to describe relationships among the measurements that they make using equa- tions. Each measurement is associated with a symbol that is used in physics equations. The symbols are called variables.
Significant Digits All measured quantities are approximated and have significant digits. The number of significant digits indicates the precision of the measurement. Precision is a measure of exactness. The number of significant digits in a measurement depends on the smallest unit on the measuring tool. The digit farthest to the right in a measurement is estimated. Example: What is the estimated digit for each of the measuring sticks in the figure below used to measure the length of the rod? Using the lower measuring tool, the length is between 9 and 10 cm. The measurement would be estimated to the nearest tenth of a centimeter. If the length was exactly on the 9-cm or 10-cm mark, record it as 9.0 cm or 10.0 cm. Using the upper measuring tool, the length is between 9.5 and 9.6 cm. The measurement would be estimated to the nearest hundredth of a centimeter. If the length was exactly on the 9.5-cm or 9.6-cm mark, record it as 9.50 cm or 9.60 cm.
0 mm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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All nonzero digits in a measurement are significant digits. Some zeros are significant and some are not. All digits between and including the first nonzero digit from the left through the last digit on the right are significant. Use the following rules when determining the number of significant digits. 1. Nonzero digits are significant. 2. Final zeros after a decimal point are significant. 3. Zeros between two significant digits are significant. Math Handbook 4. Zeros used only as placeholders are not significant.
Example: State the number of significant digits in each measurement.
5.0 g has two significant digits. Using rules 1 and 2 14.90 g has four significant digits. Using rules 1 and 2 0.0 has one significant digit. Using rules 2 and 4 300.00 mm has five significant digits. Using rules 1, 2, and 3 5.06 s has three significant digits. Using rules 1 and 3 304 s has three significant digits. Using rules 1 and 3 0.0060 mm has two significant digits (6 and the last 0). Using rules 1, 2, and 4 140 mm has two significant digits (just 1 and 4). Using rules 1 and 4
1. State the number of significant digits in each measurement. a. 1405 m d. 12.007 kg b. 2.50 km e. 5.8 106 kg c. 0.0034 m f. 3.03 10 5 mL
There are two cases in which numbers are considered exact, and thus, have an infinite number of significant digits. 1. Counting numbers have an infinite number of significant digits. 2. Conversion factors have an infinite number of significant digits.
Examples: The factor “2” in 2mg has an infinite number. The number 2 is a counting number. It is an exact integer.
The number “4” in 4 electrons has an infinite number. Because you cannot have a partial electron, the number 4, a counting number, is considered to have an infinite number of significant digits.
60 s/1 min has an infinite number. There are exactly 60 seconds in 1 minute, thus there are an infinite number of significant digits in the conversion factor.
834 Appendix A Math Handbook Math Handbook 835 Math Handbook of the decimal point. Round the Using rule 1 Using rule 2 Using rule 3 Using rule 4 Using rule 4 0.0034 m (1) (3) kg 12.007 c. d. Look at the digits to the right Look Round the result to the estimated place with the largest place value to the estimated place Round the result Add the numbers rounded to 3 significant digits is 8.77. rounded to 3 significant digits is 8.77. Round the following numbers to the statedRound the following numbers to the number of significant digits. 2.50 km (2) 1405 m (2) Add 1.456 m, 4.1 m, and 20.3 m. 1.456 m 4.1 m 20.3 m 25.856 m Round each number to the number of significantRound each number to the number digits shown in parentheses. a. b. When using a calculator, do all of the operations with as much precision as the using a calculator, When 8.7676 8.7519to 2 significant rounded digits is 8.8. 92.350to 3 significant rounded digits is 92.4. 92.25 rounded to 3 significant digits is 92.2. When the leftmost digit to be dropped is less the leftmost digit to be When than 5, that digit and any digits that remains unchanged. last digit in the rounded number the Then follow are dropped. and any digits dropped is greater than 5, that digit the leftmost digit to be When that number is increased by one. and the last digit in the rounded follow are dropped, that digit number, dropped is 5 followed by a nonzero the leftmost digit to be When and any digits number increas- last digit in the rounded follow are dropped. The that es by one. If the digit to the right of the last significant digit is equal to 5, and 5 is followed by a zero or no other digits, look at the last significant it by one; digit. If it is odd, increase if it is even, do not round up. 8.7645 rounded to 3 significant digits is 8.76. A number can tenths) or to place value (like hundreds or be rounded to a specific 25.9 m 2. The least precise valuesThe are 4.1 m and 20.3 m because to the they have only one digit right of the decimal points. The sum is only as precise as the least precise number being added. The result to the least precise value among the measurements—the smallest number of digits to the right of the decimal points. Example: Operations with Significant Digits Operations 1. 2. 3. 4. Rounding calculator allows, and then round the result to the correct number of significant digits. correct number of significantThe digits in the result on the measurements depends and on the operation. Addition and subtraction Examples: a specific number of significant digits. To do this, determine the place being rounded, do this, determine of significanta specific number digits. To following rules.and then use the 833-857 EM MHB-845813 6/8/04 10:26 PM Page 835 Page PM 10:26 6/8/04 MHB-845813 EM 833-857 833-857 EM MHB-845813 3/22/04 8:44 AM Page 836
Multiplication and division Look at the number of significant digits in each measure- ment. Perform the calculation. Round the result so that it has the same number of significant digits as the measurement with the least number of significant digits. Example: Multiply 20.1 m by 3.6 m. (20.1 m)(3.6 m) 72.36 m2 The least precise value is 3.6 m with two significant digits. The product can only have as many digits as the least precise of the multiplied numbers. Math Handbook 72 m Round the result to two significant digits
3. Simplify the following expressions using the correct number of significant digits. a. 5.012 km 3.4 km 2.33 km b. 45 g 8.3 g c. 3.40 cm 7.125 cm d. 54 m 6.5 s
Combination When doing a calculation that requires a combination of addition/ subtraction and multiplication/division, use the multiplication/division rule. Examples: d 19 m (25.0 m/s)(2.50 s) 1 ( 10.0 m/s2 )(2.50 s)2 2 5.0 101 m 19 m only has two significant digits, so the answer should only have two significant digits slope 70.0 m 10.0 m 29 s 11 s 3.3 m/s 26 s and 11 s only have two significant digits each, so the answer should only have two significant digits
Multistep calculations Do not round to significant digits in the middle of a multistep calculation. Instead, round to a reasonable number of decimal places that will not cause you to lose significance in your answer. When you get to your final step where you are solving for the answer asked for in the question, you should then round to the correct number of significant digits. Example: F (24 N) 2 (36 N)2
576 N2 1296 N2 Do not round to 580 N2 and 1300 N2 1872 N 2 Do not round to 1800 N2 43 N Final answer, so it should be rounded to two significant digits
836 Appendix A Math Handbook Math Handbook 837 Math Handbook 1 2 ) y 1 )( a x 3 5 2 ( total of parts number number of parts chosen c. d. . 1 r t b r in the numerator and the denominator, and break break and and the denominator, in the numerator to Multiply each fraction by a fraction equal to 1 by a fraction Multiply each fraction and the denominators Multiply the numerators with the common denominator a single fraction Write to a ) . . p a p 2 b t in b / and er p s a om m by To multiply fractions, multiply the numerators and multiply multiply fractions, multiply the numerators To n u ) and e n s a a a To add or subtract two fractions, first write them as To d a 1 )( 2 b ( the fraction into the product of two fractions of two into the product the fraction Factor out the Factor Multiply the first fraction by the reciprocal of the second fraction by the reciprocal Multiply the first fraction and the denominators Multiply the numerators Substitute ( and the denominators Multiply the numerators . a b ) 2 a n w ) a p b b p t 2 b Sometimes,an expression it is easier to simplify substituting before )( 3 b ) )( ab ) y t 3 b a 1 s b a t n b b n w w a a b s s ( ( a ( )( p p b n a w (1) ( x 1 2 Simplify Multiply the fractions Add the fractions Divide the fraction ) t 2 b b t b Perform the indicated operation. Write the answer in simplestPerform the indicated form. operation. Write a. b. )( n w s a p s a 1 a p ( by the reciprocal divide fractions, multiply the first fraction of the second fraction. To A fraction names a part of a whole or a part also can of a group. A fraction express 4. Simplification the known values often cancel of the variables. of the expression. out Variables Example: the denominators. Example: Addition and subtraction find a To fractions with a common denominator; that is, with the same denominator. add or subtract multiply the denominators of both fractions. Then, common denominator, the numerators and use the common denominator. Example: Multiplication and division III. Proportions Ratios, Rates, and Fractions, Fractions To find the reciprocal a fraction, invert of denominator. it—switch the numerator and the To Example: a ratio (see page 838). It consists of a numerator, a division bar, and a denominator. 838).a ratio (see page a division bar, It consists of a numerator, 833-857 EM MHB-845813 6/8/04 10:28 PM Page 837 Page PM 10:28 6/8/04 MHB-845813 EM 833-857 833-857 EM MHB-845813 6/8/04 8:06 PM Page 838
Ratios A ratio is a comparison between two numbers by division. Ratios can be written in several different ways. The ratio of 2 and 3 can be written in four different ways: 2 to 3 2 out of 3 2:3 2 3 Rates A rate is a ratio that compares two quantities with different measurement units.
Math Handbook A unit rate is a rate that has been simplified so that the denominator is 1. Example: Write 98 km in 2.0 hours as a unit rate. 98 km in 2.0 hours is a ratio of 98 km 2.0 hours 98 km 98 km Split the fraction into the product of a number fraction 2.0 hours (2.0 )(hour) and a unit fraction km (49) Simplify the number fraction (hour) 49 km per hour or 49 km/h
Example: Write 16 Swedish crowns in 2 U.S. dollars as a unit rate. 16 Swedish crowns 16 Swedish crowns in $2.00 American currency is a ratio of 2 U.S. dollars 16 Swedish crowns 1 6 Swedish crowns 2 U.S. dollars ( 2 )( U.S. dollars ) = (8) Swedish crowns ( U.S. dollars ) = 8 Swedish crowns per U.S. dollar or 8 Swedish crowns/U.S. dollar
Proportions A proportion is an equation that states that two ratios are equal: a c , where b and d are not zero. b d Proportions used to solve ratio problems often include three numbers and one vari- able. You can solve the proportion to find the value of the variable. To solve a proportion, use cross multiplication. Example: Solve the proportion a c for a. b d Cross multiply: a c b d ad bc Write the equation resulting from cross multiplying bc a Solve for a d
5. Solve the following proportions. a. 4 2 c. 3 6 s x 3 12 16 b. 1 3 n d. 2. 5 7.5 15 75 5.0 w
838 Appendix A Math Handbook 833-857 EM MHB-845813 3/22/04 8:47 AM Page 839
IV. Exponents, Powers, Roots, and Absolute Value Math Handbook Exponents An exponent is a number that tells how many times a number, a, is used as a factor. An exponent is written as a superscript. In the term a n, a is the base and n is the exponent. a n is called the nth power of a or a raised to the nth power.
Exponent an
Base
Connecting Math to Physics A subscript is not an exponent. In physics, a subscript is used to further describe the variable. For example, v0 can be used to represent the velocity at time 0. A subscript is a part of the variable. Positive exponent For any nonzero number, a, and any integer, n, n a (a1)(a2)(a3) . . .(an) Example: Simplify the following exponent terms. 104 (10)(10)(10)(10) 10,000 23 (2)(2)(2) 8
Zero exponent For any nonzero number, a, a 0 1 Examples: Simplify the following zero exponent terms. 20 1 130 1
Negative exponent For any nonzero number, a, and any integer, n, a n 1 a n Examples: Write the following negative exponent terms as fractions. 1 1 1 1 2 1 2 2 21 2 22 4 Square and Cube Roots A square root of a number is one of its two equal factors. A radical sign, , 1 1 indicates a square root. A square root can be shown as exponent , as in b b 2. You 2 can use a calculator to find square roots. Examples: Simplify the following square root terms. a 2 ( a)(a) a 9 (3)(3) 3 The answer has a zero to the right of the decimal 64 (8.0)(8 .0) 8.0 to keep two significant digits Place two zeros to the right of the calculator answer 38.44 6.200 to keep four significant digits
39 6.244997 . . . 6.2 Round the calculator answer to keep two significant digits
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A cube root of a number is one of its three equal factors. A radical sign with the 3 number 3, , indicates a cube root. A cube root also can be shown as exponent 1 , 3 1 3 as in b b 3. Example: Simplify the following cube root terms. 3 125 3 (5.00)( 5.00)(5 .00) 5.00 3 39.304 3.4000 Math Handbook
6. Find each root. Round the answer to the nearest hundredth. a. 22 c. 676 3 3 b. 729 d. 46.656 7. Simplify by writing without a radical sign. a. 16 a 2b 4 b. 9 t 6 8. Write using exponents.
a. n 3 b. 1 a
Operations with Exponents In the following operations with exponents, a and b can be numbers or variables. Product of powers To multiply terms with the same base, add the exponents, as in (a m )(a n ) a m n. Quotient of powers To divide terms with the same base, subtract the bottom exponent from the top exponent, as in am/an am n. Power of a power To calculate the power of a power, use the same base and multiply the exponents, as in (am )n a mn. n th root of a power To calculate the root of a power, use the same base and n m divide the power exponent by the root exponent, as in a m a n . Power of a product To calculate the power of a product of a and b, raise both to the power and find their product, as in (ab)n a nb n.
9. Write an equivalent form using the properties of exponents. 2 a. x t b. t 3 c. (d 2n)2 d. x 2 x x 3 2qv 10. Simplify m q m
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Absolute Value Math Handbook The absolute value of a number, n, is its magnitude, regardless of its sign. The absolute value of n is written as n. Because magnitudes cannot be less than zero, absolute values always are greater than or equal to zero. Examples: 3 units 3 units 3 3 3 3 4 3 2 1 01 234
V. Scientific Notation A number of the form a 10n is written in scientific notation, where 1 a 10, and n is an integer. The base, 10, is raised to a power, n. The term a must be less than 10.
Power a 10n
Term Base 10
Connecting Math to Physics Physicists use scientific notation to express, compare, and calculate with measurements that are greater than 10 or less than 1. For example, the mass of a proton is written as 6.73 10 28 kg. The density of water is written as 1.000 103 kg/m3. This shows, using significant digit rules, that this measurement is exactly 1000 to four significant digits. However, writing the density of water as 1000 kg/m3 would imply that it has only one significant digit, which is incorrect. Scientific notation helps physicists keep accurate track of significant digits.
Large Numbers—Using Positive Exponents Multiplying by a power of 10 is like moving the decimal point that same number of places to the left (if the power is negative) or right (if the power is positive). To express a large number in scientific notation, first determine the value for a, 1 a 10. Count the number of decimal places from the decimal point in a to the decimal point in the number. Use that count as the power of 10. A calculator shows scientific notation with e for exponent, as in 2.4e 11 2.4 1011. Some calculators use an E to show the exponent, or there is often a place on the display where the calculator can show smaller-sized digits representing the exponent. Example: Write 7,530,000 in scientific notation. The value for a is 7.53. (The decimal point is to the right of the first nonzero digit.) So the form will be 7.53 10n.
7,530,000 7.53 106 There are six decimal places, so the power is 6
To write the standard form of a number expressed in scientific notation, write the value of a, and place extra zeros to the right of the number. Use the power and move the decimal point in a that many places to the right. Example: Write the following number in standard form. 2.389 105 2.38900 105 238,900
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842 Math Handbook Appendix A Example: Example: Multiplication (seepage840). nents 1 Example: Division Operations withScientificNotation Small Numbers—UsingNegative Exponents Example: corresponding asdividingbythatnumberwiththe by anumberwithnegativepoweristhesame to thedecimalpointinnumber. Usethat to theleft. zeros totheleftof To form,writethevaluefor asmallnumberinstandard express The valuefor So theformwillbe2.85 12. 11. 1.6 (4.0 ofexpo- theproperties uses Calculating withnumberswritteninscientificnotation To firstdeterminethevaluefor asmallnumberinscientificnotation, express 0.000000285 9 a 1 . . 6 6 0 0 10. Then count the number of decimal places fromthedecimalpointin 10. Then countthenumberofdecimalplaces a. a. Express each number in standard notation. eachnumberinstandard Express eachnumberinscientificnotation. Express 10 Simplify. Simplify. Write 0.000000285inscientificnotation. 10 1 1 Divide the base numbers and subtract the exponents of10. Divide thebasenumbersandsubtractexponents 0 0 3.03 456,000,000 3 7 4 8 )(1.2 positive power. Math Handbook ( 6.00 6.00 a Multiply thetermsandaddpowersof10. 00001.6 9 1 10 is 2.85.(The decimalpointistotherightoffirstnonzerodigit.) . . 6 6 2.85 0 0 10 ) a. 7 10 10 5 Use thepowerandmovedecimalpointin ) 4 7 ( 10 1 1 10 3 0 0 (4.0 4.8 (4.8)(10 (4.8)(10 10 3 7 ) 7 4 n . 10 0.00016 1.2)(10 There are seven decimalplaces,sothepower is 3 3 8 ) 5 ) b. b. 8 number asthepowerof10.Multiplying 9.7 0.000020 10 5 ) 10 Divide termsandsubtract powers of10 Group termsandbasesof10 10 Recombine inscientificnotation Add powers of10 Multiply terms Group termsandbasesof10 a and placeextra a that manyplaces 7 a a , 833-857 EM MHB-845813 6/8/04 10:32 PM Page 843
Addition and subtraction Adding and subtracting numbers in scientific notation is more challenging, because the powers of 10 must be the same in order to add or Math Handbook subtract the numbers. This means that one of the numbers may need to be rewritten with a different power of 10. If the powers of 10 are equal, then use the distributive property. Example: Simplify. (3.2 105 ) (4.8 105 ) (3.2 4.8) 105 Group terms 8.0 105 Add terms Example: Simplify. (3.2 105 ) (4.8 104 ) (3.2 105 ) (0.48 105 ) Rewrite 4.8 104 as 0.48 105 (3.2 0.48) 105 Group terms 3.68 105 Add terms 3.7 105 Round using addition/subtraction rule for significant digits
13. Evaluate each expression. Express the result in scientific notation. a. (5.2 10 4 )(4.0 108 ) b. (2.4 103 ) (8.0 104 )
VI. Equations Order of Operations Scientists and mathematicians have agreed on a set of steps or rules, called the order of operations, so that everyone interprets mathematical symbols in the same way. Follow these steps in order when you evaluate an expression or use a formula. 1. Simplify the expressions inside grouping symbols, like parentheses ( ), brackets [ ], braces { }, and fraction bars. 2. Evaluate all powers and roots. 3. Do all multiplications and/or divisions from left to right. 4. Do all additions and/or subtractions from left to right. Example: Simplify the following expression. 4 3(4 1) 23 4 3(3) 23 Order of operations step 1 4 3(3) 8 Order of operations step 2 4 9 8 Order of operations step 3 8 Order of operations step 4 Connecting Math to Physics The previous example was shown step-by-step to demonstrate order of operations. When solving a physics problem, do not round to the correct number of siginificant digits until after the final calculation. In calculations involving an expression in a numerator and an expression in a denominator, the numerator and the denominator are separate groups and are to be calculated before dividing the numerator by the denominator. So, the multiplication/division rule is used to determine the final number of significant digits.
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Solving Equations To solve an equation means to find the value of the variable that makes the equation a true statement. To solve equations, apply the distributive property and the properties of equality. Any properties of equalities that you apply on one side of an equation, you also must apply on the other side. Distributive property For any numbers a, b, and c, a(b c) ab ac a(b c) ab ac
Math Handbook Example: Use the distributive property to expand the following expression. 3(x 2) 3x (3)(2) 3x 6
Addition and subtraction properties of equality If two quantities are equal and the same number is added to (or subtracted from) each, then the resulting quantities also are equal. a c b ca c b c Example: Solve x 3 7 using the addition property. x 3 7 x 3 3 7 3 x 10 Example: Solve t 2 5 using the subtraction property. t 2 5 t 2 2 5 2 t 7 Multiplication and division properties of equality If two equal quantities each are multiplied by (or divided by) the same number, then the resulting quantities also are equal. ac bc a b , for c 0 c c Example: Solve 1 a 3 using the multiplication property. 4 1 a 3 4 1 a (4) 3(4) (4 ) a 12 Example: Solve 6n 8 using the division property. 6n 8 6 n 1 8 6 6 n 3 Example: Solve 2t 8 5t 4 for t. 2t 8 5t 4 8 4 5t 2t 12 3t 4 t
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Isolating a Variable Math Handbook Suppose an equation has more than one variable. To isolate a variable—that is, to solve the equation for a variable—write an equivalent equation so that one side contains only that variable with a coefficient of 1. Connecting Math to Physics Isolate the variable P ( pressure) in the ideal gas law equation. PV nRT PV nRT Divide both sides by V V V V nRT P Group v (V ) V v nRT P Substitute v 1 V v
14. Solve for x. a. 2 3x 17 d. a b x c b. x 4 2 3x e. 2x 3 6 x c. t 1 x 4 f. ax bx c d 3
Square Root Property If a and n are real numbers, n 0, and a 2 n, then a n .
Connecting Math to Physics Solve for v in Newton’s second law for a satellite orbiting Earth. 2 Gm m mv E r r 2 rmv 2 rGm m E Multiply both sides by r r r 2 Gm m mv 2 E Substitute r 1 r r mv 2 Gm m E Divide both sides by m m rm Gm v 2 E Substitute m 1 r m Gm v 2 E Take the square root r Gm v E Use the positive value for speed r When using the square root property, it is important to consider for what you are solving. Because we solved for speed in the above example, it did not make sense to use the negative value of the square root. Also, you need to consider if the negative or positive value gives you a realistic solution. For example, when using the square root property to solve for time, a negative value may give you a time before the situation even started.
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846 Math Handbook Appendix A Acceleration ismeasuredinmeterspersecondsquared. a Connecting MathtoPhysics units. onits performed is writtenin of thesolutioninmindwhensolving. theuseofquadraticformulawhensolvingequations,sokeeprealism requires itisunrealistic.Projectile motionoften throwoutoneofthesolutionsbecause you can quadratic formulagiveyouarealisticanswertotheproblemaresolving.Usually, formula. The solutionsof Dimensional Calculations Quadratic Formula Quadratic Equations graphing onacalculator. If variable tothefirstpower. by beestimated The solutionsofaquadraticequationcan equation hasonevariablewithapower(exponent)of2.Italsomayincludethatsame the squarerootofeachsideequationusingproperty. besolvedbyisolatingthesquaredvariableandfinding equation. The equationcan 15. a a a ofeachmeasurementthat youmustincludetheunits When doingcalculations, toconsiderifthesolutions Like inthesquarerootproperty, itisimportant byusingthequadratic becalculated The solutionsofanyquadraticequationcan A quadraticequationhastheform x 2 t 2 x . Afree-fallingobjectneartheMoondrops20.5min5.00 s.Findtheacceleration, Solve for 2 d. b. 1.6 2 a. c. ( ( 5 t b 2 s .0 2 x 4 0 2 24 x 12 4 the calculation. All operations that are performed onthenumberalsoare Alloperationsthatareperformed the calculation. 0 .5 m x 2 s x 2 m ) 2 or 1.64 m/s or 1.64 Math Handbook 2 2 ) a b 2 3 x. 2 x 19 x 14 2 4 x ac 24 17 ax 9 6 2 2 0 0 bx The accelerationduetogravity, Calculate andround tothree significant digits not affect thedeterminationofsignificantdigits The numbertwo isanexactnumber, soitdoes b c ax = 0,thenthereisno 0, where 2 bx a c 0, aregivenby 0, where x -term inthequadratic a, a is givenbytheequation 0. Aquadratic a . Math Handbook 847 Math Handbook 1 is in m f d n s i will have the units m. 0 m 2 = 5.0 min. Use the = 5.0 min. Use the 6 1 t at = 1 1 2 2 ) /s 2 t i cm m v 0 1 10 i )( d in h m f = 67 m/s and 1 d 0 60 v )( n s i Substitute the units for each variable Substitute the units for property using the distributive Simplify the fractions Substitute s/s = 1, s simplifies to m, thus Everything 0 m when 6 1 x )( Calculate and round to two significant digits. The num- digits. The significant to two Calculate and round bers 60 exact numbers, so they do not s and 1 min are the determination of significant digits affect Multiply by the conversion factor factor Multiply by the conversion . 2 m s c 1 . 32 Find ( ) 2 m 2 2 ) m s 2 s s / n (s) 4 ( 0 s i ) 9.80 m/s m 1 2 0 m 10 when first setting up the dimensional analysis. m s . 6 6 ( (m) 1 (m)(1) 2 1 1 2 1 2 1 2 1 2 4.0 )( 2.0 a m . ) 1 2 min t Verify that the final answer of that the Verify t 1 s s Use a conversion factor to convertUse a conversion from one measurement unit (s) ( and ) 0 5.0 in the above does not apply to the units. It applies only to any number v t s m ( (m) (m)(1) m ( 1 1 2 t a m s x 0 67 v 20100 m m m m m Simplify after 5.0 s using Find the velocity of a dropped brick v Calculate the product: is the speed s. What An Olympic record for 100.0 m is 9.87 in kilometers per hour? ds te n u is measured in m. is measured in m/s. o is measured in m/s x x x is measured in s. n f i c i i 17. Dimensional analysis is a method of doing algebra with the units. It often is used d v t a d e 16. 18. 19. m s 1 60 equation, The factor of The Dimensional Analysis Unit conversion to Physics Connecting Math to another of the sameto another of the as from minutes type, such is equivalent to to seconds. This multiplying by one. values that would be inserted the variables for in the equation. It is easiest to remove number factors like the to check the validity of the units of a final result and the equation being used, without completely redoing the calculation. Physics Example 833-857 EM MHB-845813 3/22/04 8:53 AM Page 847 Page AM 8:53 3/22/04 MHB-845813 EM 833-857 833-857 EM MHB-845813 6/9/04 4:35 PM Page 848
VII. Graphs of Relations The Coordinate Plane Points are located in reference to two perpendicular number lines, called axes. The horizontal number line is called the x-axis; the vertical number line is called the y-axis. The x-axis represents the independent variable. The y-axis represents the dependent variable. A point is represented by two coordinates (x, y), which also is called an ordered pair. The value of the independent variable, x, always is listed first in the ordered pair.
Math Handbook The ordered pair (0, 0) represents the origin, which is the point where the two axes intersect.
y The vertical axis The coordinate system also is called the also is called the 4 y-axis. (4, 3) coordinate plane.
2 Each point is named by an ordered pair. 44 2 0 2 x
2
The origin, at (0, 0), 4 is the point where The horizontal axis the axes intersect. also is called the x-axis.
Graphing Data to Determine a Relationship Use the following steps to graph data. 1. Draw two perpendicular axes. 2. Identify the independent and the dependent variables. Label each axis using the variable names. 3. Determine the range of data for each variable. Use the ranges to decide on a conven- ient scale for each axis. Mark and number the scales. 4. Plot each data point. 5. When the points seem to lie approximately in a line, draw a “best-fit” line through the points. When the points do not lie in a line, draw a smooth curve through as many data points as possible. When there does not appear to be a trend or a pattern to the dots, do U.S. Dollars and British Pounds not draw any line or curve. 70 6. Write a title that clearly describes what the 60 graph represents. 50 40 Expense Pounds Dollars
Dollars 30 Hotel 40 58 20 Meals 30 43 10 Entertainment 15 22 0 10203040 50 60 70 Transportation 6 9 Pounds
848 Appendix A Math Handbook 833-857 EM MHB-845813 3/22/04 8:59 AM Page 849
Interpolating and Extrapolating Math Handbook Interpolation is a process used to estimate a value for a relation that lies between two known values. Extrapolation is a process used to estimate a value for a relation that lies beyond the known values. The equation of a line through the points (the known values) helps you interpolate and extrapolate. Example: Using the data and the graph, estimate the value, in dollars, of 20 pounds. Use interpolation. Locate two points on either side of 20 pounds— U.S.Dollars and 15 pounds and 30 pounds. Draw a line (or place British Pounds a straight edge) through the graphed points. 70 Draw a line segment from 20 on the x-axis to 60 that line. Draw a line segment from that inter- section point to the y-axis. Read the scale on the 50 y-axis. 20 pounds is about 28 or 29 dollars. 40
Example: Use extrapolation to estimate the value Dollars 30 of 50 pounds. 20 Draw a line segment from 50 on the x-axis to the line through the points. Extend the line if 10 necessary. Read the corresponding value on 0 102030 40 50 60 the y-axis. Extend the axis scale if necessary. 50 pounds is a little more than 70 dollars. Pounds
Interpreting Line Graphs A line graph shows the linear relationship between two variables. Two types of line graphs that describe motion are used frequently in physics.
Connecting Math to Physics The following line graph shows a changing relationship between the two graphed variables.
Move back Move ahead toward quickly starting
Position Move ahead point slowly Maintain position
0 Time
This line graph shows a constant relationship between the two graphed variables.
Constant velocity Position
0 Time
Math Handbook 849 833-857 EM MHB-845813 3/22/04 8:59 AM Page 850
Linear Equations A linear equation can be written as a relation (or a function), y mx b, where m and b are real numbers, m represents the slope of the line, and b represents the y-intercept, the point at which the line crosses the y-axis.
Dependent Independent variable variable Math Handbook y mx b
Slope y-intercept
The graph of a linear equation is a line. The line represents all of the solutions of the linear equation. To graph a linear equation, choose three values for the independent variable. (Only two points are needed, but the third point serves as a check.) Calculate the corresponding values for the dependent variable. Plot each ordered pair (x, y) as a point. Draw a best-fit line through the points. Example: Graph y 1 x 3 2 Calculate three ordered pairs to obtain points Plot of Ordered Pairs to plot. y
Ordered Pairs x y 0 3 2 2 6 0 x
Slope The slope of a line is the ratio of the change in y-coordinates to the change in x-coordinates. It is the ratio of the vertical change (rise) to the horizontal change (run). This number tells how steep the line is. It can be a positive or a negative number. To find the slope of a line, select two points, (x1, y1) and (x2, y2). Calculate the run, which is the difference (change) y between the two x-coordinates, x x x. 2 1 y2 Calculate the rise, which is the difference ∆y (x2, y2) (change) between the two y-coordinates, y1 (x , y ) y2 y1 y. Form the ratio. 1 1 rise y y y 2 1 0 Slope m , x1 x2 x run x2 x1 x ∆ where x1 x2 x
850 Appendix A Math Handbook 833-857 EM MHB-845813 6/15/04 11:41 PM Page 851
Direct Variation Math Handbook If there is some nonzero constant, m, such that y mx, then y varies directly as x. That means as the independent variable x increases, the dependent variable y increases. The variables x and y also are said to be proportional. This is a linear equation of the form y mx b in which the value of b is zero. The graph passes through the origin, (0, 0).
Connecting Math to Physics In the force equation for an ideal spring, F kx, where F is the spring force, k is the spring constant, and x is the spring displacement, spring force varies directly as ( is proportional to) spring displacement. That is, the spring force increases as the spring displacement increases.
Inverse Variation m If there is some nonzero constant, m, such that y , then y varies inversely as x. x That means as the independent variable x increases, the dependent variable y decreases. The variables x and y also are said to be inversely proportional. This is not a linear equation because it contains the product of two variables. The graph of an inverse relationship is a hyperbola. This relationship can be written as m y x 1 y m x xy m
Example: Graph the equation xy 90.
Ordered Pairs x y 10 9 6 15 3 30 2 45
2 45 Graph of an Inverse Variation 3 30 y 6 15 40 10 9 20 x 8 4 0 4 8 20
Connecting Math to Physics In the equation for the speed of a wave, v , where f is wavelength, f is frequency, and v is wave speed, wavelength varies inversely as ( is inversely proportional to) frequency. That is, as the frequency of a wave increases, the wavelength decreases. v is constant.
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Quadratic Graphs A quadratic relationship is a relationship of the form y ax 2 bx c, where a 0. A quadratic relationship includes the square of the independent variable, x. The graph of a quadratic relationship is a parabola. Whether the parabola opens upward or downward depends on whether the value of the coefficient of the squared term, a, is positive or negative. Math Handbook Example: Graph the equation y x 2 4x 1.
Ordered Pairs x y 1 6 0 1 1 2 2 3 Graph of a Quadratic Equation 3 2 y 4 1 5 6 x 0
y x2 4x 1
Connecting Math to Physics A position-time graph in the shape of a quadratic relation means that the object is moving at a constant acceleration.
Ordered Pairs Time (s) Position (m) 1 3 2 6 Quadratic Graph of 3 11 Constant Acceleration 4 18 20
16
12
8 Position (m) 4
0 2 4 Time (s)
852 Appendix A Math Handbook Math Handbook 853 3 h r 2 r 3 4 3 a -axis to (a). x Math Handbook V Volume Cubic units V V Area 1 Area 3… 2 Time r 2 Area 2 2 Total area r rh 2 a 4 6 2
SA Surface Area Surface Squared units SA SA Position 0 b 2 bh r 2 1 2 a lw Area Squared units A A A A Look for geometric shapes in your physics problems. Look w 2 r a l 2 4 2 Time Using more rectangles base will provide a closer with a smaller Perimeter, Circumference unitsLinear P P C Area of the rectangle (b). Area of the triangle h l h r r r w
b a a Position 0 Total area Circle radius Cylinder radius height Sphere radius Square, side Rectangle, length width Triangle base height Cube side To approximate the area under a curve, draw several rectangles from the To To calculate into smaller pieces the approximate area under a graph, cut the area To a the curve, as in Area Under a Graph Area Connecting Math to Physics be in the form of objects could They or spaces. example, two-dimensional shapes For could be formed by velocity vectors, as well as position vectors. VIII. and Trigonometry Geometry and Volume Area, Perimeter, approximation of the area. and find the area of each piece using the formulas shown above. To approximate the approximate and find the area of each piece using the formulas shown above. To area under a line, cut the area into a rectangle a triangle, as shown in and 833-857 EM MHB-845813 3/22/04 9:02 AM Page 853 Page AM 9:02 3/22/04 MHB-845813 EM 833-857 833-857 EMMHB-8458133/22/049:03AMPage854
854 Math Handbook Appendix A of the shorter leg. of theshorter is 45 Example: Right Triangles hypotenuse is twice the length of the shorter leg. hypotenuse istwicethelengthofshorter 30 value does nothavemeaning. value does ispositive,thenegative distance Because hypotenuse, usethesquarerootproperty. hypotenuse, then and triangle and The lengthofthelongerlegis ° ° -45 -60 The Pythagorean theorem states thatif theoremstates The Pythagorean To determinethelengthof c b 2 are the measures ofthelegsaright are themeasures times thelengthofaleg. times ° ° 5 cm -90 -90 In thetriangle, 25 cm 16 cm (4 cm) a ° ° c 2 triangles triangles is themeasureof Math Handbook c b 2 2 c 2 2 2 9 c (3 a 2 a m cm) The lengthofthehypotenuse The lengthofthe a 2 2 b 2 4 cmand 2 . b 2 3 times thelength times b 3 cm a . Find Leg c. a Right Triangle 30 Right Triangle 45 ° -
30 ° 60 - 45
° 45 ° c ( - °
° 90 3 Hypotenuse - 2
( 90 ° Leg ) x b 2 ° 3 x c ) x x 4 45 60 ° ° x x Math Handbook 855 b Side opposite c b a b a c djacent. a C B Math Handbook c Symbols sin cos tan ypotenuse. CAH pposite, A ) ° a b e 10.0 t s se n u c t te u i e n te n ) n s i c ° e e te o s t ja c Side adjacent o angent, O p o pposite, H o a d p p j p p a )(cos 1 o p 10.0 hy ad o hy ine, O Hypotenuse A 2.0 cm )(cos 1 °. is 2 Memory Aid SOH sin CAH cos TOA tan , the ° . cm)(1 is 110.0 and cm 0 cm b ° is 90 (60. 20.0 2(10.0 30.0 3 cm, ro. If 2 cos and cos ° 2 a ab 17.3 2 if if 10.0 4 cm 12.0 cm, ypotenuse. TOA stands for T ypotenuse. TOA cm) 14 ) 2 cos 30.0 ) ° If the angle b cos b ° ABC, ABC, (12.0 b 2 cos b. c. a except for the last term. 2 2 cm ab a 2 0.8 cm djacent, H 2 0.6 cm cm 2 and 5 cm, find sin a m) 2 a 10 The law of cosinesThe looks like the 10.0 cm, 2 b 2 , its cosine is a number. negative 20.0 c m m ° c m m b c c c c a 4 5 2 osine, A 3 5 (10.0 c (10.0 1.00 ° a 2 In right triangle Find the length of the third side of a In right triangle a 16.3 (20.0 cm)(cos 30.0 (20.0 cm)(sin 30.0 0 and the last term equals ze equals 0 and the last term Words of the length sine is the ratio The of the side opposite to the angle over the length of the hypotenuse. of cosine is the ratio of the length The the side adjacent to the angle over the length of the hypotenuse. tangentThe of is the ratio of the length the side opposite to the angle over the length of the side adjacent to the angle. 2 4 cm, and 20.0 cm, find sin 30.0 b c cos c a laws of cosinesThe and sines let you calculate sides and angles in any triangle. A trigonometric ratio is a ratio of the lengths of sidesA trigonometric ratio most The of a right triangle. sin c the angle opposite side Example: Example: triangle with Law of Cosines and Law of Sines Trigonometric Ratios Trigonometric Example: b greater than 90 Pythagorean theorem, Law of cosines common trigonometric ratios are sine, cosine, and tangent.To memorize these ratios, ratios are sine, cosine, and tangent.To common trigonometric SOH stands for S SOH-CAH-TOA. learn the acronym stands for C cos 833-857 EM MHB-845813 3/22/04 9:04 AM Page 855 Page AM 9:04 3/22/04 MHB-845813 EM 833-857 833-857 EM MHB-845813 3/22/04 9:05 AM Page 856
Law of sines The law of sines is an equation of three ratios, where a, b, and c are the sides opposite angles A, B, and C, respectively. Use the law of sines when you know the measures of two angles and any side of a triangle. sin A sin B sin C a b c
Example: In a triangle, C 60.0°, a 4.0 cm, C c 4.6 cm. Find the measure of angle A. b
Math Handbook sin A sin C a c a sin C A sin A a c ° (4.0 cm) (sin 60.0 ) 4.6 c 49°
B
Inverses of Sine, Cosine, and Tangent The inverses of sine, cosine, and tangent allow you to do the reverse of the sine, cosine, and tangent functions and find the angle. The trigonometric functions and their inverses are as follows: Trigonometric Function Inverse y sin xx sin 1 y or x arc sin y y cos xx cos 1 y or x arc cos y y tan xx tan 1 x or x arc tan y
Graphs of Trigonometric Functions The sine function, y sin x, and the cosine function, y cos x are periodic functions. The period for each function is 2 . x can be any real number. y is any real numbers between 1 and 1, inclusive.
y sin x y 1
x 2 0 2
1
y cos x y 1
x 2 0 2
1
856 Appendix A Math Handbook 833-857 EM MHB-845813 6/8/04 10:41 PM Page 857
IX. Logarithms Math Handbook Logarithms with Base b Let b and x be positive integers, b 1. The logarithm of x with base b, written logb x, equals y, where y is the exponent that makes the equation by x true. The log to the base b of x is the number to which you can raise b to get x. y logb x y if and only if b x Memory aid: “the log is the exponent” Examples: Calculate the following logarithms. 1 log 4 Because 2 4 1 2 16 16 3 log10 1000 3 Because 10 1000 When you want to find the log of a number, you also can use a calculator.
Connecting Math to Physics Physicists use logarithms to work with measurements that extend over several orders of magnitude, or powers of 10. Geophysicists use the Richter scale, a logarithmic scale that allows them to rate earthquakes from 0 to 7, or larger, though the power of earthquakes differ by 7 or more powers of 10. Common Logarithms Base 10 logarithms are called common logarithms. They often are written without the subscript 10. log10 x log xx 0 Antilogarithms or Inverse Logarithms An antilogarithm is the inverse of a logarithm. An antilogarithm is the number which has a given logarithm. Example: Solve log x 4 for x. log x 4 x 104 104 is the antilogarithm of 4 Connecting Math to Physics An equation for loudness, L, in decibels, is L 10 log10 R, where R is the relative intensity of the sound. Calculate R for a fireworks display with a loudness of 130 decibels. 130 10 log10 R Divide by 10 13 log10 R Use logarithm rule R 1013
When you know the logarithm of a number and want to know the number itself, use a calculator to find the antilogarithm.
20. Write in exponential form. log3 81 4 21. Write in logarithmic form. 10 3 0.001 22. Find x. log x 3.125
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Chapter 1 7. How many significant digits are there in each of the following measurements? 1. The density, , of an object is given by the a. 100 m ratio of the object’s mass, m, and volume, b. 0.0023 m/s V, according to the equation m/V. c. 100.1 m What is the density of a cube that is 1.2 cm d. 2.0023 on each side and has a mass of 25.6 g? 8. The buoyant (upward) force exerted by 2. An object that is moving in a straight line water on a submerged object is given by with speed v covers a distance, d vt, in the formula F Vg, where is the time t. Rewrite the equation to find t in density of water (1.0 103 kg/m3), V is the terms of d and v. How long does it take volume of the object in m3, and g is the a plane that is traveling at 350 km/h to acceleration due to gravity (9.80 m/s2). travel 1750 km? The force is in newtons. Rewrite the equa- 3. Convert 523 kg to milligrams. tion to find V in terms of F. Use this to 4. The liquid measure milliliter, mL, is the find the volume of a submerged barrel if 3 same as 1 cm . How many milliliters of the buoyant force on it is 9200 N. Appendix B liquid can be held in a 2.5-m3 container? 9. What is 2.3 kg 0.23 g? 5. Part of the label from a vitamin container is shown below. The abbreviation “mcg” 10. Solve the following problems. stands for micrograms. Convert the values a. 15.5 cm 12.1 cm to milligrams. b. 14.67 8 m 3.2 m/s 11 . An experiment was performed to deter- Each Tablet Contains %DV mine the period of a pendulum as a function of the length of its string. Folic Acid 400 mcg 100% The data in the table below were Vitamin B12 6 mcg 100% measured. Biotin 30 mcg 10% a. Plot period, T, versus length, l. b. Are the data linear? c. Plot the period versus the square root of the length. d. What is the relationship between the 6. What type of relationship is shown in the period and the square root of the scatter plot? Write an equation to model length? the data.
Length (m) Period (s) 1.2 0.1 0.6 0.2 0.9 1.0 0.4 1.3 0.8 0.6 1.6 0.6 0.8 1.8 1.0 2.0 0.4
0.2 12. Based on the previous problem, what should be the period of a pendulum 0 123456 whose length is 0.7 m?
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Chapter 2 3. A jogger runs at a constant rate of 10.0 m every 2.0 s. The jogger starts at the origin, 1. A position-time graph for a bicycle is and runs in the positive direction for shown in the figure below. 3600.0 s. The figure below is a position- a. What is the position of the bicycle at time graph showing the position of the 1.00 min? jogger from time t 0.0 s to time t 20.0 b. What is the position of the bicycle at s. Where is the runner at time t 5.0 s? 3.50 min? t 15.0 s? c. What is the displacement of the 100.0 bicycle between the times 1.00 min Additional Problems and 5.00 min? d. Describe the motion of the bicycle. 75.0
40.0 50.0
30.0 Position (m) 25.0
20.0 0.0
Position (m) 4.0 8.0 12.0 16.0 20.0 10.0 Time (s)
4. Two trains simultaneously leave the same 0.001.00 2.00 3.00 4.00 5.00 train station at noon. One train travels Time (min) north and the other travels south. The position-time graph for both trains is 2. The position of an automobile is plotted shown in the accompanying figure. as a function of time in the accompanying a. What is the position of the train figure. traveling north at 6.0 h? a. What is the position of the car at b. What is the position of the train 0.00 s? traveling south at 6.0 h? b. What is the position of the automobile c. What is the distance between the trains after 2.00 s has elapsed? at 6.0 h? What is the distance at 10.0 h? c. How far did the automobile travel d. At what time are the trains 600.0 km between the times 1.00 s and apart? 3.00 s? e. Which train is moving more quickly?
50.0 North 1000.0
40.0
30.0
0.0 Time 20.0 4.0 6.0 8.0 10.0 Position (m)
10.0 Position (km)
0.0 1.00 2.00 3.00 4.00 5.00 Time (s) South ؊1000.0
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5. Two cars head out in the same direction. 7. A child’s toy train moves at a constant Car A starts 1.0 min before car B. The speed of 2.0 cm/s. position-time graphs for both cars are a. Draw the position-time graph showing shown in the accompanying figure. the position of the toy for 1.0 min. a. How far apart are the two cars when car b. What is the slope of the line represent- B starts out at t 1.0 min? ing the motion of the toy? b. At what time do the cars meet? 8. The position of an airplane as a function c. How far apart are the cars at time of time is shown in the figure below. t 3.0 min? a. What is the average velocity of the airplane? 2.0 Car A b. What is the average speed of the airplane?
1.5 Car B Time (h) 0.0 1.0 2.0 3.0 4.0 5.0 1.0 Appendix B Position (km) ؊200.0 0.5
؊400.0 0.01.0 2.0 3.0 4.0 5.0 Time (min)
Position (km) ؊600.0 6. The position-time graph for two joggers, A and B, is shown in the accompanying figure. ؊800.0 a. How far apart are the two runners at 10.0 min? b. At what time are they 1.00 km apart? 9. The position-time graph for a hot-air c. How far apart are they at 50.0 min? balloon that is in flight is shown in d. At what time do they meet? the accompanying figure. e. What distance does jogger B cover a. What is the average velocity of the between 30.0 min and 50.0 min? balloon? f. What distance does jogger A cover b. What is the average speed of the between 30.0 min and 50.0 min? balloon?
Time (h) 2.00 Jogger B 0.01.0 2.0 3.0 4.0 5.0
1.50 ؊10.0 1.00 ؊20.0 Position (km) 0.50 Jogger A Position (km) ؊30.0
0.0010.0 20.0 30.0 40.0 50.0 ؊40.0 Time (min)
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Chapter 3 5. A cheetah can reach a top speed of 27.8 m/s in 5.2 s. What is the cheetah’s average 1. Jason and his sister, Tara, are riding bicycles. acceleration? Jason tries to catch up to Tara, who has a 6. After being launched, a rocket attains a 10.0-s head start. speed of 122 m/s before the fuel in the a. What is Jason’s acceleration? motor is completely used. If you assume b. What is Tara’s acceleration? that the acceleration of the rocket is con- c. At what time do they have the same stant at 32.2 m/s2, how much time does velocity? it take for the fuel to be completely consumed? Additional Problems 8.0 7. An object in free fall has an acceleration Jason 2 Tara of 9.80 m/s assuming that there is no air resistance. What is the speed of an object 6.0 dropped from the top of a tall cliff 3.50 s after it has been released, if you assume 4.0 the effect of air resistance against the
Velocity (m/s) Velocity object is negligible? 2.0 8. A train moving with a velocity of 51 m/s east undergoes an acceleration of 2.3 m/s2 as it approaches a town. What is the 0.010.0 20.0 30.0 40.0 velocity of the train 5.2 s after it has Time (s) begun to decelerate? 9. The v-t graph of a runner is shown in the 2. A dragster starts from rest and accelerates accompanying figure. for 4.0 s at a rate of 5.0 m/s2. It then trav- a. What is the displacement of the runner els at a constant speed for 2.5 s. A para- between t 0.00 s and t 20.0 s? chute opens, stopping the vehicle at a con- b. What is the displacement of the runner stant rate in 2.0 s. Plot the v-t graph between t 20.0 s and t 50.0 s? representing the entire motion of the dragster. c. What is the displacement of the runner between t 50.0 s and t 60.0 s? 3. A car traveling at 21 m/s misses the turnoff on the road and collides into the safety guard rail. The car comes to a complete 8.0 stop in 0.55 s. a. What is the average acceleration of the 6.0 car? b. If the safety rail consisted of a section of rigid rail, the car would stop in 4.0
0.15 s. What would be the acceleration (m/s) Velocity in this case? 2.0 4. On the way to school, Jamal realizes that he left his physics homework at home. His car was initially heading north at 24.0 m/s. 0.00 10.0 20.0 30.0 40.0 50.0 60.0 It takes him 35.5 s to turn his car around Time (s) and head south at 15.0 m/s. If north is designated to be the positive direction, 10. Draw the v-t graph of an automobile that what is the average acceleration of the car accelerates uniformly from rest at t 0.00 s during this 35.5-s interval? and covers a distance of 180.0 m in 12.0 s.
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11 . The v-t graph of a car is shown in the accom- 17. A cyclist rides at a constant speed of panying figure. What is the displacement 12.0 m/s for 1.20 min and then coasts of the car from t 0.00 s to t 15.0 s? to a stop with uniform acceleration 21.2 s later. If the total distance traveled 30.0 is 1321 m, then what is the acceleration while the bike coasts to a stop? 18. A hiker tosses a rock into a canyon. He 15.0 hears it strike water 4.78 s later. How far down is the surface of the water? 19. A rock is thrown upward with a speed of 0.00 4.00 8.00 12.00 16.00 26 m/s. How long after it is thrown will Time (s) the rock have a velocity of 48 m/s toward Velocity (m/s) Velocity the ground? ؊15.0 20. The high-dive board at most pools is 3.00 m above the water. A diving instruc- tor dives off the board and strikes the ؊30.0 Appendix B water 1.18 s later. a. What was the initial velocity of the 12. Suppose a car rolls down a 52.0-m-long diver? inclined parking lot and is stopped by a b. How high above the board did the fence. If it took the car 11.25 s to roll diver rise? down the hill, what was the acceleration of the car before striking the fence? 13. A sky diver in free fall reaches a speed of Chapter 4 65.2 m/s when she opens her parachute. The parachute quickly slows her down to 1. Draw a free-body diagram for the space 7.30 m/s at a constant rate of 29.4 m/s2. shuttle just after it leaves the ground. During this period of acceleration, how Identify the forces acting on the shuttle. far does she fall? Make sure that you do not neglect air 14. A child rolls a ball up a hill at 3.24 m/s. resistance. Also be sure that you indicate If the ball experiences an acceleration of the direction of the acceleration, as well 2.32 m/s2, how long will it take for the as the net force. ball to have a velocity of 1.23 m/s down 2. Draw a free-body diagram for a goldfish the hill? that is motionless in the middle of a fish- 15. A cheetah can accelerate from rest to a bowl. Identify the forces acting on the speed of 27.8 m/s in 5.20 s. The cheetah fish. Indicate the direction of the net force can maintain this speed for 9.70 s before on the fish and the direction of the accel- it quickly runs out of energy and stops. eration of the fish. What distance does the cheetah cover during this 14.9-s run? 16. A cab driver in a hurry is sitting at a red light. When the light turns green she rap- idly accelerates for 3.50 s at 6.80 m/s2. The next light is still red. She then slams on the brakes, accelerating at a rate of 9.60 m/s2 before coming to rest at the stop light. What was her total distance for this trip?
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3. Draw a free-body diagram for a submerged 7. Two dogs fight over a bone. The larger of beach ball as it rises toward the surface just the two pulls on the bone to the right with after being released. Identify the forces act- a force of 42 N. The smaller one pulls to ing on the beach ball and indicate the direc- the left with a force of 35 N. tion of the net force and the acceleration. a. Draw the free-body diagram for the bone. b. What is the net force acting on the bone? c. If the bone has a mass of 2.5 kg, what is its acceleration? Additional Problems
4. Muturi is rearranging some furniture. He pushes the dresser with a force of 143 N, and there is opposing frictional force of Dog 1 Dog 2 112 N. What is the net force? 5. One of the floats in a Thanksgiving Day parade requires four people pulling on 8. A large model rocket engine can produce ropes to maintain a constant speed of a thrust of 12.0 N upon ignition. This 3.0 km/h for the float. Two people pull engine is part of a rocket with a total mass with a force of 210 N each, and the other of 0.288 kg when launched. two pull with a force of 140 N each. a. Draw a free-body diagram. a. Draw a free-body diagram of the rocket just after launch. b. What is the force of friction between the float and the ground? b. What is the net force that is acting on the model rocket just after it leaves the ground? c. What is the initial acceleration of the rocket?
6. Five people are playing tug-of-war. Anders and Alyson pull to the right with 45 N and 35 N, respectively. Calid and Marisol pull to the left with 53 N and 38 N, respectively. With what force and in what direction does Benito pull if the game is tied?
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9. Erika is on an elevator and presses the 14. A 7.25-g bullet is fired from a gun. The button to go down. When the elevator muzzle velocity of the bullet is 223 m/s. first starts moving, it has an acceleration of Assume that the bullet accelerates at a 2.5 m/s2 downward. Erika and the elevator constant rate along the barrel of the gun have a combined mass of 1250 kg. before it emerges with constant speed. a. Draw a free-body diagram for the The barrel of the gun is 0.203 m long. elevator. What average force does the bullet exert b. What is the tension in the cable that on the gun? provides the upward force on the 15. A 15.2-kg police battering ram exerts an elevator car? average force of 125 N on a 10.0-kg door. a. What is the average acceleration of the 10. Ngan has a weight of 314.5 N on Mars and door? a weight of 833.0 N on Earth. b. What is the average acceleration of the a. What is Ngan’s mass on Mars? battering ram? b. What is the acceleration due to gravity 16. As a demonstration, a physics teacher
on Mars, gMars? attaches a 7.5-kg object to the ceiling by a Appendix B nearly massless string. This object then 11 . Alex is on the wrestling team and has a supports a 2.5-kg object below it by anoth- mass of 85.3 kg. Being a whiz at physics, er piece of string. Finally, another piece of he realizes that he is over the 830.0-N cut- string hangs off the bottom of the lower off for his weight class. If he can convince object to be pulled with ever increasing the trainers to measure his weight in the force until the string breaks somewhere. elevator, what must be the acceleration The string will break when the tension of the elevator so that he just makes his reaches 156 N. weight class? a. Which length of string will break first? b. What is the maximum downward force 12. During a space launch, an astronaut typi- the physics teacher can apply before the cally undergoes an acceleration of 3 gs, string breaks? which means he experiences an accelera- tion that is three times that of gravity alone. What would be the apparent weight of a 205-kg astronaut that experiences a 3-g liftoff? 7.5 kg 2.5 kg 13. Alfonso and Sarah like to go sky diving together. Alfonso has a mass of 88 kg, and Sarah has a mass of 66 kg. While in free fall together, Alfonso pushes Sarah hori- zontally with a force of 12.3 N. a. What is Alfonso’s horizontal acceleration? b. What is Sarah’s horizontal acceleration?
17. A 10.0-kg object is held up by a string that will break when the tension exceeds 1.00 102 N. At what upward acceleration will the string break?
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18. A large sculpture is lowered into place by a 4. A cue ball on a billiards table travels at crane. The sculpture has a mass of 2225 kg. 1.0 m/s for 2.0 s. After striking another When the sculpture makes contact with ball, it travels at 0.80 m/s for 2.5 s at an the ground, the crane slowly releases the angle of 60.0° from its original path. tension in the cable as workers make final a. How far does the cue ball travel before adjustments to the sculpture’s position on and after it strikes the other ball? the ground. b. What is the net displacement of the cue a. Draw a free-body diagram of the sculp- ball for the entire 4.5-s time interval? ture when it is in contact with the ground, and there is still tension in the cable while the workers make the Additional Problems final adjustments. b. What is the normal force on the sculp- 120.00° ture when the tension in the cable is 19,250 N?
5. The table below represents a set of force vectors. These vectors begin at the origin of a coordinate system, and end at the coordinates given in the table.
Vector # x-value (N) y-value (N) A 0.0 6.0 B 5.0 0.0 C 0.0 10.0
a. What is the magnitude of the resultant of the sum of these three vectors? b. What is the size of the angle, , that the Chapter 5 resultant makes with the horizontal? c. Into which quadrant does the resultant 1. A soccer ball is kicked from a 22-m-tall point? platform. It lands 15 m from the base of the platform. What is the net displacement ϩy of the ball? 2. If the net displacement is 32 m for the B same situation, as described in problem 1, how far from the platform base must the ball land? 3. For any single force vector, there is only one A angle for which its x- and y-components C are equal in size. ϩ a. What is that angle? x b. How many times bigger is a vector at R this particular angle than either of its components?
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6. A 9.0-kg crate sits on a level, rough floor. 9. A boat travels 75 km southeast, then 56 km A 61-N force is needed just to start it mov- due east, then 25 km 30.0° north of east. ing. What is the size of the coefficient of a. Sketch the vector set on a N-E-S-W grid. maximum static friction? b. Find its net E-W component of dis- 7. Given the graph below answer the follow- placement and net N-S component ing questions. of displacement. c. Find its net displacement. a. What is the value of k for this system? b. If the frictional force is 1.5 N, what is d. Find its net angle relative to an E-W axis.
FN? 10. A 1.25-kg box is being pulled across a level c. Does tripling FN triple Fapplied? surface where k is 0.80. If the string is suddenly cut, causing the applied force to d. Do Fapplied and FN act in the same direction? Explain why or why not. immediately go to 0.0 N, what is the rate of acceleration of the block? Hint: The 4 acceleration will be a negative value. 11 . If the velocity of the box in problem 10 3 was 5.0 m/s at time zero, what will be its Appendix B speed after 0.50 s? How far will it travel (N)
f in that time interval? F 2 12. A 0.17-kg hockey puck leaves the stick on 1 a slap shot traveling 21 m/s. If no other forces act on the puck, friction eventually will bring it to rest 62 m away. 0 2468 a. Based on these data, determine the FN (N) value of k for this hockey puck on ice. b. Will the answer change if a puck of different mass, but same material and 8. A wooden block sits on a level lab table. A shape is used? Explain why or why not. string draped over a pulley connects to a bucket that can be filled with lead pellets. 13. A 105-N suitcase sits on a rubber ramp at ° Maggie wants to measure how much an airport carousel at a 25 angle. The applied mass (pellets bucket) is needed weight vector can be broken into two to move the block along the table at a perpendicular components. constant speed. a. What is the magnitude of the compo- a. If the applied mass of the bucket and nent parallel to the ramp surface? the lead pellets is 0.255 kg, and the b. What is the magnitude of the compo- block has a weight of 12 N, what is nent at a right angle to the ramp surface? the value of k? c. Which of those components is the b. If some extra pellets are added, describe normal force? the behavior of the block. 105 N
Fx Fy
Fg
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14. In problem 13, which force offsets the 2. In a certain cathode-ray tube, a beam of
kinetic friction force? If Fx exceeds Ff, will electrons, moving at a constant velocity, the suitcase accelerate down the ramp? enters a region of constant electric force 15. Dalila decides to determine the coefficient midway between two parallel plates that are of maximum static friction for wood 10.0 cm long and 1.0 cm apart. In this against wood by conducting an experiment. region, the electrons experience an acceler- First she places a block of wood on a small ation, a, toward the upper plate. If the plank; next, she slowly lifts one end of the electrons enter this region at a velocity of plank upward. She notes the angle at which 3.0 106 m/s, what is the acceleration that the block just begins to slide, and claims needs to be applied so that the electrons Additional Problems that s tan . She is correct. Show why. just miss the upper deflection plate? ϩy Electron beam d
ϩ x Ϫd Deflector plates
3. A skateboard track has a horizontal segment followed by a ramp that declines at a 45° 16. Jonathan, with a mass of 81 kg, starts at angle, as shown. rest from the top of a water slide angled at a. How long would the ramp need to be 42° from the ground. He exits at the bottom to provide a landing for a skateboarder 3.0 s later going 15 m/s. What is k? who launches from the horizontal 17. A 64-N box is pulled by a rope at a constant segment at a velocity of 5.0 m/s? speed across a rough horizontal surface. b. If the initial velocity is doubled, what If the coefficient of kinetic friction is 0.81, happens to the required length of the what is the magnitude of the applied force ramp? if that force is directed parallel to the floor? 18. Suppose that in problem 17 the applied force is directed by the rope at an angle, , to the floor.
a. The normal force is no longer simply Fg. Show how to compute net vertical force. b. The frictional force still opposes the horizontal motion of the box. Show 45° how to compute net horizontal force. 4. In an attempt to make a 3-point shot from Chapter 6 a distance of 6.00 m, a basketball player 1. A football player kicks a field goal from a lofts the ball at an angle of 68° above the distance of 45 m from the goalpost. The horizontal. The ball has an initial velocity football is launched at a 35° angle above of 10.0 m/s and an initial distance from the horizontal. What initial velocity is the floor of 1.50 m. required so that the football just clears a. What is the maximum height reached the goalpost crossbar that is 3.1 m above by the ball? the ground? Ignore air resistance and the b. If the basket rim height is 3.05 m, how dimensions of the football. far above the rim is the ball?
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5. How far does a baseball that is thrown 10. Two objects are placed on a flat turntable horizontally at 42.5 m/s drop over a at 10.0 cm and 20.0 cm from the center, horizontal distance of 18.4 m? respectively. The coefficient of static 6. A projectile is launched from zero height friction with the turntable is 0.50. The with an initial angle, , above the horizon- turntable’s rotational speed is gradually
tal and with an initial velocity, vi. increased. a. Show that the range of the projectile—the a. Which of the two objects will begin to distance from the launch point at which slide first? Why? the height is again zero—is given by: b. At what rotational speed does the inner v 2 R i sin 2 object begin to slide? g 11 . An airplane’s airspeed is 2.0 102 km/h b. What launch angle, , results in the due east. Because of a wind blowing to largest range? the north, it is approaching its destination 7. If a ring were constructed as part of a space 15° north of east. station, how fast must a 50.0-m-radius a. What is the wind speed? ring rotate to simulate Earth’s gravity? b. How fast is the airplane approaching
Appendix B 8. A turntable for vinyl records works by its destination? constraining the needle to track inside a 12. A river is flowing 4.0 m/s to the east. A groove in a very close approximation of boater on the south shore plans to reach uniform circular motion. If the turntable a dock on the north shore 30.0° downriver rotational speed is 33 1 rpm, what is the 3 by heading directly across the river. needle’s centripetal acceleration when it is a. What should be the boat’s speed relative 14.6 cm from the center? to the water? 9. A park ride is designed so that the rider is b. What is the boat’s speed relative to the on the edge of a revolving platform, 3.5 m dock? from the platform’s center. This platform is mounted 8.0 m from the center of a larger revolving platform. The smaller platform makes one revolution in 6.0 s and com- pletes 2.0 rev for each revolution of the larger platform. All rotations are counter- 30.0° clockwise. At the instant shown, what are the magnitude and the direction of the rid- er’s velocity with respect to the ground?
Q Chapter 7 1. A year is defined as the time it takes for a 8.0 m vRP planet to travel one full revolution around the Sun. One Earth year is 365 days. Using P the data in Table 7-1, calculate the number vPQ R of Earth days in one Neptune year. If Nep- tune takes about 16 h to complete one of 3.5 m its days, how many Neptunian days long is Neptune’s year?
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2. Suppose a new planet was discovered to 6. A 92-kg man uses a 3.05-m board to attempt orbit the Sun with a period 5 times that to move a boulder, as shown in the diagram of Pluto. Using the data in Table 7-1, below. He pulls the end of the board and is calculate the average distance from the Sun able to move it to 45° from the perpendi- for this new planet. cular. Calculate the torque applied. 3. If a meteorite hit the Earth and moved it 2.41 1010 m closer to Venus, how many days would there be in an Earth year? Use the data in Table 7-1. 4. The Moon is a satellite of the Earth. The
° Additional Problems Moon travels one full revolution around the 45 Earth in 27.3 days. Given that the mass of the Earth is 5.97 1024 kg, what is the aver- age distance from the Earth to the Moon? 5. A satellite travels 7.18 107 m from the center of one of the planets in our solar system at a speed of 4.20 104 m/s. Using the data in Table 7-1, identify the planet. 7. If a 25-kg child tries to apply the same torque as in the previous question, what 6. Earth’s atmosphere is divided into four would the length of the lever arm need layers: the troposphere (0–10 km), the to be? stratosphere (10–50 km), the mesosphere (50–80 km), and the thermosphere (80– 8. Logan, whose mass is 18 kg, sits 1.20 m 500 km). What is the minimum velocity an from the center of a seesaw. If Shiro must object must have to enter the thermosphere? sit 0.80 m from the center to balance Logan, what is Shiro’s mass? 9. Two forces—a 55-N force in the clockwise Chapter 8 direction and a 35-N force in the counter- 1. The rotational velocity of a merry-go-round clockwise direction—are applied to a merry- is increased at a constant rate from 1.5 rad/s go-round with a diameter of 4.5 m. What to 3.5 rad/s in a time of 9.5 s. What is is the net torque on the merry-go-round? the rotational acceleration of the merry- go-round? 2. A record player’s needle is 6.5 cm from the center of a 45-rpm record. What is the velocity of the needle? 4.5 m 3. Suppose a baseball rolls 3.2 m across the floor. If the ball’s angular displacement is 82 rad, what is the circumference of the ball? 35 N 55 N 4. A painter uses a 25.8-cm long screwdriver to pry the lid off of a can of paint. If a force of 85 N is applied to move the screwdriver 60.0° from the perpendicular, calculate the torque. 10. A student sits on a stool holding a 5.0-kg 5. A force of 25 N is applied vertically at the dumbbell in each hand. He extends his arms end of a wrench handle that is 45 cm long such that each dumbbell is 0.60 m from the to tighten a bolt in the clockwise direction. axis of rotation. The student’s moment of What torque is needed by the bolt to keep inertia is 5.0 kg m2. What is the moment of the wrench from turning? inertia of the student and the dumbbells?
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11 . A basketball player spins a basketball with 2. If the ball in the previous problem inter- a radius of 15 cm on his finger. The mass acts with the wall for a time interval of of the ball is 0.75 kg. What is the moment 0.22 s, what is the average force exerted of inertia about the basketball? on the wall? 12. A merry-go-round in the park has a radius 3. A 42.0-kg skateboarder traveling at of 2.6 m and a moment of inertia of 1.50 m/s hits a wall and bounces off of 2 1773 kg m . What is the mass of the it. If the magnitude of the impulse is merry-go-round? 150.0 kg m/s, calculate the final velocity 13. The merry-go-round described in the of the skateboarder. previous problem is pushed with a con- 4. A 50.0-g toy car traveling with a velocity of stant force of 53 N. What is the angular 3.00 m/s due north collides head-on with acceleration? an 180.0-g fire truck traveling with a veloc- 14. What is the angular velocity of the merry- ity of 0.50 m/s due south. The toys stick go-round described in problems 12 and 13 together after the collision. What are the after 85 s, if it started from rest? magnitude and direction of their velocity 15. An ice-skater with a moment of inertia of after the collision? Appendix B 1.1 kg m2 begins to spin with her arms 5. A 0.040-kg bullet is fired into a 3.50-kg extended. After 25 s, she has an angular block of wood, which was initially at rest. velocity of 15 rev/s. What is the net torque The bullet remains embedded within the acting on the skater? block of wood after the collision. The 16. A board that is 1.5 m long is supported in bullet and the block of wood move at a two places. If the force exerted by the first velocity of 7.40 m/s. What was the original support is 25 N and the forced exerted by velocity of the bullet? the second is 62 N, what is the mass of the board? 6. Ball A, with a mass of 0.20 kg, strikes ball 17. A child begins to build a house of cards by B, with a mass of 0.30 kg. The initial laying an 8.5-cm-long playing card with a velocity of ball A is 0.95 m/s. Ball B is mass of 0.75 g across two other playing initially at rest. What are the final speed cards: support card A and support card B. and direction of ball A and B after the If support card A is 2.0 cm from the end collision if they stick together? and exerts a force of 1.5 10 3 N, how far 7. An ice-skater with a mass of 75.0 kg pushes from the end is support card B located? Let off against a second skater with a mass of the axis of rotation be at the point support 42.0 kg. Both skaters are initially at rest. card A comes in contact with the top card. After the push, the larger skater moves off 18. If support card A in the previous problem with a speed of 0.75 m/s eastward. What was moved so that it now is 2.5 cm from is the velocity (magnitude and direction) the end, how far from the other end does of the smaller skater after the push? support card B need to be to reestablish 8. Suppose a 55.0-kg ice-skater, who was equilibrium? initially at rest, fires a 2.50-kg gun. The 0.045-kg bullet leaves the gun at a velocity of 565.0 m/s. What is the velocity of the Chapter 9 ice-skater after she fires the gun? 1. A ball with an initial momentum of 9. A 1200-kg cannon is placed at rest on 6.00 kg m/s bounces off a wall and travels an ice rink. A 95.0-kg cannonball is shot in the opposite direction with a momen- from the cannon. If the cannon recoils at tum of 4.00 kg m/s. What is the magnitude a speed of 6.80 m/s, what is the speed of of the impulse acting on the ball? the cannonball?
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10. An 82-kg receiver, moving 0.75 m/s north, 3. A man pushes a couch a distance of 0.75 m. is tackled by a 110.0-kg defensive lineman If 113 J of work is done, what is the magni- moving 0.15 m/s east. The football players tude of the horizontal force applied? hit the ground together. Calculate their 4. Two blocks are tied together by a horizon- final velocity (magnitude and direction). tal string and pulled a distance of 2.7 m 11 . A 985-kg car traveling south at 29.0 m/s across an air hockey table with a constant hits a truck traveling 18.0 m/s west, as force of 35 N. The force is directed at an shown in the figure below. After the colli- upward angle of 35° from the 9.0-kg block, sion, the vehicles stick together and travel as shown in the figure. What is the change with a final momentum of 4.0 104 kg m/s in kinetic energy in the two-block system? at an angle of 45°. What is the mass of Additional Problems 35 N the truck? 35° 6.0 kg 9.0 kg
29.0 m/s 5. If the two-block system described in the previous problem was initially at rest, what is the final velocity? 18.0 m/s 6. A toy car with a mass of 0.75 kg is pulled 45° 3.2 m across the floor with a constant force of 110 N. If 67 J of work is done, what is the upward angle of the force? 7. If a 75-W lightbulb is left on for 2.0 h, how much work is done? p ϭ 4.0ϫ104 kgиm/s 8. A 6.50-horsepower (hp) self-propelled lawn mower is able to go from 0.00 m/s to 0.56 m/s in 0.050 s. If the mass of the 12. A 77.0-kg woman is walking 0.10 m/s east lawn mower is 48.0 kg, what distance in the gym. A man throws a 15.0-kg ball does the lawn mower travel in this time? south and accidentally hits the woman. (Use 1 hp 746 W.) The woman and the ball move together with a velocity of 0.085 m/s. Calculate the 9. A winch that’s powered by a 156-W motor direction the woman and the ball move. lifts a crate 9.8 m in 11 s. What is the mass of the crate? 10. A man exerts a force of 310 N on a lever to Chapter 10 raise a crate with a mass of 910 kg. If the efficiency of the lever is 78 percent, what 1. A toy truck is pushed across a table 0.80 m is the lever’s IMA? north, and pulled back across the table 11 . A worker uses a pulley to lift a 45-kg object. 0.80 m south. If a constant horizontal If the mechanical advantage of the pulley force of 15 N was applied in both direc- is 5.2, what is the effort force exerted by tions, what is the net work? the worker? 2. A 15-kg child experiences an acceleration 12. When the chain on a bicycle is pulled of 0.25 m/s2 as she is pulled 1.7 m hori- 0.95 cm, the rear wheel rim moves a zontally across the floor by her sister. distance of 14 cm. If the gear has a radius Calculate the change in the child’s kinetic of 3.5 cm, what is the radius of the rear energy. wheel?
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Chapter 11 7. A 35-kg child is riding on a swing that rises to a maximum height of 0.80 m. 1. A crate with a mass of 210 kg is horizontally Neglecting friction, what is the child’s accelerated by a force of 95 N. The force gravitational potential energy at the top is directed at an upward angle so that the of the swing? What is the child’s kinetic vertical part of the force is 47.5 N and energy at the top of the swing? the horizontal part of the force is 82.3 N 8. A sled and its rider are perched at the top of (see the diagram below). If the crate is a hill that is 35 m tall. If the gravitational pulled 5.5 m across the floor, what is the potential energy is 3.0 104 J, what is the change in kinetic energy of the crate? weight of the sled and rider? 9. The big hill on a roller-coaster ride is 91 m 47.5 N 95 N tall. If the mass of the roller-coaster car and its two riders is 314 kg and the maxi- 82.3 N mum velocity reached by this roller-coaster 210 kg ride is 28 m/s, how much energy was lost to friction? Appendix B Smooth floor 10. A dartboard with a mass of 2.20 kg is suspended from the ceiling such that it is initially at rest. A 0.030-kg dart is thrown 2. Assuming that the crate described in prob- at the dartboard with a velocity of 1.3 m/s. lem 1 was initially at rest, what is the final After the dart hits the dartboard, the dart velocity of the crate? and the board initially move with a velocity 3. If the crate described in problem 1 experi- of 0.025 m/s. How much kinetic energy is enced a frictional force of 15 N, what is lost in the system? the final kinetic energy of the crate? 11 . In a physics laboratory, students crash carts 4. A 150-kg roller-coaster car climbs to the together on a frictionless track. According top of a 91-m-high hill. How much work to the following data, was kinetic energy is done against gravity as the car is lifted to conserved? the top of the hill? 5. A pendulum bob with a mass of 0.50 kg Mass (kg) vi (m/s) vf (m/s) swings to a maximum height of 1.0 m. Cart A 0.25 0.18 0.21 What is the kinetic energy when the pen- dulum bob is at a height of 0.40 m? Cart B 0.36 0.20 0.11 6. A sled and its rider, with a total mass of 95 kg, are perched on top of a 25-m-tall 12. A 0.150-kg ball that is thrown at a velocity hill. A second hill is 12 m tall (see the dia- of 30.0 m/s hits a wall and bounces back gram below). The rider is given an initial in the opposite direction with a speed of push providing 3674 J of kinetic energy. 25.0 m/s. How much work was done by Neglecting friction, what is the velocity at the ball? the top of the top of the 12-m-tall hill? Chapter 12
25 m 1. Convert the following Celsius tempera- 12 m tures to Kelvin temperatures. a. 196°C d. 273°C b. 32°C e. 273°C c. 212°C f. 27°C
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2. Find the Celsius and the Kelvin tempera- 8. A 220-g iron horseshoe is heated to 825°C tures for the following objects. and then plunged into a bucket filled with a. average body temperature 20.0 kg of water at 25.0°C. Assuming that b. hot coffee no energy is transferred to the surround- c. iced tea ings, what is the final temperature of the d. boiling water water at equilibrium? 3. Convert the following Kelvin temperatures to Celsius temperatures. a. 4 K
b. 25 K Additional Problems c. 272 K d. 373 K e. 298 K Water f. 316 K T ϭ 25.0°C ϭ 4. A 9.8-g lead bullet with a muzzle velocity m 20.0 kg of 3.90 102 m/s is stopped by a wooden Horseshoe ϭ ° block. What is the change in temperature T 825 C of the bullet if one-fourth of its original kinetic energy goes into heating the bullet? 9. A cook adds 1.20 kg of soup bones to 2 v ϭ 3.90ϫ10 m/s 12.5 kg of hot broth for flavoring. The temperatures of the bones and the broth Wooden ° ° Bullet are 20.0 C and 90.0 C, respectively. block Assume that the specific heat of the broth m ϭ 9.8 g is the same as that of water. Also assume that no heat is lost to the environment. If ° 5. What is the change in temperature of the equilibrium temperature is 87.2 C, 2.2 kg of the following substances if what is the specific heat of the bones? 8.5 103 J of thermal energy is added to each of the substances? a. ice Bones b. water m ϭ 1.20 kg Broth c. steam t ϭ 20.0 C T ϭ 90.0 C d. aluminum e. silver f. copper 6. A 2350-kg granite tombstone absorbs 2.8 107 J of energy from the Sun to ° change its temperature from 5.0°C at night 10. A 150.0-g copper cylinder at 425 C is ° to 20.0°C during an autumn day. Deter- placed on a large block of ice at 0.00 C. mine the specific heat of granite from this Assume that no energy is transferred to the information. surroundings. What is the mass of the ice that will melt? 7. A 2.00 103-g sample of water at 100.0°C is mixed with a 4.00 103-g sample of 11 . How much energy is needed to melt one water at 0.0°C in a calorimeter. What is the troy ounce, 31.1 g, of gold at its melting equilibrium temperature of the mixture? point?
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12. Trying to make an interesting pattern, 4. As shown in the figure below, a bubble of an artist slowly pours 1.00 cm3 of liquid gas with a volume of 1.20 cm3 is released gold onto a large block of ice at 0.00°C. under water. As it rises to the surface, the While being poured, the liquid gold is temperature of the bubble increases from at its melting point of 1064°C. The density 27°C to 54°C, and the pressure is cut to of gold is 19.3 g/cm3, and its specific one-third of its initial value. What is the heat is 128 J/kg K. What mass of ice will volume of the bubble at the surface? melt after all the gold cools to 0.00°C? 13. A cylinder containing 1.00 g of water at the boiling point is heated until all the water turns into steam. The expanding steam pushes a piston 0.365 m. There is a 215-N frictional force acting against the piston. What is the change in the thermal energy of the water?
Appendix B 14. What is the change in temperature of water after falling over a 50.0-m-tall waterfall. 5. A sample of ethane gas (molar mass Assume that the water is at rest just before 30.1 g/mol) occupies 1.2 10 2 m3 at falling off and just after it reaches the 46°C and 2.4 105 Pa. How many moles bottom of the falls. of ethane are present in the sample? What is the mass of the sample? 15. Two 6.35-kg lead bricks are rubbed against 3 each other until their temperature rises 6. The constant R equals 8.31 Pa m /mol K as by 1.50 K. How much work was done on it is presented in the ideal gas law in this the bricks? chapter. One mole of an ideal gas occupies 22.4 L at standard temperature and pres- sure, STP, which is defined as 0.00°C and 1.00 atm. Given this information, deduce the value of R in L atm/mol K. Chapter 13 7. Suppose that two linked pistons are both cylindrical in shape. Show that the ratio of 1. Use Table 13.1 to estimate the pressure forces generated is directly proportional in atmospheres (atm) on a climber stand- to the square of the radii of the two cross- ing atop Mt. Everest. Is this more or less sectional circular areas. than half standard atmospheric pressure 8. The cross-sectional areas of the pistons in (1.0 atm)? the system shown below have a ratio of 2. A woman wearing high heels briefly sup- 25 to 1. If the maximum force that can be ports all her weight on the heels. If her applied to the small piston is 12 N, what mass is 45 kg and each heel has an area is the maximum weight that can be lifted? 2 of 1.2 cm , what pressure does she exert F on the floor? 3. A typical brick has dimensions of 20.0 cm 10.0 cm 5.0 cm and weighs 20.0 N. How does the pressure exerted by a typical brick when it is resting on its smallest side compare to the pressure exerted when it is resting on its largest side?
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9. A car of mass 1.35 103 kg sits on a large 15. A fishing line’s lead sinker has a volume piston that has a surface area of 1.23 m2. of 1.40 10 5 m3. The density of lead is The large piston is linked to a small piston 1.2 104 kg/m3. What is the apparent of area 144 cm2. What is the weight of the weight of the sinker when immersed in car? What force must a mechanic exert on freshwater? Seawater is slightly denser than the small piston to raise the car? freshwater. Is the sinker’s apparent weight 10. At what depth in freshwater does the water bigger or smaller in seawater? Explain. exert a pressure of 1.00 atm (1 atm 1.013 105 Pa) on a scuba diver? Chapter 14 11 . An iceberg floats in seawater, partly under Additional Problems water and partly exposed. Show that the 1. What is the mass of the watermelon shown below, if the spring constant is 128 N/m? value of Vsubmerged /Vtotal equals ice / seawater. What percentage of the iceberg is exposed? Use 1.03 103 kg/m3 for the density of sea- water, and 0.92 103 kg/m3 for the density of ice. 0.48 m 12. A concrete block ( 36 10 6 °C 1) of volume 0.035 m3 at 30.0°C is cooled to 10.0°C. What is the change in volume? 13. A glass mirror used in a mountaintop telescope is subject to temperatures rang- 2. How many centimeters will a spring stretch ing from 15°C to 45°C. At the lowest when a 2.6-kg block is hung vertically from temperature, it has a diameter of 5.1 m. a spring with a spring constant of 89 N/m? If the coefficient of linear expansion 3. How much elastic potential energy does for this glass is 3.0 10 6 °C 1, what a spring with a constant of 54 N/m have is the maximum change in diameter when it is stretched 18 cm? the mirror undergoes due to thermal 4. What is the period of the pendulum of expansion? the clock below? 14. As shown in the figure below, a bimetallic strip is made from a piece of copper ( 16 10 6 °C 1) and a piece of steel 6 1 XII ( 8 10 °C ). The two pieces are XI I X II IX III equal in length at room temperature. VIII IV VII V a. As the strip is heated from room tem- VI perature, what is the ratio of the change in the length of the copper to that of the steel? 62 cm b. How will the strip bend when it is heated above room temperature? When it is cooled below room temperature? 0.52 kg Copper
5. A clock pendulum has a period of 0.95 s. Wooden How much longer will it have to be to Steel handle have a period of 1.0 s?
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6. What is the length of a pendulum with a 6. Boat A is traveling at 4.6 m/s. Boat B is period of 89.4 ms? moving away from boat A at 9.2 m/s, as 7. Al is chopping wood across a clearing shown in the figure below. The captain of from Su. Su sees the axe come down and boat B blows an air horn with a frequency hears the sound of the impact 1.5 s later. of 550 Hz. What frequency does boat A How wide is the clearing? hear? Use 343 m/s for the speed of sound. 8. When an orchestra is tuning up, the first
violinist plays a note at 256 Hz. vd vs a. What is the wavelength of that sound wave if the speed of sound in the con- cert hall is 340 m/s? b. What is the period of the wave? Boat A Boat B 9. Geo is standing on a breakwater and he notices that one wave goes by every 4.2 s. The distance between crests is 12.3 m. 7. A submarine is traveling toward a station- a. What is the frequency of the wave? ary detector. If the submarine emits a 260-Hz sound that is received by the
Appendix B b. What is the speed of the wave? detector as a 262-Hz sound, how fast is the submarine traveling? Use 1533 m/s Chapter 15 for the speed of sound in seawater. 1. Sound waves are being used to determine 8. The end of a pipe is inserted into water. the depth of a freshwater lake, as shown in A tuning fork is held over the pipe. If the the figure below. If the water is 25°C and pipe resonates at lengths of 15 cm and it takes 1.2 s for the echo to return to the 35 cm, what is the frequency of the tuning sensor, how deep is the lake? fork? Use 343 m/s for the speed of sound. 9. A 350-Hz tuning fork is held over the end of a pipe that is inserted into water. What is the spacing between the resonance lengths of the pipe if the speed of sound is 348 m/s? Detector Sound source Chapter 16 1. What is the distance, r, between the light- bulb and the table in the figure below? 2. Find the wavelength of an 8300-Hz wave in copper. 3. Janet is standing 58.2 m from Ninovan. If Ninovan shouts, how long will it take P ϭ 2152 lm Janet to hear her? Use 343 m/s for the speed of sound. r 4. The engine on a motorcycle hums at 85 Hz. If the motorcycle travels toward a resting E ϭ 180 lx observer at a velocity of 29.6 m/s, what frequency does the observer hear? Use 343 m/s for the speed of sound. 5. If the speed of a wave on a 78-cm-long guitar string is known to be 370 m/s, what is the fundamental frequency?
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2. What is the luminous flux of a flashlight 5. What is the magnification of the object in that provides an illuminance of 145 lx to problem 4? the surface of water when held 0.50 m 6. If the object in problem 4 is 3.5 cm tall, above the water? how tall is the image? 3. An overhead light fixture holds three light- 7. A 6.2-m-tall object is 2.3 m from a convex bulbs. Each lightbulb has a luminous flux of mirror with a 0.8-m focal length. What 1892 lm. The light fixture is 1.8 m above the is the magnification? floor. What is the illuminance on the floor? 8. How tall is the image in problem 7? 4. What is the wavelength in air of light that 9. A ball is 6.5 m from a convex mirror with has a frequency of 4.6 1014 Hz?
a magnification of 0.75. If the image is Additional Problems 5. A helium atom is in a galaxy traveling at 0.25 m in diameter, what is the diameter 6 a speed of 4.89 10 m/s away from the of the actual ball? Earth. An astronomer on Earth observes a frequency from the helium atom of 6.52 1014 Hz. What frequency of light Chapter 18 is emitted from the helium atom? 6. An astronomer observes that a molecule 1. A piece of flint glass is lying on top of a in a galaxy traveling toward Earth emits container of water (see figure below). When light with a wavelength of 514 nm. The a red beam of light in air is incident upon ° astronomer identifies the molecule as one the flint glass at an angle of 28 , what is that actually emits light with a wavelength the angle of refraction in the flint glass? of 525 nm. At what velocity is the galaxy Air moving? Flint glass Chapter 17 Water 1. A light ray is reflected off a plane mirror at an angle of 25° from the normal. A light ray from another source is reflected 54° from the normal. What is the difference in the angles of incidence for the two light sources? 2. A light ray is reflected off of a plane mirror, 2. When the angle of refraction in the flint as shown. What is the angle of reflection? glass of problem 1 is 22°, what is the angle of refraction in the water? 3. When the beam of light in problem 1 13° enters the flint glass from the water, what is the maximum angle of incidence in the 3. The angle between an incident and a reflected water such that light will transmit into the ray is 70.0°. What is the angle of reflection? air above the flint glass? Hint: Use an angle 4. An image is produced by a concave mirror, of refraction of the light beam in air that is as shown. What is the object’s position? almost 90°. 4. An object that is 24 cm from a convex 25 cm lens produces a real image that is 13 cm 15 cm from the lens. What is the focal length of the lens? C 5. A 5.0-cm-tall object is placed 16 cm from a convex lens with a focal length of 8.4 cm. Image What are the image height and orientation?
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6. An object is 185 cm from a convex lens 2. A laser of unknown wavelength replaces with a focal length of 25 cm. When an the helium-neon laser in the experiment inverted image is 12 cm tall, how tall is described in problem 1. To obtain the best the associated object? diffraction pattern, the screen had to be 7. What are the image height and orientation moved to 104.0 cm. The distance between produced by the setup in the following the centers of the central band and the figure? first-order band is 1.42 cm. What wave- length of light is produced by the laser? 3. Light with a wavelength of 454.5 nm passes Object through two slits that are 95.2 cm from a screen. The distance between the centers 5.0 cm of the central band and the first-order band is 15.2 mm. What is the slit separation? F 4. What color of light would be reflected from the soapy water film shown in the 10.0 cm figure below? Appendix B 15.0 cm Air Soapy water 8. A convex lens can be used as a magnifying 76.1 nm n ϭ 1.33 glass. When an object that is 15.0 cm from SW the lens has an image that is exactly 55 Air times the size of the object, what is the 5. A 95.7-nm film of an unknown substance is focal length of the lens? able to prevent 555-nm light from being 9. A concave lens with a focal length of reflected when surrounded by air. What is 220 cm produces a virtual image that the index of refraction of the substance? is 36 cm tall. When the object is placed 6. An oil film (n 1.45) on the surface of a 128 cm from the lens, what is the puddle of water on the street is 118 nm magnification? thick. What frequency of light would be reflected? Chapter 19 7. Violet light ( 415 nm) falls on a slit that is 0.040 mm wide. The distance 1. A physics student performs a double-slit between the centers of the central bright diffraction experiment on an optical band and the third-order dark band is bench, as shown in the figure below. The 18.7 cm. What is the distance from the slit light from a helium-neon laser has a wave- to the screen? length of 632.8 nm. The laser light passes through two slits separated by 0.020 mm. 8. Red light ( 685 nm) falls on a slit that What is the distance between the centers of is 0.025 mm wide. The distance between the central band and the first-order band? the centers of the central bright band and the second-order dark band is 6.3 cm. Screen What is the width of the central band? Laser Diffraction 9. The width of the central bright band of a grating diffraction pattern is 2.9 cm. Laser light of unknown wavelength passes through a single slit that is 0.042 mm wide and onto 50.0 cm a screen that is 1.5 m from the slit. What 150.0 cm is the wavelength of the light?
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10. A diffraction grating has 13,400 lines per 2. As shown in the figure below, four charges, inch. What is the slit separation distance? each with charge q, are distributed sym- (Use 1 in 2.54 cm) metrically around the origin, O(0, 0), at 11 . Light from a helium-neon laser ( A(1.000, 0), B(0, 1.000), C( 1.000, 0), 632.8 nm) passes through the diffraction and D(0, 1.000). Find the force on a grating described in problem 10. What is fifth charge, qT, located at T(5.000, 0). the angle between the central bright line and the first-order bright line? y (m) 12. A diffraction grating with slits separated by 3.40 10 6 m is illuminated by light with B a wavelength of 589 nm. The separation Additional Problems between lines in the diffraction pattern is C 0 A T 0.25 m. What is the distance between the x (m) diffraction grating and the screen? D
Chapter 20 3. Consider that the four charges in the previ- 1. The magnitude of a charge, q, is to be ous problem are now combined into a determined by transferring the charge single charge, 4q, located at the origin.
equally to two pith balls. Each of the pith What is the force on charge qT? balls has a mass of m, and is suspended by an insulating thread of length l. When Chapter 21 the charge is transferred, the pith balls separate to form an equilibrium in which 1. What are the magnitude and the sign of a each thread forms an angle, , with the point charge that experiences a force of vertical. 0.48 N east when placed in an electric a. Draw a force diagram showing the field of 1.6 105 N/C west? forces that are acting on the rightmost 2. A test charge of 1.0 10 6 C, located at pith ball. the point T(0, 1) m, experiences a force of b. Derive an expression for q as a function 0.19 N directed toward the origin, along of , m, and l. the y-axis, due to two identical point charges c. Use your derived expression to deter- located at A( 1, 0) m and B(1, 0) m. mine the value of q when 5.00°, a. What is the sign of the charges at A m 2.00 g, and l 10.0 cm. and B? b. What are the magnitude and direction of the electric field at T? ϩy
qT T(0, 1) l
qA qB ϩx A(Ϫ1, 0) B(1, 0)
dd
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3. A test charge of 0.5 10 7 C is placed in 8. The electric field strength, defined as a force an electric field of 6.2 104 N/C, directed per unit charge, has the units newtons per 15° north of east. What is the force experi- coulomb, N/C. The formula for electric enced by the charge? potential difference, V Ed, however, 4. By what percent must the distance from a suggests that E also can be expressed as point charge increase in order to have a volts per meter, V/m. reduction in the electric field strength by a. By analysis of the units, show that these 40 percent? two expressions for the units of electric 5. A particle of mass m 2.0 10 6 kg is field strength are equivalent. in a circular orbit about a point charge. b. Suggest a reason why V/m is often a The charge, q, is 3.0 10 5 C and is at a more useful way to express electric distance of r 20.0 cm. field strength. a. What is the electric field strength at 9. Suppose you have two parallel, metal all points on the orbit around the plates that have an electric field between point charge? them of strength 3.0 104 N/C, and are b. Considering only electrostatic forces, 0.050 m apart. Consider a point, P, located Appendix B what charge, q, on the particle is 0.030 m from plate A, the negatively required to sustain an orbital period charged plate, when answering the of 3.0 10 3 s? following questions. a. What is the electric potential at P relative to plate A? b. What is the electric potential at P
FE relative to plate B, the positively charged plate? 20.0 cm q 10. A certain 1.5-V size-AA battery has a stor- age capacity of 2500 C. How much work can this battery perform? 11 . In a vacuum tube, electrons accelerate from the cathode element to the plate 6. Two charges of equal magnitude and element, which is maintained at a positive opposite sign are placed 0.50 m apart. potential with respect to the cathode. If the The electric field strength midway between plate voltage is 240 V, how much kinetic 4 them is 4.8 10 N/C toward the negative energy has an electron acquired when it charge. What is the magnitude of each reaches the plate? charge? 12. An oil drop with five excess electrons is sus- 3 .؉q E ؊q pended in an electric field of 2.0 10 N/C What is the mass of the oil drop? r r 13. An oil drop weighing 7.5 10 15 N carries 2 2 three excess electrons. a. What potential difference is required 7. A pith ball weighing 3.0 10 2 N carries a to suspend the drop between parallel charge of 1.0 10 6 C. The pith ball is plates separated by 2.3 cm? placed between two large, parallel, metal b. If the oil drop picks up another elec- plates, that are separated by 0.050 m. tron, by how much must the potential What is the potential difference, V, that difference between the plates be must be applied in order to suspend the reduced to maintain the oil drop pith ball between the plates? in suspension?
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14. A charge of 2.00 10 6 C is moved against Chapter 22 a constant electric field. If 4.50 10 4 J of work is done on the charge, what is 1. A decorative lightbulb rated at 7.50 W the potential difference between the draws 60.0 mA when lit. What is the initial and the final locations of the voltage drop across the bulb? charge? 2. A 1.2-V nickel-cadmium battery has a rated storage capacity of 4.0 103 mAh 15. Capacitors C1 220 F and C2 470 F are connected across a 48.0-V electric (milliamp-hours). potential difference. a. What is the battery charge capacity in a. What are the charges, q and q , on coulombs? Hint: 1 C 1 A s. 1 2 Additional Problems each of the capacitors? b. How long can this battery supply a current of 125 mA? b. What is the total charge, qT, on both capacitors? 3. A heating element of an electric furnace consumes 5.0 103 W when connected c. Repeat steps a and b for a new potential across a 240-V source. What current flows difference, v 96.0 V. through the element? d. Now consider the two capacitors as a 4. The cold filament resistance of a lightbulb system. What would be a single equiva- is 20.0 . The bulb consumes 75 W when lent capacitor, C , that could replace eq it is operating from a 120-V source. By C and C , and be capable of yielding 1 2 what factor does the start-up current in the same results? the bulb exceed the operating current? e. Based on your responses to the above, 5. In the circuit shown below, a potentiome- make a conjecture concerning the ter is used to vary the current to the lamp. equivalent capacitance of a system of If the only resistance is due to the lamp, capacitors—all of which are connected what is the current in the circuit? across the same potential difference.
16. A new 90.0-V battery with a storage capaci- I ty of 2.5 104 C charges a 6800- F capaci- tor with the switch in position A. Then ؉ the switch is thrown to position B to 12 V discharge the capacitor. ؊ ؍ a. How many times can this cycle be Rlamp 20.0 repeated before the battery is completely discharged? b. If the capacitor discharge occurs in 6. An electric toaster consumes 1875 W in 120 ms, what is the average power operation. If it is plugged into a 125-V dissipated in the discharge circuit source, what is its resistance? during one cycle? 7. Draw a circuit diagram to include a 90.0-V BA battery, a 220- resistor, and a 680- resistor in series. Show the direction of conventional current. ؉ Discharge 8. Modify the diagram of the previous prob- circuit 90.0 ؊ lem to include an ammeter and a voltmeter to measure the voltage drop across the 680- resistor. 17. A 0.68- F capacitor carries a charge on one 9. If the total resistance in the circuit in plate of 1.36 10 5 C. What is the potential problem 8 is 9.0 102 , what would the difference across the leads of this capacitor? ammeter and the voltmeter indicate?
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10. An electric motor with a load delivers Chapter 23 5.2 hp to its shaft (1 hp 746 W). Under these conditions, it operates at 82.8 percent 1. A series circuit contains a 47- resistor, an efficiency. (Efficiency is defined as the ratio 82- resistor, and a 90.0-V battery. What
of power output to power input.) resistance, R3, must be added in series to a. How much current does the motor reduce the current to 350 mA? draw from a 240-V source? 2. What is the minimum number of 100.0- b. What happens to the remaining resistors that must be connected in series 17.2 percent of the input power? together with a 12.0-V battery to ensure 11 . An industrial heating process uses a current that the current does not exceed 10.0 mA? of 380 A supplied at 440-V potential. 3. A 120.0-V generator is connected in series a. What is the effective resistance of the with a 100.0- resistor, a 400.0- resistor, heating element? and a 700.0- resistor. b. How much energy is used by this a. How much current is flowing in the process during an 8-h shift? circuit? 12. An 8.0- electric heater operates from b. What is the voltage drop in the 400- Appendix B a 120-V source. resistor? a. How much current does the heater 4. Show that the total power dissipated in require? a circuit of series-connected resistors is 2 b. How much time does the heater need P I R, where R is the equivalent resistance. to generate 2.0 104 J of thermal energy? 5. In an experiment, three identical light- 13. A manufacturer of lightbulbs advertises bulbs are connected in series across a that its 55-W bulb, which produces 120.0-V source, as shown. When the switch 800.0 lm of light output, provides almost is closed, all of the bulbs are illuminated. the same light as a 60.0-W bulb with an However, when the experiment is repeated energy savings. The 60.0-W bulb produces the next day, bulbs A and B are illuminat- 840.0 lm. ed brighter than normal, and bulb C is a. Which bulb most efficiently converts dark. A voltmeter is used to measure the electric energy to light? voltages in the circuit as shown. The voltmeter readings are: b. Assume a bulb has a lifetime of 1.0 103 h and an electric energy cost V1 120.0 V of $0.12/kWh. How much less does V2 60.0 V the 55-W bulb cost to operate over V3 0.0 V its lifetime? a. What has happened in this circuit? c. Is most of the cost savings due to b. Explain why bulbs A and B are brighter higher bulb efficiency, or due to the than normal. consumer’s willingness to accept lower c. Is there more or less current flowing light output? now in the circuit? 14. By what factor would the I2R loss in trans- (Bulb A) (Bulb B) (Bulb C) mission wires be reduced if the transmis- RA RB RC sion voltage were boosted from 220 V to 22 kV? Assume that the rate of energy delivered is unchanged. 120.0 V 15. The electric-utility invoice for a household V1 V2 V3 shows a usage of 1245 kWh during a certain 30-day period. What is the average power consumption during this period?
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6. A string of holiday lights has 25 identical 10. Two lightbulbs, one rated at 25.0 W and bulbs connected in series. Each bulb dissi- one rated at 75.0 W, are connected in pates 1.00 W when the string is connected parallel across a 125-V source. to a 125-V outlet. a. Which bulb is the brightest? a. How much power must be supplied by b. What is the operating resistance of each the 125-V source? of the bulbs? b. What is the equivalent resistance of c. The bulbs are rewired in series. What is this circuit? the dissipated power in each bulb? c. What is the resistance of each bulb? Which bulb is the brightest? d. What is the voltage drop across each 11 . A 10.0-V battery has an internal resistance Additional Problems bulb? of 0.10 . The internal resistance can be 7. Two resistors are connected in series across modeled as a series resistor, as shown. a 12.0-V battery. The voltage drop across a. Derive an expression for the battery one of the resistors is 5.5 V. terminal voltage, V, as a function of a. What is the voltage drop across the the current, I. other resistor? b. Create a graph of voltage versus current b. If the current in the circuit is 5.0 mA, for a current range of 0.0 to 1.0 A.
what are the two resistor values? c. What value of load resistor RL needs to 8. In problem 7, the specifications for the be placed across the battery terminals resistors state that their resistance may vary to give a current of 1.0 A? from the listed nominal value. If the possi- d. How does the V-I function differ from ble ranges of actual resistance values are that of an ideal voltage source? as follows, 1050 R 1160 , and 1 ϭ RI 0.10 1240 R2 1370 , what is the possi- ble minimum and maximum value of the nominal 5.5-V voltage drop? 9. A voltage-divider circuit is constructed with a potentiometer, as shown below. ϩ 10.0 V V RL There are two fixed resistances of 113 k Ϫ and 294 k . The resistance of the poten- tiometer can range from 0.0 to 100.0 k .
a. What is Vout when the potentiometer is at its minimum setting of 0.0 ? Battery Load b. What is Vout when the potentiometer is at its maximum setting of 100.0 k ? 12. Show that the total power dissipated in a c. What potentiometer setting is required circuit of parallel-connected resistors is to adjust Vout to exactly 65.0 V? 2 P V , where R is the equivalent resistance. R 13. A holiday light string of ten bulbs is 113 k equipped with shunts that short out the bulbs when the voltage drop increases to ؉ ؉ line voltage, which happens when a bulb 100.0 V 100.0 k ؊ burns out. Each bulb has a resistance of 200.0 . The string is connected to a Vout 294 k household circuit at 120.0 V. If the string is protected by a 250.0-mA fuse, how many ?؊ bulbs can fail without blowing the fuse
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14. A 60.0-W lightbulb and a 75.0-W light- 3. Jingdan turned a screwdriver into a magnet bulb are connected in series with a by rubbing it with a strong bar magnet to 120-V source. pick up a screw that has fallen into an a. What is the equivalent resistance of inaccessible spot. How could he demag- the circuit? netize his screwdriver after picking up the b. Suppose an 1875-W hair dryer is now screw? plugged into the parallel circuit with 4. A long, straight, current-carrying wire car- the lightbulbs. What is the new equiva- ries a current from west to east. A compass lent resistance of the circuit? is held above the wire. 15. What is the equivalent resistance of the a. Which direction does the north pole of following resistor network? the compass point? b. When the compass is moved under- 29.4 k 25.5 k neath the wire, in which direction does the north pole point? 5. Consider the sketch of the electromagnet 6.34 k in the figure below. Which components
Appendix B could you change to increase or decrease 47.5 k the strength of the electromagnet? Explain 7.87 k your answer.
Chapter 24 1. The magnetic field of Earth resembles the field of a bar magnet. The north pole of a compass needle, used for navigation, generally points toward the geographic 6. Sketch a graph showing the relationship north pole. Which magnetic pole of the between the magnetic field around a Earth is the compass needle pointing straight, current-carrying wire, and the toward? distance from the wire. 2. A magnet is used to collect some spilled 7. How long is a wire in a 0.86-T field that paper clips. What is the magnetic pole at carries a current of 1.4 A and experiences the end of the paper clip that is indicated a force of 13 N? in the figure? 8. A 6.0-T magnetic field barely prevents a 0.32-m length of copper wire with a current
N of 1.8 A from dropping to the ground. What is the mass of the wire? 9. How much current will be needed to S produce a force of 1.1 N on a 21-cm-long piece of wire at right angles to a 0.56-T field? 10. Alpha particles (particles containing two protons, two neutrons, but no electrons) are traveling at right angles to a 47- T field with a speed of 36 cm/s. What is the force on each particle?
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11 . A force of 7.1 10 12 N is exerted on some 8. A step-down transformer has 9000 turns Al3 ions (an atom missing three electrons) on the primary coil and 150 turns on the that are traveling at 430 km/s perpendicular secondary coil. The EMF in the primary to a magnetic field. What is the magnetic coil is 16 V. What is the voltage being field? applied to the secondary coil? 12. Electrons traveling at right angles to a 9. A transformer has 124 turns on the magnetic field experience a force of primary coil and 18,600 turns on the 8.3 10 13 N when they are in a magnetic secondary coil. field of 6.2 10 1 T. How fast are the a. Is this a step-down or a step-up electrons moving? transformer? Additional Problems b. If the effective voltage in the secondary Chapter 25 coil is 3.2 kV, what is the peak voltage being delivered to the primary coil? 1. A 72-cm wire is moved at an angle of 72° through a magnetic field of 1.7 10 2 T and experiences an EMF of 1.2 mV. How Chapter 26 fast is the wire moving? 1. A stream of singly ionized (1 ) fluorine 2. A 14.2-m wire moves 3.12 m/s perpendi- atoms passes undeflected through a mag- cular to a 4.21-T field. netic field of 2.5 10 3 T that is balanced a. What EMF is induced in the wire? by an electric field of 3.5 103 V/m. The b. Assume that the resistance in the wire is mass of the fluorine atoms is 19 times that 0.89 . What is the amount of current of a proton. in the wire? a. What is the speed of the fluorine ions? 3. A 3.1-m length of straight wire has a resist- b. If the electric field is switched off, ance of 3.1 . The wire moves at 26 cm/s what is the radius of the circular path ° at an angle of 29 through a magnetic field followed by the ions? of 4.1 T. What is the induced current in 2. An electron moves perpendicular to Earth’s the wire? magnetic field with a speed of 1.78 106 4. A generator delivers an effective current m/s. If the strength of Earth’s magnetic of 75.2 A to a wire that has a resistance field is about 5.00 10 5 T, what is the of 0.86 . radius of the electron’s circular path? a. What is the effective voltage? 3. A proton with a velocity of 3.98 104 m/s b. What is the peak voltage of the generator? perpendicular to the direction of a mag- 5. What is the RMS voltage of a household netic field follows a circular path with a outlet if the peak voltage is 165 V? diameter of 4.12 cm. If the mass of a 6. An outlet has a peak voltage of 170 V. proton is 1.67 10 27 kg, what is the a. What is the effective voltage? strength of the magnetic field? b. What effective current is delivered to an 4. A beam of doubly ionized (2 ) calcium 11 - toaster? atoms is analyzed by a mass spectrometer. If 7. A step-up transformer has a primary coil B 4.5 10 3 T, r 0.125 m, and the mass consisting of 152 turns and a secondary of the calcium ions is 6.68 10 26 kg, what coil with 3040 turns. The primary coil is the voltage of the mass spectrometer? receives a peak voltage of 98 V. 5. The speed of light in crown glass is a. What is the effective voltage in the 1.97 108 m/s. What is the dielectric primary coil? constant of crown glass? b. What is the effective voltage in the 6. The dielectric constant of diamond is 6.00. secondary coil? What is the speed of light in diamond?
Appendix B 885 858-889 EM APP B-845813 6/9/04 4:07 PM Page 886
7. By curving different isotopes through paths 11 . What is the frequency of an X ray with a with different radii, a mass spectrometer wavelength of 1.00 10 10 m? can be used to purify a sample of mixed 12. In recent years, physicists have slowed the uranium-235 and uranium-238 isotopes. speed of light passing through a material Assume that B 5.00 10 3 T, V 55.0 V, to about 1.20 mm/s. What is the dielectric and that each uranium isotope has a 5 constant of this material? ionization state. Uranium-235 has a mass that is 235 times that of a proton, while uranium-238 has a mass that is 238 times Chapter 27 that of a proton. By what distance will the two isotopes be separated by the mass 1. If the maximum kinetic energy of emitted spectrometer? photoelectrons is 1.4 10 18 J, what is the stopping potential of a certain photocell? 2. The stopping potential of a photocell is R1 ϭ Uranium-235 R2 ϭ Uranium-238 2.3 V. What is the initial velocity of an emitted photoelectron that is brought to R2
Appendix B a stop by the photocell? R1 3. If a photoelectron traveling at 8.7 105 m/s is stopped by a photocell, what is the photocell’s stopping potential? 4. Light with a frequency of 7.5 1014 Hz is Uranium ion beam able to eject electrons from the metal surface of a photocell that has a threshold frequency of 5.2 1014 Hz. What stopping potential is needed to stop the emitted photoelectrons? 8. A mass spectrometer often is used in car- 5. A metal has a work function of 4.80 eV. bon dating to determine the ratio of C-14 Will ultraviolet radiation with a wave- isotopes to C-12 isotopes in a biological length of 385 nm be able to eject a sample. This ratio then is used to estimate photoelectron from the metal? how long ago the once-living organism died. Because a mass spectrometer is sensi- 6. When a metal is illuminated with radia- tive to the charge-to-mass ratio, it is possi- tion with a wavelength of 152 nm, ble for a contaminant particle to alter the photoelectrons are ejected with a velocity 5 value measured for the C-14/C-12 ratio, of 7.9 10 m/s. What is the work function, and thus, yield erroneous results. When in eV, of the metal? ionized, C-14 forms an ion with a 4 charge, and the mass of C-14 is 14 times Cathode Anode that of a proton. Consider a contaminant lithium particle. If the most common lithium isotope has a mass that is seven v ϭ 7.9ϫ105 m/s times that of a proton, what must be the charge of the lithium ion needed to ϭ 152 nm contaminate a carbon-14 experiment? 9. What is the wavelength of a radio wave with a frequency of 90.7 MHz? ϩϪIncident 10. What is the frequency of a microwave with radiation a wavelength of 3.27 mm?
886 Appendix B 858-889 EM APP B-845813 6/10/04 9:11 PM Page 887
7. The de Broglie wavelength for an electron 5. At 400.0 K, silicon has 4.54 1012 free traveling at 9.6 105 m/s is 7.6 10 10 m. electrons/cm3. How many free electrons What is the mass of the electron? per Si atom are there at this temperature? 8. What is the de Broglie wavelength of a 6. At 200.0 K, silicon has 3.79 10 18 free 68-kg man moving with a kinetic energy electrons per atom. How many free elec- of 8.5 J? trons/cm3 are there in silicon at this 9. An electron has a de Broglie wavelength of temperature? 5.2 10 10 m. What potential difference is 7. Silicon has 1.45 1010 free electrons/cm3 responsible for this wavelength? at room temperature. If you wanted to have 3 106 as many electrons from Additional Problems arsenic doping as thermal free electrons Chapter 28 from silicon at room temperature, how many arsenic atoms should there be for 1. An electron in a hydrogen atom makes each silicon atom? Each arsenic atom a transition from E to E . How much 3 1 provides 1 free electron. Use Appendix D energy does the atom lose? for physical constants. 2. An electron in the hydrogen atom loses 8. At 200.0 K, germanium has 1.16 1010 3.02 eV as it falls to energy level E . From 2 thermally liberated charge carriers/cm3. If which energy level did the atom fall? it is doped with 1 As atom to 525,000 Ge 3. Which energy level in a hydrogen atom atoms, what is the ratio of doped carriers 9 has a radius of 7.63 10 m? to thermal carriers at this temperature? 4. When an electron falls from E4 to E1, what See Appendix D for physical constants. is the frequency of the emitted photon? 9. At 200.0 K, silicon has 1.89 105 thermally 3 5. If an electron moves from E3 to E5, what is liberated charge carriers/cm . If it is doped the wavelength of the photon absorbed by with 1 As atom to 3.75 million Si atoms, the atom? what is the ratio of doped carriers to 6. If a hydrogen atom in its ground state thermal carriers at this temperature? See absorbs a photon with a wavelength of Appendix D for physical constants. 93 nm, it jumps to an excited state. 10. The diode shown below has a voltage What is the value of the energy in that drop, Vd, of 0.45 V when I 11 mA. If a excited state? 680- resistor, R, is connected in series,
what power supply voltage, Vb is needed?
Chapter 29 R 1. Indium has 3 free electrons per atom. Use Appendix D and determine the number I of free electrons in 1.0 kg of indium. 2. Cadmium has 2 free electrons per atom. Vb Use Appendix D and determine the num- Diode ber of free electrons in 1.0 dm3 of Cd. 3. Copper has 1 free electron per atom. What Vd length of 1.00-mm diameter copper wire contains 7.81 1024 free electrons? Use 11 . A diode in a circuit similar to the one in Appendix D for physical constants. Figure 29-26 has a voltage drop, Vd, of 4. At 400.0 K, germanium has 1.13 1015 free 0.95 V when I 18 mA. If a 390- resistor, electrons/cm3. How many free electrons R, is connected in series, what power
per Ge atom are there at this temperature? supply voltage, Vb is needed?
Appendix B 887 858-889 EM APP B-845813 6/24/04 11:36 AM Page 888
12. What power supply voltage would be 9. The graph below shows a sequence of needed to produce a current of 27 mA alpha and beta decays, labeled 1, 2, 3, and in the circuit in problem 10? Assume the 4. Consult Table 30-1 as needed. diode voltage is unchanged. a. Which represent alpha decays, and which represent beta decays ? Chapter 30 b. What is the overall change in mass in the sequence? In the number of neutrons? 1. Carbon-14, or 14C, is an isotope of the 12 common 6C, and is used in dating A ancient artifacts. What is the composition 218 of its nucleus? 1 2. An isotope of iodine (Z 53) is used to 216 treat thyroid conditions. Its mass number is 131. How many neutrons are in its 3 nucleus? 214 2 3. The only nonradioactive isotope of fluo- Mass number
Appendix B rine has nine protons and ten neutrons. 212 4 a. What is its mass number? b. The atomic mass unit, u, is equal to 210 1.66 10 27 kg. What is fluorine-19’s approximate mass in kilograms? 80 82 84 Z c. Write the full symbol of this atom. Atomic number 25 4. The magnesium isotope 12Mg has a mass of 24.985840 u. 10. Use Appendix D to complete the two a. Calculate its mass defect. nuclear equations. Include correct b. Calculate its binding energy in MeV. subscripts and superscripts for each 10 5. The isotope 5B has a mass of 10.012939 u. of the particles. a. Calculate the mass defect. a. 32P → ? antineutrino b. Calculate its binding energy in MeV. 15 b. 235U → ? c. Calculate its binding energy per 92 nucleon. 11 . Write the complete nuclear equation for 56 the beta decay of 34S. 6. The most stable isotope of all is 26Fe. 16 Its binding energy per nucleon is 12. A positron is identical to a beta particle, 8.75 MeV/nucleon. except that its charge is 1 instead of 1. 37 a. What is the binding energy of this 19K undergoes spontaneous positron isotope? decay to form an isotope of argon. Identify b. What is the mass defect of this isotope? the isotope of argon by writing a nuclear 239 equation. 7. The isotope 94Pu can be transmuted to an 235 13. Iodine-131 has a half-life of 8.0 days. If isotope of uranium, 92U. a. Write the nuclear equation for this there are 60.0 mg of this isotope at time transmutation. zero, how much remains 24 days later? b. Identify the particle that is ejected. 14. Refer to Table 30-2. Given a sample of 222 cobalt-60, 8. The radioisotope 84Po undergoes alpha decay to form an isotope of lead (lead has a. how long a time is needed for it to go atomic number 82). Determine what the through four half-lives? mass number of that isotope must be by b. what fraction remains at the end of that writing a nuclear equation. time?
888 Appendix B 858-889 EM APP B-845813 3/31/04 4:51 AM Page 889
15. The graph shows the activity of a certain 17. One source of a star’s energy is the fusion radioisotope over time. Deduce its half-life of two deuterons to form an alpha particle from this data. plus a gamma ray.
Particle Mass in u 48 2 1H 2.0136 4He 4.0026 36 2 (Bq) 0
5 0 0.0000
24
a. Write the nuclear equation for this Additional Problems fusion. Activity ؋ 10 12 b. Calculate the mass “lost” in this process. 0 c. Calculate the energy released in MeV. 3 6912 18. When 1 mol (235 g) of uranium-235 Time (h) undergoes fission, about 2.0 1010 kJ of energy are released. When 4.0 g of hydro- 16. The mass of a proton and of an antiproton gen undergoes fusion, about 2.0 109 kJ is 1.00728 u. Recall that the conversion of are released. exactly 1 u into energy yields 931.5 MeV. a. For each, calculate the energy yield per a. Calculate the mass used up when a gram of fuel. proton and an antiproton annihilate b. Which process produces more energy one another. per gram of fuel? b. Calculate the energy released here.
Appendix B 889 890-909 EM APP C-845813 6/15/04 10:39 PM Page 890
Chapter 1 27. Because the bicycle is moving in the positive direction, the average speed and average velocity are the same. 1. I V 9.0 V 0.18 A Using the points (0.00 min, 0.0 km) and (15.0 min, R 50.0 Ω 10.0 km), d 3. t v 4.00 m/s 10.0 s v a 0.400 m/s2 t d d 2 1 1000 Hz 1 MHz t t 5. 750 kHz ( )( ) 0.75 MHz 2 1 1 kHz 1,000,000 Hz 10.0 km 0.0 km 15.0 min 0.0 min 7. 366 days 24 h 60 m in 60 s 31,622,400 s (1 day)( 1 h )(1 min) 0.67 km/min 9. a.6.201 cm b. 1.6 km 1600 m The bicycle is moving in the positive direction at 7.4 cm 1.62 m 1.62 m a speed of 0.67 km/min. 0.68 cm 1200 m 12 m 12.0 cm 1613.62 m 26.281 cm 1600 m or 1.6 km Chapter 3 26.3 cm rounded to two 1. 1 2 3 significant digits Time 2 2 2 interval 11 . a . 320 cm or 3.2 10 cm v1 v2 v3 Velocity b. 13.6 km2 Position Start Stop
v2 ؊ v1 Chapter 2 a 9. The car begins at a position of 125.0 m and moves 3. a. 5.0 to 15.0 s b. 0.0 to 5.0 s toward the origin, arriving at the origin 5.0 s after it begins moving. The car continues beyond the origin. c. 15.0 to 20.0 s
5. 11 . a . 4.0 s b. 100.0 m 1.0 13. a. 19 s b. 58 s c. 100.0 Appendix C 80.0
60.0 (m/s) Velocity 40.0 20.0 0.05.0 10.015.0 20.0 Distance from cafeteria (m) 0.00 Time (s) 10.0 30.0 50.0 70.0 v 15 m/s 36 m/s 7. a 7.0 m/s2 Time (s) t 3.0s v 0.0 m/s 25 m/s 9. a. a 8.3 m/s2 15. runner B t 3.0 s b. Half as great ( 4.2 m/s2) 17. approximately 30 m v 0.5 cm/y 1.0 cm/y 2 d 11 . a 0.5 cm/y 25. a. v t 1.0 y t 19. v v at d d f i 2 1 1 km 3600s 30.0 km/h (3.5 m/s2)(6.8 s) t2 t1 (1000 m)( 1 h ) 120 km/h 1.0 m 0.0 m 3.0 s 0.0 s 21. vf vi at 0.33 m/s v v so t f i 0.33 m/s a 3.0 m/s 22 m/s b. The average velocity is the slope of the line, includ- 2.1 m/s2 ing the sign, so it is 0.33 m/s or 0.33 m/s north. 9.0 s
890 Appendix C 890-909 EM APP C-845813 6/15/04 10:40 PM Page 891
23. 75 m 360 0s 1 k m 2.7 102 km/h 31. ( 1 s )( 1 h )(1000 m) 3.0 25. a. 25 12
20 (m/s) Velocity 15 6.0 12.0 10 Time (s)
5 Part 1: Constant acceleration: 0 Time (s) d 1 (3.0 m/s)(6.0 s) 1 2 ؊5
500 9.0 m 1000 1500 2000 2500 3000 3500 4000 Velocity (m/s) Velocity ؊10 Part 2: Constant velocity: ؊ 15 d2 (3.0 m/s)(12.0 s 6.0 s) ؊20 18 m ؊25 thus, d d1 d2 9.0 m 18 m 27 m
Distance the driver walked to the gas station: 33. Part 1: Constant velocity: d vt (4.3 m/s)(19 min) 60 s 4902 m d vt ( 1 min ) 60 s (1.5 m/s)(20.0 min) Part 2: Constant acceleration: ( 1 min ) d d v t 1 at2 1800 m f i i 2 1.8 km 2(df di vit) a Practice Problems t2
Time to walk back to the car: 2(5.0 103 m 4902 m (4.3 m/s)(19.4 s)) Solutions for t d 1800 m 1500 s 25 min (19.4 s)2 v 1.2 m/s 0.077 m/s2 b. 20,000 43. a. Now the positive direction is downward. 2 vf vi at, where a g 9.80 m/s 15,000 2 vf 0.0 m/s (9.80 m/s )(4.0 s) 39 m/s when the downward direction is positive 10,000 b. d v t 1 at2 i 2 Position (m) (0.0 m/s)(4.0 s) 1 (9.80 m/s2)(4.0 s)2 5000 2 78 m The brick still falls 78 m. 0 1000 2000 3000 4000 5000 45. a. a g, and at the maximum height, vf 0 Time (s) 2 2 vf vi 2ad becomes v 2 2gd (v v ) i v f i 27. v v 2 (22.5 m/s)2 2 2 d i 25.8 m (v v ) t 2gd 2(9.80 m/s2) d v t f i 2 (22 m/s 44 m/s)(11 s) b. Calculate time to rise using vf vi at, 1.2 102 m 2 with a g and vf 0. v 22.5 m/s i v (vf vi) t 2.30 s 29. v g 9.80 m/s2 2 2 (v v ) t The time to fall equals the time to rise, d v t f i 2 so the time to remain in the air is 2(19 m) t 2t (2)(2.30 s) 4.60 s so v 2 d v 7.5 m/s 0.94 m/s air rise i t f 4.5 s
Appendix C 891 890-909 EM APP C-845813 6/15/04 10:41 PM Page 892
Chapter 4 19. a. The scale reads 585 N. Since there is no accelera- tion, your weight equals the downward force of 1. gravity: System Fg mg F so m g 585 N 59.7 kg g 9.80 m/s2 ϩ y b. On the Moon, g changes: Fg mgMoon vaFnet (59.7 kg)(1.60 m/s2) FEarth’s mass on flowerpot 95.5 N
29. The only force acting on the brick is the gravitational 3. System attraction of Earth’s mass. The brick exerts an equal and opposite force on Earth.
31. Suitcase Cart
Fsurface on cart Fcart on suitcase FEarth’s ϩx mass on cart v v v v Fsuitcase on cart FEarth’s mass a ϭ 0 on suitcase
Ffriction Fpull on crate on crate F ϭ 0 33. Identify the tire as the system and the direction net of pulling as positive. Fnet Fwheel on tire FMika on tire FDiego on tire ma 0 5. ϩy Fwheel on tire FMika on tire FDiego on tire Appendix C v 23 N 31 N Frope on bucket 54 N System v
v ϭ ϭ a 0 Fnet 0 Chapter 5
v 1. 141 km FEarth’s mass on bucket 65.0 km
125.0 km 1 7. Fnet 225 N 165 N 6.0 10 N in the direction of the larger force R2 A2 B2 R A 2 B 2 15. The scale reads the weight of the watermelon: 2 (65.0 km) 2 (125.0 km) 2 Fg mg (4.0 kg)(9.80 m/s ) 39 N 141 km 17. Identify Reiko’s direction as positive and the rope as the system. 3. R2 A2 B2 2AB cos 2 2 Fnet FReiko on rope FTaru on rope ma R A B 2AB cos (4.5 k m)2 (6.4 k m)2 2(4.5 km)( 6.4 km )(cos 1 35°) FReiko on rope ma FTaru on rope 1 (0.75 kg)(1.25 m/s2) 16.0 N 1.0 10 km 17 N
892 Appendix C 890-909 EM APP C-845813 6/15/04 10:42 PM Page 893
5. Identify north and west as the positive directions. 25.The initial velocity is 1.0 m/s, the final velocity 2 ° is 2.0 m/s, and the acceleration is 2.0 m/s , so d1W d1(sin ) (0.40 km)(sin 60.0 ) 0.35 km v v ° f i d1N d1(cos ) (0.40 km)(cos 60.0 ) 0.20 km a ; let ti 0 and solve for tf. tf ti d 0.50 km d 0.00 km v v 2.0 m/s 1.0 m/s 2W 2N t f i 0.50 s f a 2.0 m/s2 RW d1W d2W 0.35 km 0.50 km 0.85 km 33. RN d1N d2N 0.20 km 0.00 km 0.20 km ؉x R R 2 R 2 W N ؉y Ff (0.85 km) 2 (0.20 km)2 FN 0.87 km Fgy R tan 1( W ) tan 1( 0.85 km) RN 0.20km Fgx 77° Fg 0.87 km at 77° west of north 60.0° Fg 7. The resultant is 10.0 km. Using the Pythagorean theorem, the distance east is R2 A2 B2, so B R2 A 2 35. Fg, perpendicular Fg cos mg cos F (10.0 km)2 (8.0 k m)2 cos 1 g, perpe ndicular mg 6.0 km
449 N Practice Problems cos 1 (50.0 kg)(9.80 m/s2)
9. It could never be shorter than one of its components, Solutions for but if it lies along either the x- or y-axis, then one of 23.6° its components equals its length. 37. Fg, parallel Fg(sin ), 17. FN mg 52 N when the angle is with respect to the horizontal. Since the speed is constant, the friction force equals Fg , perpendicular Fg(cos ), when the angle is with the force exerted by the girl, 36 N. respect to the horizontal. Ff kFN Fg, perpendicular 2Fg, parallel Ff 36 N so 0.69 F F cos k F 52 N g, perpe ndicular g 1 N 2 Fg, parallel Fg sin tan 19. FAmes on box Ffriction 1 1 ° tan ( ) 26.6 relative to the horizontal, sFN 2 or 63.4° relative to the vertical. smg (0.55)(134 N) 39. Since a g(sin cos ), 74 N k a (9.80 m/s2)(sin 31° (0.15)(cos 31°)) 3.8 m/s2 21. Ff, before k, before FN F f, be fore 5.8 N 1 so FN 1.0 10 N k, before 0.58 41. a g(sin k cos ) F F f, after k, after N a g(sin ) g k(cos ) (0.06)(1.0 101 N) 0.6 N If a 0, 0 g(sin ) g k(cos ) 23. Fnet F kFN = F kmg ma k(cos ) sin F ma sin k mg k cos 2 ° 65 N (41 kg)(0.12 m/s ) sin 37 (41 kg)(9.80 m/s2) cos 37° 0.15 0.75
Appendix C 893 890-909 EM APP C-845813 6/15/04 10:44 PM Page 894
2 2 13.a v (22 m /s) 8.6 m/s2 Chapter 6 c r 56 m 1 1. a. Since 0, y t gt2 becomes Recall that Ff FN. The friction force must supply y y 2 the centripetal force, so Ff mac. The magnitude y 1 gt2 of the normal force is F mg. The coefficient of 2 N 2y friction must be at least or t2 g F ma a 8.6 m/s2 f c c 0.88 F mg g 9.80 m/s2 2y N t g 15. F F 2( 78.4 m) f c 2 9.80 m/s2 mv r 4.00 s 2 (45 kg)(4. 1 m/s) 6.3 m 120 b. x vxt (5.0 m/s)(4.00 s) 23. vc/g w/g vc/w 1 2.0 10 m 0.75 m/s 0.020 m/s 0.73 m/s c. vx 5.0 m/s. This is the same as the initial hori- zontal speed because the acceleration due to gravity 2 2 25. v vp vw influences only the vertical motion. For the vertical (150 km/h) 2 (75 km/h) 2 component, use v vi gt with v vy and vi, the initial vertical component of velocity, zero. 1.7 102 km/h At t 4.00 s v gt (9.80 m/s2)(4.00 s) 39.2 m/s y Chapter 7
T 2 r 3 3. x v t; G G x 1. ( ) ( ) TI r1 t x vx 3 32 days 2 1 2 r (4.2 units)3 y gt G (1.8 days) 2 2 Appendix C 1 x 3 g( ) 23.4 10 3 units 3 2 vx 2 1 (9.80 m/s2) 0.07 0m 29 units 2 ( 2.0 m/s ) 3 6.0 10 m or 0.60 cm T 2 r 3 M M 3. ( ) ( ) with rM 1.52rE TE rE
5. Following the method of Practice Problem 4, r 3 Thus, T M T 2 Hangtime: M ( r ) E E 2v sin i 2(27.0 m/s)(sin 60.0°) t 2 4.77 s g 9.80 m/s 1.52r 3 E (365 days)2 ( r ) E Distance: 4.68 10 5 days 2 x (vi cos )t (27.0 m/s)(cos 60.0°)(4.77 s) 684 days 64.4 m T 2 r 3 5. s s (T ) (r ) Maximum height: M M 1 at t (4.77 s) 2.38 s 2 2 3 T 1 Thus, r r 3 s y (v sin )t gt2 s M (T ) i 2 M (27.0 m/s)(sin 60.0°)(2.38 s) 2 3 1.00 days 1 ( 9.80 m/s2)(2.38 s)2 (3.90 105 km)3 2 (27.3 d ays) 27.9 m 3 7.96 10 13 km 3 4.30 104 km
894 Appendix C 890-909 EM APP C-845813 3/31/04 6:22 AM Page 895
Gm Vertical: 0.0° E 13. a. v rE h Fr sin mgr sin (6.67 10 11 N m2/kg2)(5.97 1024 kg) (65 kg)(9.80 m/s2)(0.18 m)(sin 0.0°) (6.38 106 m 1.5 105 m) 0.0 N m 7.8 103 m/s 17. chain Fgr ( 35.0 N)(0.0770 m) 2.70 N m (r h)3 Thus, a torque of 2.70 N m must be exerted to b. T 2 E GmE balance this torque. m r 6.38 106 m 1.5 105 m 3 2 2 ( ) 19. m1 2 r (6.67 10 11 N m2/kg2)(5.97 1024 kg) 1 (0.23 kg)(1.1 cm) m 0.042 kg 5.3 103 s 1 6.0 cm 88 min 21. For the mass of the two children, I mr 2 + mr 2 2mr 2 When r is doubled, I is multiplied by a factor of 4. Chapter 8 23. The moments of inertia are different. If the spacing 1. a. (60)( 2 rad) 120 rad or 377 rad between spheres is r and each sphere has mass m, then rotation about sphere A is b. 2 rad or 6.28 rad I mr 2 m(2r)2 5mr 2 c. 1 ( 2 rad) rad or 0.524 rad (12) 6 Rotation about sphere C is I mr 2 mr 2 2mr 2
3. a. The changes in velocity are the same, so the linear The moment of inertia is greater when rotating Practice Problems accelerations are the same. around sphere A. Solutions for b. Because the radius of the wheel is reduced from 25. Torque is now twice as great. The angular acceleration 35.4 cm to 24 cm, the angular acceleration will is also twice as great, so the change in angular velocity be increased. is twice as great. Thus, the final angular velocity is 2 1 5.23 rad/s 32 rad/s, or 16 rev/s. a 2 2 r 27. The torque on the wheel comes from either the chain 2 1.85 m/s or the string. 0.24 m I 7.7 rad/s2 chain wheel wheel wheel Iwheel wheel 11 . Fr sin Thus, chain wheel so F r sin Fchain rgear Fstring rwheel 35 N m F r chain gear (0.25 m)(sin 90.0°) Fstring rwheel 1.4 102 N (15 N)(0. 14 m) 0.38 m 13. Fr sin 5.5 N so sin 1( ) Fr 29. F r I I 1 32.4 N m I sin () so F (232 N)(0.234 m) r 36.6° (I I ) small large r 1 2 15. Fr sin msmall rsmall Ilarge 2 Horizontal: 90.0° r Fr sin mgr sin 1 (2.5 kg)(0.090 m)2 0.26 kg m2 (2.57 rad/s2) 2 (65 kg)(9.80 m/s2)(0.18 m)(sin 90.0°) 0.090 m 1.1 102 N m 7.7 N
Appendix C 895 890-909 EM APP C-845813 3/31/04 6:23 AM Page 896
37. a. clockwise: A FA rA Chapter 9 FA(0.96 m 0.30 m) 1. E (0.66 m)FA counterclockwise: F r B B B v FB(0.96 m 0.45 m) p (0.51 m)FB b. net A B 0 a. p mv so B A (725 kg)(115 km/h) 1000 m 1 h ( 1 km )( 3600s) (0.51 m)FB (0.66 m)FA 2.32 104 kg m/s eastward c. Fg FA FB p b. v thus, FA Fg FB m
(0.66 m)F 4 3600s 1 km F A (2.32 10 kg m/s) g 0.51 m 1 h 1000 m 2175 kg F g or FA 38.4 km/h eastward 1 0.66 m 0.51m 3. a. F t p p mv mv ma f i f i 0.66 m F t mv 1 v f 0.51m f m (7.3 kg)(9.80 m/s2) (5.0 N)(1.0 s) (7.0 kg)(2.0 m/s) 7.0 kg 1 0.66 m 0.51m 2.7 m/s in the same direction as the original velocity 31 N F t mv b. v f d. FA would become greater, and FB would be less. f m ( 5.0 N)(1.0 s) (7.0 kg)(2.0 m/s) 39. Choose the center of mass of the board as the pivot. 7.0 kg
Appendix C The force of Earth’s gravity on the board is exerted 1.3 m/s in the same direction as totally on the support under the center of mass. the original velocity end diver Fendrend Fdiverrdiver 5. Before After F r v 0 dive r diver f Thus, Fend rend m gr vi dive r diver rend 2 (85 kg)(9.80 m/s )(1.75 m) x 1.75 m 2 8.3 10 N a. F t p = pf pi p p F f i To find the force on the center support, notice that t because the board is not moving. p mv f i F Fend Fcenter Fdiver Fg t 1000 m 1 h Thus, F F F F (0.0 kg m/s) (60.0 kg)(94 km/h) center diver g end 1 km 3600s 0.20 s 2Fdiver Fg 7.8 103 N opposite to the direction of motion 2mdiverg mboardg b. F mg g(2m m ) g diver board F 3 m g 7.8 1 0 N 8.0 102 kg (9.80 m/s2)(2(85 kg) 14 kg) g 9.80 m/s2 Such a mass is too heavy to lift. You cannot safely 1.8 103 N stop yourself with your arms.
896 Appendix C 890-909 EM APP C-845813 6/15/04 10:47 PM Page 897
13. pi pf pf pi mv mv 2mv 2 2 Ai Bi f (pi, x) (pi, y) mv mv v Ai Bi ( m v ) 2 (m v ) 2 f 2 1 2i 1 1i p 2.2 m/s 0.0 m/s f vf 2 m1 m2 1.1 m/s ( m v ) 2 (m v ) 2 1 2i 1 1i m m 1 2 15. mbvbi mwvwi (mb mw)vf where v is the common final speed of the bullet ((1732 kg)(31.3 m/s)) 2 ((1383 kg)( 11 . 2 m/s)) 2 f and piece of lumber. 1383 kg 1732 kg Because vwi 0.0 m/s, 18.1 m/s (m m )v v b w f p bi m 1 i, y b tan ( ) pi, x (0.0350 kg 5.0 kg)(8.6 m/s) m v 0.0350 kg tan 1 1 1i (m v ) 1.2 103 m/s 2 2i (1383 kg)( 11.2 m/s) tan 1 (1732 kg)(31.3 m/s) 17. The system is the bullet and the ball. 15.9° south of east mbulletvbullet, i mballvball, i mbulletvbullet, f mballvball, f vball, i 0.0 m/s and vbullet, f 5.0 m/s 25. Before: m (v v ) p m v bullet bullet, i bullet, f i, x 1 1i so vball, f mball (1345 kg)(15.7 m/s)
4 Practice Problems 2.11 10 kg m/s (0.0350 kg)(475 m/s ( 5.0 m/s)) 2.5 kg Solutions for pf pi (m1 m2)vf 6.7 m/s (1345 kg + 1923 kg)(14.5 m/s) 4.74 104 kg m/s 19. pri pfuel, i prf pfuel, f 4 ° pf, y pf sin (4.74 10 kg m/s)(sin 63.5 ) where prf pfuel, f 0.0 kg m/s 4.24 104 kg m/s If the initial mass of the rocket (including fuel) is mr 4.00 kg, then the final mass of the rocket is pf, y pi, y m2v2i mrf 4.00 kg 0.0500 kg 3.95 kg p 4.24 104 kg m/s v f, y 2i m 1923 kg 0.0 kg m/s mrfvrf mfuelvfuel, f 2 mfuelvfuel, f 22.1 m/s v rf m rf Yes, it was exceeding the speed limit. (0.0500 kg)( 625 m/s) 3.95 kg 7.91 m/s Chapter 10
21. pCi pJi pCf pJf 1. a. Because W Fd and KE W, doubling the force where p p 0.0 kg m/s would double the work, which would double the Ci Ji change in kinetic energy to 1.35 J. mCvCf mJvJf b. Because W Fd, halving the distance would cut m v C Cf in half the work, which also would cut the change so vJf mJ in kinetic energy in half, to 0.68 J. (80.0 kg)(4.0 m/s) 115 kg 3. a. W mgd 2.8 m/s in the opposite direction (7.5 kg)(9.80 m/s2)(8.2 m) 2 23. Car 1 is moving south. Car 2 is moving east. 6.0 10 J Before: b. W Fd 6.0 102 J 2 pi, x p1, x p2, x 0 m2v2i (645 N)(8.2 m) 6.0 10 J 3 pi, y p1, y p2, y m1v1i 0 5.9 10 J
Appendix C 897 890-909 EM APP C-845813 7/29/04 4:05 PM Page 898
c. P W t Chapter 11 3 1 min 5.9 1 0 J 1. To bring the skater to a stop: 30.0 min ( 60 s ) 3.3 W W KEf KEi 1 mv 2 1 mv 2 2 f 2 i 5. W Fd cos 1 (52.0 kg)(0.00 m/s)2 1 (52.0 kg)(2.5 m/s)2 2(255 N)(15 m)(cos 15°) 2 2 160 J 6.5 103 J To speed up again: 7. W Fd cos W KEf KEi (628 N)(15.0 m)(cos 46.0°) 1 mv 2 1 mv 2 2 f 2 i 3 6.54 10 J 1 (52.0 kg)(2.5 m/s)2 1 (52.0 kg)(0.00 m/s)2 2 2 W 9. P 160 J t (575 N)( 20.0 m) 10.0 s 3. KE 1 mv2 1.15 103 W 2 1 (7.85 1011 kg)(2.50 104 m/s)2 1.15 kW 2 2.45 1020 J KE 2.45 1020 J W mgd co met 11 . P KE 4.2 1015 J t t bomb 5.8 104 bombs would be required to m (35 L/min)(1.00 kg/L) t produce the same amount of energy used 35 kg/min by Earth in stopping the comet. Thus, m P gd 5. W Fd t (35 L/min)(1 min/60 s)(9.80 m/s2)(110 m) mg(hf hi) 2 0.63 kW (20.0 kg)(9.80 m/s )(0.00 m 1.20 m) 2.35 102 J
Appendix C 13. P F d t (6.8 103 N)(15 m) 7. Choose the ground as the reference level. t F d P 0.30 103 W PE mg(hf hi) 340 s (1.8 kg)(9.80 m/s2)(0.00 m 6.7 m) 1.2 102 J 5.7 min
15. The system is the bike the rider Earth. There are de (0.20 m) 25. a. IMA 4.0 no external forces, so total energy is conserved. dr (0.050 m) KE 1 mv2 4 2 Fr (1.7 10 N) b. MA 1.5 1 F (1.1 10 4 N) (85.0 kg)(8.5 m/s)2 e 2 3.1 103 J c. efficiency M A 100 1. 5 100 38% IMA 4.0 KEi PEi KEf PEf W 1 o mv2 0 0 mgh 27. efficiency 100 2 Wi 2 (8.5 m/s)2 h v 3.7 m F d 2g (2)(9.80 m/s2) r r 100 Fede F d (100) r r So de Fe(efficiency) 3 (1.25 10 N)(0.13 m)(100) (225 N)(88.7) 0.81 m
898 Appendix C 890-909 EM APP C-845813 6/15/04 10:50 PM Page 899
17. Bottom of the valley: 9. Heat gained by the water: Q mC T KEi PEi KEf PEf 0 mgh 1 mv2 0 (0.100 kg)(4180 J/kg °C)(15.0°C) 2 v 2 gh 6.27 kJ 2(9.80 m/s2)(45.0 m) Thus, heat lost by the aluminum block 29.7 m/s 6.27 kJ maluminumCaluminum T Q Top of the next hill: hence, C aluminum m T aluminum KE PE KE PE i i f f 6.27 kJ 1 2 (0.100 kg)( 75.0°C) 0 mghi mv mghf 2 2 ° 8.36 10 J/kg C v 2g(hi hf) 2 2(9.80 m/s )(45.0 m 40.0 m) 19. Q mC T mHf 9.90 m/s (0.100 kg)(2060 J/kg °C)(20.0°C) No, the angles of the hills do not affect the answers. (0.100 kg)(3.34 105 J/kg) 3.75 104 J 19. Conservation of momentum: mv (m M)V, or 21. Q mCice T mHf mCwater T mHv mCsteam T ° ° ° v (m M)V (0.300 kg)(2060 J/kg C)(0.0 C ( 30.0 C)) m 5 (0.300 kg)(3.34 10 J/kg) (0.00800 kg 9.00 kg)(0.100 m/s) 0.00800 kg (0.300 kg)(4180 J/kg °C)(100.0°C 0.0°C) 2 1.13 10 m/s (0.300 kg)(2.26 106 J/kg) (0.300 kg)
(2020 J/kg °C)(130.0°C 100.0°C) Practice Problems
Chapter 12 9.40 102 kJ Solutions for
1. a. T T 273 11 5 273 158°C C K 23. U Q Wblock; since Wdrill Wblock ° and assume no heat added to drill: b. TC TK 273 172 273 101 C 0 Wdrill mC T c. T T 273 125 273 148°C C K (0.40 kg)(897 J/kg °C)(5.0°C) ° 3 d. TC TK 273 402 273 129 C 1.8 10 J ° e. TC TK 273 425 273 152 C 25. U mC T ° (0.15 kg)(4180 J/kg °C)(2.0°C) f. TC TK 273 212 273 61 C 1.3 103 J 3. Q mC T ° ° The number of stirs is (2.3 kg)(385 J/kg K)(80.0 C 20.0 C) 3 1.3 10 J 2.6 104 5.3 104 J 0.050 J 5. Q mC T Chapter 13 (75 kg)(4180 J/kg K)(43°C 15°C) 8.8 106 J 1. F PA 6 8.8 1 0 J 2.4 kWh Plw 3.6 106 J/kWh (1.0 105 Pa)(1.52 m)(0.76 m) (2.4 kWh)($0.15 per kWh) = $0.36 1.2 105 N 7. m C (T T ) m C (T T ) 0 A A f Ai W W f Wi 3. mbrick V Since in this particular case, mA mW, the masses cancel and lwh C T C T A Ai W Wi F Fgbrick mbrick g lwhg Tf P hg CA CW A A lw lw (2450 J/kg K)(16.0°C) (4180 J/kg K)(85.0°C) 1 106 cm3 1 kg 2450 J/kg K 4180 J/kg K (11.8 g/cm3) (0.200 m)(9.80 m/s2) ( 1m3 )(1000 g) 59.5°C 23.1 kPa
Appendix C 899 890-909 EM APP C-845813 6/15/04 10:51 PM Page 900
Fg mg 5. The maximum pressure is P . 31. The buoyant force on the foam must equal 480 N. A A Therefore We are assuming the canoe is made of dense material. mg F Vg A buoyant water P F buo yant (454 kg)(9.80 m/s2) therefore, V waterg 5.0 104 Pa 480 N 8.9 10 2 m2 (1.00 103 kg/m3)(9.80 m/s2) 4.9 10 2 m3 7. PV nRT; so PV n 39. L2 L1 L1(T2 T1) ; so RT L L (T T ) m nM 1 2 1 (25 10 6 °C 1)(3.66 m)(39°C ( 28°C)) m PV M RT 6.1 10 3 m 6 3 6.1 mm (15.5 10 Pa)(0.020 m ) (4.00 g/mol) (8.31 Pa m3/mol K)(293 K) 5.1 102 g 41. At the beginning, 400 mL of 4.4°C water is in the beaker. Find the change in volume at 30.0°C. 9. PV nRT; so V V T 6 ° 1 6 3 ° ° V nR T (210 10 C )(400 10 m )(30.0 C 4.4 C) P 6 3 m 1.0 103 g 2 10 m where n M 29 g/mol 2 mL T 20.0°C 273 293K 1.0 103 g 43. The aluminum shrinks more than the steel. Let L be (8.31 Pa m3/mol k)(293 K) 29 g/mol the diameter of the rod. V (1.013 105 Pa) Laluminum L T 3 0.83 m (25 10 6 °C 1)(0.85 cm)(0.0°C 30.0°C) 4 F A 6.4 10 cm 1 2 23. F2 A1 The diameter of the steel hole shrinks by 2 (1600 N)(72 cm ) Lsteel L T 2 Appendix C 1440 cm (12 10 6 °C 1)(0.85 cm)(0.0°C 30.0°C) 1 8.0 10 N 3.1 10 4 cm
F A The spacing between the rod and the hole will be 25. F 1 2 . Thus, 2 A 1 (6.4 10 4 cm 3.1 10 4 cm) 1.6 10 4 cm 1 2 A F 2 2 400 N 0.4. A F 1100 N 1 1 Chapter 14 The adult stands on the larger piston. 1. F kx 27. Fapparent Fg Fbuoyant (95 N m)(0.25 m) 24 N brickVg waterVg ( brick water)Vg 3. F kx 3 3 (1.8 10 kg/m k F x 1.00 103 kg/m3)(0.20 m3)(9.80 m/s2) 24 N 1.6 103 N 0.12 m 2.0 102 N/m 29. To hold the camera in place, the tension in the wire must equal the apparent weight of the camera. 5. PE 1 kx2 sp 2 T Fapparent 2PEsp Fg Fbuoyant x k Fg waterVg 2(48 J) 1250 N (1.00 103 kg/m3)(16.5 10 3 m3)(9.80 m/s2) 256 N /m 1.09 103 N 0.61 m
900 Appendix C 890-909 EM APP C-845813 6/15/04 10:52 PM Page 901
l Chapter 16 7. T 2 g 2 l g T P (2 ) E 4 d 2 1. af ter after 2 2.0 s 2 E (1.6 m/s )( ) before P 2 2 4 dbefore 0.16 m d 2 bef ore d 2 d 515 m after 15. a. v 343 m/s 2 t 1.50 s (30 c m) (90 cm)2 b. T 1 1 m 0.00229 s f 436 Hz 1 9 c. v 343 m/s 0.787 m f 436 Hz Therefore, after the lamp is moved the illumination is one-ninth of the original illumination. 17. Lower 15.0 m/s 3. Illuminance of a 150-W bulb 19. v f, so v 2.50 m f 6.00 Hz P 2275, d 0.50, 0.75, . . . , 5.0 21. v f (0.600 m)(20.0 Hz) 12.0 m/s E(d) P 4 d2 Chapter 15 720
343 m/s 1. v 19 m f 18 Hz
v 5130 m/s 3 P ϭ 2275 lm 3. f 4.10 10 Hz E (lx)
1.25 m Practice Problems
5. v , Solutions for f 7.2 so v f (0.655 m)(2280 Hz) 1490 m/s 0.50 5.0 This speed corresponds to water at 25°C. r (m)
7. v 343 m/s, f 365 Hz, s 5. E P 4 d2 vs 0 m/s, vd 25.0 m/s P 4 Ed2 v v d fd fs ( ) 4 (160 lm/m2)(2.0 m)2 v vs 343 m/s 25.0 m/s 3 365 Hz 8.0 10 lm ()343 m/s 392 Hz 15. The relative speed along the axis is much less than the speed of light. Thus, you can use the observed light frequency equation. 9. v 1482 m/s, f 3.50 MHz, v 9.20 m/s, s s Because the astronomer and the galaxy are moving vd 0 m/s away from each other, use the negative form of the v v f f d observed light frequency equation. d s ( v v ) s v 1482 m/s f f (1 ) 3.50 MHz obs c ()1482 m/s 9.20 m/s 6 14 6.55 1 0 m/s (6.16 10 Hz)(1 8 ) 3.52 MHz 3.00 10 m/s 6.03 1014 Hz 19. Resonance spacing 1.1 m, so 2.2 m 2 17. Assume that the relative speed along the axis is much v f (2.2 m)(440 Hz) = 970 m/s less than the speed of light. Thus, you can use the Doppler shift equation. 21. a. 1 2L 2(2.65 m) 5.30 m ( ) v The lowest frequency is obs c v 343 m/s The observed (apparent) wavelength appears to f1 64.7 Hz 1 5.30 m be longer than the known (actual) wavelength v v 343 m/s of the oxygen spectral line. This means that the b. f2 129 Hz 2 L 2.65 m astronomer and the galaxy are moving away from v 3 v 3(343 m/s) each other. So use the positive form of the Doppler f3 194 Hz 3 2L 2(2.65 m) shift equation.
Appendix C 901 890-909 EM APP C-845813 6/15/04 10:54 PM Page 902
v 1 1 1 ( obs ) 19. c f di do Solve for the unknown variable. d d so f o i ( ) d d v c obs o i d d i i (525 nm 513 nm) and m , so do (3.00 108 m/s) do m 513 nm d 24 cm and m 0.75, so 7.02 106 m/s i ( 24 cm) d 32 cm o 0.75 and Chapter 17 (32 cm)( 24 cm) f 96 cm 32 cm ( 24 cm) 1. Polishing makes the surface smoother. h d i i ° 21. m 3. i r 35 ho do d h o i 5. 30° di r1 i1 ho ° ° ° ° i2 90 r1 90 30 60 (2.4 m)(0.36 m) 1.8 m 0.48 m 13. 1 1 1 f do di 1 1 1 d f o f do di di do f d d i o (36.0 cm)(16.0 cm) f di do 36.0 cm 16.0 cm ( 0.48 m)(2.4 m) 28.8 cm 0.48 m 2.4 m 0.60 m 15. 1 1 1 f d d o i Chapter 18 d f o di do f 1. n1 sin 1 n2 sin 2 (16.0 cm)(7.0 cm) n sin Appendix C 16.0 cm 7.0 cm sin 1 1 1 2 ( n ) 12.4 cm 2 (1.00)(sin 37.0°) sin 1 ( 1.36 ) h d m i i 26.3° ho do d h 3. n sin n sin h i o 1 1 2 2 i d o n sin 1 1 1 (12.4 cm)(2.4 cm) 2 sin ( ) n2 16.0 cm (1.00)(sin 30.0°) sin 1 1.9 cm ( 1.33 ) 22.1°
17. 5. n sin n sin O1 Ray 1 1 1 2 2 n sin n 1 1 I1 2 sin Ray 2 2 F ° (1.33)(s in 31 ) ° ؊ ؍ Horizontal scale: di 8.6 cm sin 27 cm 1.5 1.0 ؍ block 1
15. 1 1 1 1 1 1 f do di d d f d f o i d o d f i d f d o o i d f o (8.5 cm)(5 .5 cm) (20.0 cm)( 15.0 cm) 8.5 cm 5.5 cm 8.57 cm 20.0 cm ( 15.0 cm) 15.6 cm, or 16 cm to two significant digits
902 Appendix C 890-909 EM APP C-845813 6/15/04 10:55 PM Page 903
h d m i i Chapter 19 ho do d h xd i o 1. hi L do (13.2 10 3 m)(1.90 10 5 m) (15.6 cm)(2.25 cm) 0.600 m 8.5 cm 418 nm 4.1 cm 3. x d 17. 1 1 1 L f d d i o d L x with do di because 9 d (632.8 10 m)(1.000 m) m i and m 1 65.5 10 3 m d o Therefore, 9.66 10 6 m 1 2 9.66 m f di 1 1 di 2f 2(25 mm) 5.0 10 mm 5. 2t (m ) 2 n d d 5.0 101 mm oil o i For the thinnest film, m 0. 635 nm 1 1 1 t 109 nm 19. 4noil (4)(1.45) f do di d f 7. Because n n , there is a phase inversion on o film air di do f the first reflection. Because nsilicon nfilm, there is (25 cm)(5.0 cm) a phase inversion on the second reflection. 25 cm 5.0 cm
For destructive interference to keep yellow-green from Practice Problems 6.2 cm being reflected: Solutions for h d 1 i i 2t m m 2 n ho do film d h For the thinnest film, m 0. h i o i d o t 555 nm 95.7 nm 4n (4)(1.45) (6.2 cm)(2.0 cm) film 25 cm 9. For constructive interference 0.50 cm (inverted image) 2t m 1 ( 2)n 1 1 1 film 21. f di do For the thinnest film, m 0. d f 521 nm o t 97.9 nm so di 4n (4)(1.33) do f film (3.4 cm)(12.0 cm) 3.4 cm 12.0 cm 17. 2x 2 L 1 w 4.7 cm (2x )w L 1 h d 2 o i hi 2 3 do (2.60 10 m)(0.110 10 m) 2(589 10 9 m) (2.0 cm)( 4.7 cm) 3.4 cm 2.43 m 2.8 cm 19. 2x 2 L d 1 w i 23. m (2x )w do 1 2L so di mdo (4.0)(3.5 cm) 14 cm (2.40 10 3 m)(0.0295 10 3m) 1 1 1 2(60.0 10 2 m) f di do d d 5.90 102 nm o i so f do di 21. A full spectrum of color is seen. Because of the (3.5 cm)( 14 cm) 3.5 cm ( 14 cm) variety of wavelength, dark fringes of one wavelength would be filled by bright fringes of another color. 4.7 cm
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23. d sin (3.6 10 6 C)(4.0 10 6 C) (9.0 109 N m2/C2) (0.20 m)2 sin d (2.0 10 6 C)(3.6 10 6 C) (9.0 109 N m2/C2) sin 1 (0.60 m)2 d 3.1 N toward the right tan x L x L tan Chapter 21 1 4 L tan sin 1. E F 2.0 10 N 4.0 101 N/C d q 5.0 10 6 C 9 1 421 10 m (0.800 m) tan sin 8.60 10 2 m 3. E F q 0.449 m so F Eq (27 N/C)(3.0 10 7 C) 8.1 10 6 N
25. d sin 5. a. No. The force on the 2.0- C charge would be twice that on the 1.0- C charge. There is one slit per distance, d, so 1 gives slits d per centimeter. b. Yes. You would divide the force by the strength of the test charge, so the results would be the same. d sin sin tan 1 x L 7. Because the field strength varies as the square of the distance from the point charge, the new field 9 632 10 m strength will be one-fourth of the old field strength, sin tan 1 0.05 6 m 3 0.55m or 6.5 10 N/C. 6.2 10 6 m 6.2 10 4 cm q 9. E F K q’ d 2 1 slit 2 Ed2 (450 N/C)(0.25 m) 6.2 10 4cm so q 3.1 10 9 C K 9.0 109 N m2/C2 3 1.6 10 slits/cm The charge is negative, because the field is directed toward it.
Appendix C Chapter 20 17. V Ed E V 400 V 2 104 N/C Kq q d 0.020 m A B 9. F 2 dAB V 125 V (9.0 109 N m2/C2)(2.0 10 4 C)(8.0 10 4 C) 19. V Ed, so d 2.94 10 2 m E 4.25 103 N/C (0.30 m)2 4 1.6 10 N 21. W q V (3.0 C)(1.5 V) 4.5 J The force is attractive. 23. W q V (1.60 10 19 C)(1.8 104 V) 11 . F F 15 ؉y ABnet C on A 2.9 10 J rAB ؉x r qA F 25. W q V AC qB B on A qC qEd C (1.60 10 19 C)(4.5 105 N/C)(0.25 m) Magnitudes of all forces remain the same. The direc- 1.8 10 14 J tion changes to 42° above the x axis, or 138°. 27. Fg Eq qAqB 15 Fg 1.9 10 N 13. FA on B K 2 q 3.2 10 19 C dAB E 6.0 103 N/C q q B C # electrons q FC on B K 2 q dBC e 19 F F F 3.2 10 C net C on B A on B 1.60 10 19 C q q q q B C A B 2 K 2 K 2 dBC dAB
904 Appendix C 890-909 EM APP C-845813 6/15/04 10:57 PM Page 905
29. E V 240 V 3.8 104 N/C 15. d 6.4 10 3 m Lamp 14 F F 1.2 10 N 19 E , so q 4 3.2 10 C q E 3.8 10 N/C ؉ q # electrons Battery qe ؊ 19 3.2 10 C 1.60 10 19 C Switch 2 Potentiometer 23. a. I V 120 V 8.0 A 31. q C V, so the larger capacitor has a greater charge. R 15 Ω q (6.8 10 6 F)(24 V) 1.6 10 4 C b. E I2Rt (8.0 A)2(15 Ω)(30.0 s) 2.9 104 J 4 33. q C V c. 2.9 10 J, because all electrical energy is converted to thermal energy. so q C( V2 V1) 60 s 6 25. a. E Pt (0.22)(100.0 J/s)(1.0 min) (2.2 10 F)(15.0 V 6.0 V) 1 min 1.3 103 J 2.0 10 5 C b. E Pt (0.78)(100.0 J/s)(1.0 min) 60 s 1 min 4.7 103 J Chapter 22 27. E IVt = I(2V)( t ) 1. P IV (0.50 A)(125 V) 63 J/s 63 W 2 For a given amount of energy, doubling the voltage 3. P IV will divide the time by 2. 2.2 h P 75 W t 1.1 h I 0.60 A 2 V 125 V Practice Problems 29. a. I V 115 V 9.6 10 3 A 5. P IV R 12,000 Ω Solutions for 3 I P 0.90 W 0.30 A b. P VI (115 V)(9.6 10 A) 1.1 W V 3.0 V c. Cost (1.1 10 3 kW)($0.12/kWh) Ω 2 7. V IR (3.8 A)(32 ) 1.2 10 V (30 days)(24 h/day) $0.10 9. a. R V 120 V 2.4 102 Ω I 0.50 A 31. Echarge (1.3)IVt (1.3)(55 A)(12 V)(1.0 h) 858 Wh b. P IV (0.50 A)(120 V) 6.0 101 W t E 858 Wh 8.2 h IV (7.5 A)(14V) 11 . a . The new value of the current is 0.60A 0.30 A 2 Chapter 23 So V IR (0.30 A)(2.1 102 Ω) 6.3 101 V 1. R R R R b. The total resistance of the circuit is now 1 2 3 20 Ω 20 Ω 20 Ω R V 125 V 4.2 102 Ω total I 0.30 A 60 Ω Therefore, I V 120 V 2 A R 60 Ω Rres Rtotal Rlamp 2 Ω 2 Ω 4.2 10 2.1 10 3. a. It will increase. 2.1 102 Ω b. I V , so it will decrease. R c. P IV (0.30 A)(6.3 101 V) 19 W c. No. It does not depend on the resistance. 13. A Ω 5. V1 IR1 (3 A)(10 ) 30 V Ω ؉ 85 mA V2 IR2 (3 A)(15 ) 45 V Ω 4.5 V 53 V3 IR3 (3 A)(5 ) 15 V ؊ V V V 30 V 45 V 15 V 90 V I 1 2 3 voltage of battery
V 4.5 V Ω R 53 7. a. I V 17.0 V 66.7 mA I 0.085 A R 255.0 Ω
Appendix C 905 890-909 EM APP C-845813 7/29/04 4:18 PM Page 906
b. First, find the total resistance, then solve for voltage. 19. Neither. They both reach maximum dissipation at Ω Ω Ω the same voltage. R RA RB 255 292 547 2 P V V IR (66.7 mA)(547 Ω) 36.5 V R V PR c. P IV (66.7 mA)(36.5 V) 2.43 W The voltage is equal across parallel resistors, so: 2 2 Ω PA I RA (66.7 mA) (255 ) 1.13 W V P1R1 P2R2 P I2R (66.7 mA)2(292 Ω) 1.30 W B B (2 W)(12 Ω) (4 W)(6.0 Ω) d. Yes. The law of conservation of energy states that 5 V maximum energy cannot be created or destroyed; therefore, the rate at which energy is converted, or power is 25. By conservation of energy (and power): dissipated, will equal the sum of all parts. PT P1 P2 P3 2.0 W 3.0 W 1.5 W 9. The resistor with the lower resistance will dissipate less power; thus, it will be cooler. 6.5 W PT IV P 11 . a . R R R I T 6.5 W 0.54 A 1 2 V 12 V 22 Ω 33 Ω 55 Ω 27. Then, all of the working lights are in series. The 12 working lights will burn with equal intensity.
V 120 V b. I Ω 2.2 A R 55 Chapter 24 c. V IR 1. a. repulsive Across a 22-Ω resistor, V IR V R 120 V (22 Ω) 48 V b. attractive 1 1 R 1 55 Ω
Across a 33-Ω resistor, 3. the bottom (the point) V IR V R 120 V (33 Ω) 72 V 2 2 R 2 55 Ω 5. a. from south to north
2 Appendix C d. V 48 V 72 V 1.20 10 V b. west
VR 7. the pointed end 13. V B B R R A B 9. Yes. Connect the potentiometer in series with the Ω (45 V)(235 k ) power supply and the coil. Adjusting the potentiometer 475 kΩ 235 kΩ for more resistance will decrease the current flow and 15 V the strength of the field. 1 1 1 1 17. F BIL 15. a. R R1 R2 R3 (0.40 N/A m)(8.0 A)(0.50 m) 1.6 N 1 1 1 15.0 Ω 15.0 Ω 15.0 Ω 19. F BIL, F weight of wire 3 Ω 15.0 B F 0.35 N 0.15 T IL (6.0 A)(0.400 m) R 5.00 Ω 21. Opposite to the direction of the electron motion V 30.0 V b. I Ω 6.00 A R 5.00 23. F Bqv 2 19 4 c. I V 30.0 V 2.00 A (9.0 10 T)(2)(1.60 10 C)(3.0 10 m/s) R 15.0 Ω 1 8.6 10 16 N
17. a. Yes, it gets smaller. 25. F Bqv b. Yes, it gets larger. (5.0 10 2 T)(2)(1.60 10 19 C)(4.0 104 m/s) 16 c. No, it remains the same. Currents are independent. 6.4 10 N
906 Appendix C 890-909 EM APP C-845813 6/15/04 11:00 PM Page 907
Chapter 25 4 (1.80 10 V)(0.50 A) 60.0 V 1. a. EMF BLv 1.5 102 V (0.4 T)(0.5 m)(20 m/s) 4 V Chapter 26 EM F b. I 2 R 1. Bqv mv 4 V r 6.0 Ω r m v Bq 0.7 A 27 3 (1.67 10 kg)(7.5 10 m/s) (0.60 T)(1.60 10 19 C) 3. a. EMF BLv 1.3 10 4 m (1.0 T)(30.0 m)(2.0 m/s) 1 2 6.0 10 V 3. Bqv mv r EMF 6.0 101 V b. I 4.0 A r m v R 15.0 Ω Bq (9.11 10 31 kg)(5.0 104 m/s) 5. a. Veff (0.707)Vmax (6.0 10 2 T)(1.60 10 19 C) (0.707)(170 V) 4.7 10 6 m 2 1.2 10 V B2r2q 5. m 2V b. I (0.707)I 2 2 2 19 eff max (7.2 10 T) (0.085 m) (1.60 10 C) 2(110 V) (0.707)(0.70 A) Practice Problems 26 2.7 10 kg
0.49 A Solutions for V ma x V V 7. Bqv Eq e ff 2 m ax c. R I E Ieff ma x Imax v B 2 2 6.0 10 N/C 3 170 V 1.5 10 T 0.70 A 4.0 105 m/s
2 Ω 2.4 10 15. All electromagnetic waves travel through air or a vacuum at c, 3.00 108 m/s. V ma x 7. a. Veff 2 17. c f 425 V 8 2 3.00 1 0 m/s 8.2 1014 Hz 3.01 102 V 3.7 10 7 m V b. I eff eff R 19. v c 2 3.01 10 V K 5.0 102 Ω 299,792,458 m/s 0.60 A 1.00054 8 V N 2.99712 10 m/s 17. P P VS NS c V N 21. v V P S K S N P so K ( c )2 (60.0 V)(90,000) v 8 300 3.00 1 0 m/s 2 ( 2.43 10 8 m/s ) 1.80 104 V 1.52 VP IP VSIS V I S S IP VP
Appendix C 907 890-909 EM APP C-845813 6/15/04 11:01 PM Page 908
Chapter 27 Chapter 28
19 13.6eV 1.60 10 J 1. E 1. (2.3 eV) 3.7 10 19 J n n2 ( 1 eV ) 13.6 eV 1 E 3.40 eV 3. m 9.11 10 31 kg, KE mv2 2 (2)2 2 E 13. 6 eV 1.51 eV so v 2KE 3 (3)2 m 13.6 eV 19 E 0.850 eV 2(3.7 1 0 J) 4 (4)2 9.11 1 0 31 k g 9.0 105 m/s 3. E E4 E2 ( 13.6 eV)( 1 1 ) 42 22 5. KE qV0 ( 13.6 eV)( 1 1 ) ( 1.60 10 19 C)(3.2 J/C) 16 4 5.1 10 19 J 2.55 eV
x 5 10 11 m 1240 eV nm 5. 7. KEmax hf0 0.075m 2.5 10 15 m 3 1240 e V nm 1.96 eV x 2 10 m 425 nm 0.960 eV 7. a. E 8.82 eV 6.67 eV 2.15 eV hc 9. hf0 4.50 eV, so 4.50 eV 0 h c b. Thus, 1240 eV nm E 0 4.50 eV (6.63 10 34 J s)(3.00 108 m/s) 276 nm (2.15 eV)(1.60 10 19 J eV) 5.78 10 7 m 19. a. h mv 578 nm 34 6.63 10 J s (7.0 kg)(8.5 m/s) Chapter 29 1.1 10 35 m Appendix C 3 b. The wavelength is too small to show observable 1. free e /cm 1 mol effects. (2 e /atom)(6.02 1023 atoms/mol) (65.37 g ) (7.13 g/cm3) 21. h p 1.31 1023 h so p 3. free e /cm3 1 KE mv2 1 mol 2 (1 e /atom)(6.02 1023 atoms/mol) (196.97 g ) 2 (19.32 g/cm3) p 2m 5.90 1022 h 2 2835 g 5. free e (1.81 1023 free e /cm3) 2m (2.70 g/cm3 ) 1.90 1026 free e in the tip 34 6.63 10 J s 0.125 10 9 m 7. free e /atom 2(9.11 10 31 kg) 3 5 1 m ol 28.09 g 1 cm 1.89 10 free e (6.02 1023 atoms )( 1 mol )( 2.33g)( cm3 ) 17 1 eV (1.544 10 J)( 19 ) 1.60 10 J 3.78 10 18 free e /atom 96.5 eV, so it would have to be accelerated through 96.5 V. TK TC 273 TC TK 273
200.0 273
73°C
908 Appendix C 890-909 EM APP C-845813 7/29/04 4:20 PM Page 909
9. free e /atom b. E ( 0.113986 u)(931.49 MeV/u) 106.18 MeV 3 10 1 m ol 72. 6 g cm 1.16 10 free e ( 23 )( )( )(3 ) 6.02 10 atoms mol 5.23 g cm 234 → 230 4 15. 92U 90 Th 2He 2.67 10 13 226 → 222 4 17. 88Ra 86Rn 2He 3 free e /cm in doped Si 11 . ratio 3 14 → 14 0 0 free e /cm in Si 19. 6C 7N 1e 0
free e /cm3 in doped Si (ratio)(free e /cm3 in Si) 263 → 259 4 21. 106 Sg 104 Rf 2He
4.99 1022 Si atoms As at oms (ratio)(free e /cm3 in Si) 23. a. 210 Pb → 210 Tl 0e 0 ( Si atoms )(cm3 ) 80 81 1 0 210 → 210 0 0 4 10 3 b. 83Bi 84Po 1e 0 As at oms (1 10 )(1.45 10 free e /cm ) Si atoms 4.99 1022 Si atoms/cm3 234 → 234 0 0 c. 90Th 91 Pa 1e 0 2.91 10 9 239 → 239 0 0 d. 93Np 94Pu 1e 0
13. ratio 25. 8.0 days 4(2.0 days), which is 4 half-lives 1 free e 1 As atom 4.34 1022 electrons t remaining original 1 (1 As atom )( 1 106 electrons )(cm3 ) (2 ) 1.13 1015 thermal carriers 4 (4.0 g) 1 (2 ) 38.4 0.25 g
15. Germanium devices do not work well at such temper- Practice Problems 27. Six years is about half of tritium’s half-life of 12.3
atures because the ratio of doped carriers to thermal 1 1 7 Solutions for years, thus, the brightness is 2, or about the carriers is small enough that temperature has too (2 ) 10 much influence on conductivity. Silicon is much original brightness. better. 35. a. E mc2 23. Vb IR Vd Vd (1.67 10 27 kg)(3.00 108 m/s)2 Ω (0.0025 A)(470 ) 0.50 V 0.50 V 1.50 10 10 J 2.2 V 10 b. E 1.50 10 J 25. It would be impossible to obtain 2.5 mA of current 1.60217 10 19 J/eV with any reasonable power supply voltage because 9.36 108 eV one of the diodes would be reverse-biased. 936 MeV
c. The minimum energy is (2)(9.36 108 eV) Chapter 30 1.87 109 eV 1. A Z neutrons 37. a. E (1.008655 u)(931.49 MeV) 234 92 142 neutrons 939.56 MeV 235 92 143 neutrons b. The total -ray energy is twice the energy equivalent 238 92 146 neutrons of the neutron’s mass, or 1879.1 MeV.
3. A Z 200 80 120 neutrons
5. a. 12.000000 6(1.007825) 6(1.008665) 0.098940 u
b. E ( 0.098940 u)(931.49 MeV/u) 92.161 MeV
7. a. 15.010109 7(1.007825) 8(1.008665) 0.113986 u
Appendix C 909 910-918 EM APP D-845813 3/31/04 7:16 AM Page 910
Color Conventions Displacement vectors (d ) Negative charges Velocity vectors (v) Positive charges Acceleration vectors (a) Current direction Force vectors (F ) Electron Momentum vectors ( p) Proton Light rays Neutron Object Image Coordinate axes Electric field (E ) Magnetic field lines (B )
Electric Circuit Symbols
Conductor Electric No electric Ground connection connection Battery
Switch
Fuse
Capacitor V A
Resistor (fixed) Lamp DC generator Voltmeter Ammeter
Potentiometer (variable resistor) Appendix D
AC source Transistor Diode Inductor
910 Appendix D 910-918 EM APP D-845813 6/9/04 4:10 PM Page 911
SI Base Units Quantity Name Symbol Length meter m Mass kilogram kg Time second s Temperature Kelvin K Amount of a substance mole mol Electric current ampere A Luminous intensity candela cd
SI Derived Units Measurement Unit Symbol Expressed in Base Units Expressed in Other SI Units Acceleration m/s2 m/s2 Area m2 m2 Capacitance farad F A2 s4/kg m2 Density kg/m3 kg/m3 Electric charge coulomb C A s Electric field N/C kg m/C s2 Electric resistance ohm Ω kg m2/A2 s3 V/A EMF volt V kg m2/A s3 Energy, work joule J kg m2/s2 N m Force newton N kg m/s2 Frequency hertz Hz s 1 Illuminance lux lx cd/m2 Magnetic field tesla T kg/A s2 N s/C m Potential difference volt V kg m2/A s3 W/A or J/C Power watt W kg m2/s3 J/s
Pressure pascal Pa kg/m s2 N/m2 Tables Velocity m/s m/s Volume m3 m3
Useful Conversions 1 in 2.54 cm 1 kg 6.02 1026 u 1 atm 101 kPa 1 mi 1.61 km 1 oz ↔ 28.4 g 1 cal 4.184 J 1 mi2 640 acres 1 kg ↔ 2.21 lb 1 eV 1.60 10 19 J 1 gal 3.79 L 1 lb 4.45 N 1 kWh 3.60 MJ 1 m3 264 gal 1 atm 14.7 lb/in2 1 hp 746 W 1 knot 1.15 mi/h 1 atm 1.01 105 N/m2 1 mol 6.022 1023 items
Appendix D 911 910-918 EM APP D-845813 6/9/04 4:11 PM Page 912
Physical Constants Quantity Symbol Value Approximate Value Atomic mass unit u 1.66053886 10 27 kg 1.66 10 27 kg 23 1 23 1 Avogadro’s number NA 6.0221415 10 mol 6.022 10 mol Boltzmann’s constant k 1.3806505 10 23 Pa m3/K 1.38 10 23 Pa m3/K Constant in Coulomb’s law K 8.987551788 109 N m2/C2 9.0 109 N m2/C2 Elementary charge e 1.60217653 10 19 C 1.602 10 19 C Gas constant R 8.314472 Pa m3/mol K 8.31 Pa m3/mol K Gravitational constant G 6.6742 10 11 N m2/kg2 6.67 10 11 N m2/kg2 31 31 Mass of an electron me 9.1093826 10 kg 9.11 10 kg 27 27 Mass of a proton mp 1.67262171 10 kg 1.67 10 kg 27 27 Mass of a neutron mn 1.67492728 10 kg 1.67 10 kg Planck’s constant h 6.6260693 10 34 J s 6.63 10 34 J s Speed of light in a vacuum c 2.99792458 108 m/s 3.00 108 m/s
SI Prefixes Moments of Inertia for Various Objects Prefix Symbol Scientific Object Location Diagram Moment Notation of Axis of Inertia femto f 10 15 Thin hoop of Through Axis mr 2 12 radius r central pico p 10 r diameter nano n 10 9 micro 10 6 1 milli m 10 3 Solid, uniform Through Axis mr 2 2 cylinder of center r centi c 10 2 radius r deci d 10 1 deka da 101 Uniform sphere Through Axis 2 2 2 mr hecto h 10 of radius r center 5 kilo k 103 r mega M 106 giga G 109 1 Long, uniform Through Axis ml 2 12 12 rod of length l center Appendix D tera T 10 peta P 1015 l
1 2 Long, uniform Through Axis ml rod of length l end 3 l
1 Thin, rectangular Through Axis m(l 2 w 2) plate of length l center 12 and width w l w
912 Appendix D 910-918 EM APP D-845813 6/9/04 4:12 PM Page 913
Densities of Some Common Substances Melting and Boiling Points Substance Density of Some Substances (g/cm3 ) Substance Melting point Boiling point ° ° Aluminum 2.702 ( C) ( C) Cadmium 8.642 Aluminum 660.37 2467 Copper 8.92 Copper 1083 2567 Germanium 5.35 Germanium 937.4 2830 Gold 19.31 Gold 1064.43 2808 Hydrogen 8.99 10 5 Indium 156.61 2080 Indium 7. 3 0 Iron 1535 2750 Iron 7. 8 6 Lead 327.5 1740 Lead 11.34 Silicon 1410 2355 Mercury 13.546 Silver 961.93 2212 Oxygen 1.429 10 3 Water 0.000 100.000 Silicon 2.33 Zinc 419.58 907 Silver 10.5 Water (4°C) 1.000 Zinc 7.14
Specific Heats of Some Common Substances Material Specific Heat (J/kg K) Material Specific Heat (J/kg K) Aluminum 897 Lead 130 Brass 376 Methanol 2450 Carbon 710 Silver 235 Copper 385 Steam 2020 Glass 840 Water 4180 Ice 2060 Zinc 388
Iron 450 Tables
Heats of Fusion and Vaporization of Some Common Substances
Material Heat of Fusion, Hf (J/kg) Heat of Vaporization, Hv (J/kg) Copper 2.05 105 5.07 106 Gold 6.30 104 1.64 106 Iron 2.66 105 6.29 106 Lead 2.04 104 8.64 105 Mercury 1.15 104 2.72 105 Methanol 1.09 105 8.78 105 Silver 1.04 105 2.36 106 Water (ice) 3.34 105 2.26 106
Appendix D 913 910-918 EM APP D-845813 6/9/04 4:13 PM Page 914
Coefficients of Thermal Expansion at 20°C Material Coefficient of Linear Expansion, Coefficient of Volume Expansion, (°C) 1 (°C) 1 Solids Aluminum 25 10 6 75 10 6 Brass 19 10 6 56 10 6 Concrete 12 10 6 36 10 6 Copper 17 10 6 48 10 6 Glass (soft) 9 10 6 27 10 6 Glass (ovenproof) 3 10 6 9 10 6 Iron, steel 12 10 6 35 10 6 Platinum 9 10 6 27 10 6 Liquids Gasoline 950 10 6 Mercury 180 10 6 Methanol 1100 10 6 Water 210 10 6 Gases Air (and most other gases) 3400 10 6
Speed of Sound in Various Media Wavelengths of Visible Light Medium m/s Color Wavelength in Air (0°) 331 Nanometers (nm) Air (20°) 343 Violet light 380–430 nm Helium (0°) 972 Indigo light 430–450 nm Hydrogen (0°) 1286 Blue light 450–500 nm Water (25°) 1493 Cyan light 500–520 nm Seawater (0°) 1533 Green light 520–565 nm Rubber 1600 Yellow light 565–590 nm Copper (25°) 3560 Orange light 590–625 nm ° Red light 625–740 nm
Appendix D Iron (25 ) 5130 Ovenproof glass 5640 Dielectric Constants, K (20°C) Diamond 12,000 Vacuum 1.0000 Air (1 atm) 1.00059 Neon (1 atm) 1.00013 Glass 4–7 Quartz 4.3 Fused quartz 3.75 Water 80
914 Appendix D 910-918 EM APP D-845813 3/31/04 7:22 AM Page 915
The Planets Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto Mass 0.3302 4.8685 5.9736 0.64185 1898.6 568.46 86.832 102.43 0.0125 (kg 1024) Equatorial 2439.7 6051.8 6378.1 3397 71,492 60,268 25,559 24,764 1195 radius (km) Mean 5427 5234 5515 3933 1326 687 1270 1638 1750 density (kg/m3) Albedo 0.119 0.750 0.306 0.250 0.343 0.342 0.300 0.290 0.4–0.6 Semimajor axis 57.91 108.21 149.60 227.92 778.57 1433.53 2872.46 4495.06 5869.66 (km 106 ) Orbital period 87.969 224.701 365.256 686.980 4332.589 10,759.22 30,685.4 60,189 90,465 (Earth days) Orbital inclination 7.00 3.39 0.000 1.850 1.304 2.485 0.772 1.769 17.16 (degrees) Orbital 0.2056 0.0067 0.0167 0.0935 0.0489 0.0565 0.0457 0.0113 0.2444 eccentricity Rotational 1407.6 5832.5R 23.9345 24.6229 9.9250 10.656 17.24R 16.11 153.2928R period (hours) Axial tilt 0.01 177.36 23.45 25.19 3.13 26.73 97.77 28.32 122.53 (degrees) Average surface 440 737 288 210 112 84 53 55 50 temperature (K)
R indicates retrograde motion.
The Moon The Sun Mass 0.07349 1024 kg Mass 1,989,100 1024 kg Equatorial radius 1738.1 km Equatorial radius 696000 km Mean density 3350 kg/m3 Mean density 1408 kg/m3 Albedo 0.11 Absolute magnitude 4.83 Tables Semimajor axis 0.3844 km 106 Luminosity 384.6 1024 J/s Revolution period 27.3217 Earth days Spectral type G2 V Synodic (lunar) period 29.53 Earth days Rotational period 609.12 h Orbital inclination 18.28°–28.58° Mean energy production 0.1937 10 3 J/kg Orbital eccentricity 0.0549 Average temperature 5778 K Rotational period 655.728 h
Appendix D 915 910-918 EM APP D-845813 3/31/04 7:23 AM Page 916 18 8A 2 10 18 54 36 Ar Kr 86 Ne Xe Rn He Neon (222) 4.003 Argon 20.180 39.948 Xenon 83.798 Radon Helium 131.293 Krypton 17 7A I 9 F 85 53 Cl At 35 Br 17 Lr 71 Lu 103 (210) (262) Iodine 18.998 79.904 35.453 126.904 Fluorine Astatine 174.967 Bromine Chlorine Lutetium Lawrencium 16 6A S 8 O 16 34 Se 52 84 Te Po 70 No Yb 102 78.96 (209) Sulfur (259) 32.065 15.999 127.60 Oxygen 173.04 Selenium Tellurium Polonium Nobelium Ytterbium 15 5A P 7 N 15 Bi 51 83 33 Sb As 69 Tm 101 Md 30.974 (258) 14.007 74.922 Arsenic 121.760 208.980 Bismuth 168.934 Nitrogen Thulium Antimony Phosphorus Mendelevium 14 4A 6 C Si 32 82 50 14 Sn Pb Ge Tin 114 Gas Liquid Solid Synthetic elements Er 68 Uuq Lead (289) Fm 72.64 100 207.2 (257) 12.011 Silicon 28.086 Carbon 118.710 Erbium 167.259 Fermium Germanium Ununquadium 13 3A 5 B In Tl 49 31 81 13 Al Ga 67 Es 99 Ho Boron 10.811 69.723 (252) 26.982 Indium 114.818 Gallium 204.383 Thallium 164.930 Holmium Aluminum Einsteinium 12 2B 80 30 48 Zn Cd Hg 112 66 Zinc 98 Cf Dy Uub (285) 200.59 65.409 (251) 112.411 Mercury 162.500 Cadmium Ununbium Dysprosium Californium 11 1B Metal Metalloid Nonmetal Recently discovered Names not officially assigned. Discovery of element 114 recently reported. Further information yet available. 47 29 79 Cu Ag Au 111 97 65 Bk Uuu Tb Gold * (272) Silver (247) 63.546 Copper 107.868 196.967 158.925 Terbium ** * Berkelium Unununium 10 Pt 28 78 Ni 46 Ds Pd 64 96 110 Gd Cm (281) Nickel (247) 58.693 106.42 157.25 195.078 Curium Platinum Palladium Gadolinium Darmstadtium 9 Ir 45 95 63 27 Rh Eu 77 Mt Co 109 Am (268) (243) Cobalt 58.933 102.906 Iridium 151.964 192.217 Rhodium Europium Americium Meitnerium 8 8B 44 Hs 62 26 94 76 Fe Ru Pu Os 108 Sm Iron (277) (244) 150.36 55.845 190.23 101.07 Hassium State of matter Osmium Samarium Plutonium Ruthenium 7 7B 61 93 25 43 Tc 75 Bh Re Np Pm 107 Mn (98) (145) (264) (237) 54.938 Bohrium 186.207 Rhenium Neptunium Manganese Technetium Promethium 6 1 H 6B 1.008 U 42 74 92 60 W 24 Cr Sg Nd Mo 106 (266) 95.94 183.84 144.24 Hydrogen 51.996 238.029 Uranium Tungsten Chromium Seaborgium Molybdenum Neodymium 5 5B V 41 23 Pr 91 59 73 Pa Nb Ta Db 105 (262) 92.906 50.942 231.036 140.908 180.948 Niobium Dubnium Tantalum Vanadium Protactinium Praseodymium
Symbol 4 Element 4B Ti Rf 72 90 Zr 40 22 Hf Th 58 Ce 104 (261) The number in parentheses is the mass of longest lived isotope for that element. 178.49 91.224 47.867 Atomic mass Cerium 232.038 140.116 Thorium Hafnium Titanium Zirconium Rutherfordium Appendix D
Atomic number 3 3B Y Sc 21 57 39 89 La Ac (227) 44.956 88.906 138.906 Yttrium Actinium Scandium Lanthanum Periodic Table of the Elements 2 2A 4 12 Be 56 88 20 Sr Ba Ra Ca 38 Mg 9.012 (226) 87.62 24.305 40.078 Barium Radium 137.327 Calcium Beryllium Strontium Actinide series Magnesium Lanthanide series 1 1A 3 1 H Li K 11 Fr 87 37 19 55 Cs Na Rb (223) 6.941 1.008 22.990 85.468 39.098 Sodium Cesium Lithium 132.905 Francium Hydrogen Rubidium Potassium 2 3 4 5 6 7 1
916 Appendix D Tables 917 47.867 87.62 78.96 65.409 95.94 20.180 92.906 14.007 15.999 85.468 28.086 22.990 32.065 50.942 88.906 91.224 58.693 30.974 39.098 44.956 Mass (98) 173.04 127.60 107.868 232.038 118.710 183.84 200.59 195.078 102.906 158.925 204.383 168.934 238.029 131.293 144.24 190.23 106.42 140.908 231.036 186.207 101.07 150.36 180.948 Atomic (272) (237) (285) (145) (226) (222) (289) (259) (244) (209) (261) (266) Appendix D 7 8 47 74 37 70 76 78 45 21 14 11 16 73 43 52 65 22 92 23 42 10 93 28 15 19 75 44 62 34 38 81 90 69 50 54 39 30 40 80 60 41 46 94 84 59 61 91 88 86 111 112 114 102 104 106 Atomic Number S P V Y K U O N Tl Ti Si Pt W Pr Sr Tc Rf Ta Te Zr Ni Sc Tb Th Pa Se Po Pd Pu Sg Sn Xe Re Os Ra Yb Zn Rh Rb Ru Rn Ag Tm Na Ne Hg No Nd Np Nb Pm Sm Mo Uuu Uub Uuq Symbol Element Element 111[*] Element 112[*] Element 114[*] Rhodium Rubidium Ruthenium Rutherfordium Samarium Scandium Seaborgium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium 4.003 1.008 6.941 9.012 The Elements The 74.922 79.904 24.305 18.998 72.64 55.845 83.798 26.982 10.811 12.011 35.453 54.938 63.546 69.723 39.948 40.078 51.996 58.933 Mass 174.967 178.49 167.259 157.25 207.2 137.327 114.818 126.904 192.217 121.760 112.411 132.905 162.500 151.964 196.967 164.930 138.906 208.980 140.116 Atomic (247) (247) (277) (257) (227) (252) (223) (243) (210) (268) (258) (281) (262) (262) (264) (251) 9 2 1 3 4 5 6 87 97 17 79 67 77 57 27 12 25 29 32 72 53 26 82 13 95 18 33 85 83 35 20 55 24 96 66 99 68 63 64 31 49 36 71 89 51 56 48 98 58 107 110 105 100 103 109 101 108 Atomic Number I F Ir B C H Li Fr In Bi Lr Cl Er Al Kr Cf Br At Cr Es Fe Hf Ar La Lu Cs Eu As Pb Sb Hs Ba Bk Be Ds Dy Ac Ce Ca Bh Co Mt Ga Ge He Cu Cd Au Ho Gd Db Fm Mg Mn Md Cm Am Symbol Element Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Meitnerium Mendelevium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Hassium Helium Holmium Hydrogen Indium Iodine Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Darmstadtium Dubnium Dysprosium Einsteinium Erbium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Bohrium Boron Bromine Cadmium Calcium Actinium * Names have not yet been approved by IUPAC. 910-918 EM APP D-845813 3/31/04 7:24 AM Page 917 Page AM 7:24 3/31/04 D-845813 APP EM 910-918 910-918 EM APP D-845813 3/31/04 7:24 AM Page 918
SAFETY SYMBOLS HAZARD EXAMPLES PRECAUTION REMEDY
Special disposal pro- Certain chemicals, Do not dispose of Dispose of wastes as DISPOSAL cedures need to be living organisms these materials in the directed by your followed. sink or trash can. teacher. Organisms or other Bacteria, fungi, blood, Avoid skin contact with Notify your teacher if BIOLOGICAL biological materials unpreserved tissues, these materials. Wear you suspect contact that might be harmful plant materials mask or gloves. with material. Wash to humans hands thoroughly. EXTREME Objects that can burn Boiling liquids, hot Use proper protection Go to your teacher for skin by being too cold plates, dry ice, liquid when handling. first aid. TEMPERATURE or too hot nitrogen SHARP Use of tools or glass- Razor blades, pins, Practice common- Go to your teacher for ware that can easily scalpels, pointed tools, sense behavior and first aid. OBJECT puncture or slice skin dissecting probes, follow guidelines for broken glass use of the tool. Possible danger to Ammonia, acetone, Make sure there is Leave foul area and FUME respiratory tract nail polish remover, good ventilation. Never notify your teacher from fumes heated sulfur, smell fumes directly. immediately. moth balls Wear a mask. Possible danger from Improper grounding, Double-check setup Do not attempt to fix ELECTRICAL electrical shock or liquid spills, short with teacher. Check electrical problems. burn circuits, exposed wires condition of wires and Notify your teacher apparatus. immediately. Substances that can Pollen, moth balls, Wear dust mask and Go to your teacher for IRRITANT irritate the skin or steel wool, fiberglass, gloves. Practice extra first aid. mucous membranes of potassium perman- care when handling the respiratory tract ganate these materials. Chemicals that can Bleaches such as Wear goggles, gloves, Immediately flush the CHEMICAL react with and destroy hydrogen peroxide; and an apron. affected area with tissue and other acids such as sulfuric water and notify your materials acid, hydrochloric acid; teacher. bases such as ammo- nia, sodium hydroxide Substance may be Mercury, many metal Follow your teacher’s Always wash hands TOXIC poisonous if touched, compounds, iodine, instructions. thoroughly after use. inhaled, or swallowed. poinsettia plant parts Go to your teacher for first aid. Flammable chemicals Alcohol, kerosene, Avoid open flames and Notify your teacher FLAMMABLE may be ignited by potassium perman- heat when using immediately. Use fire open flame, spark, or ganate flammable chemicals. safety equipment if exposed heat. applicable. Open flame in use, Hair, clothing, paper, Tie back hair and loose Notify your teacher Appendix D OPEN FLAME may cause fire. synthetic materials clothing. Follow immediately. Use fire teacher’s instruction safety equipment if on lighting and extin- applicable. guishing flames.
Eye Safety Clothing Radioactivity Handwashing Proper eye protection Protection This symbol appears After the lab, wash should be worn at all This symbol appears when radioactive hands with soap and times by anyone per- when substances materials are used. water before remov- forming or observing could stain or burn ing goggles. science activities. clothing.
918 Appendix D 919-926 EM GLOSSARY-845813 3/31/04 7:45 AM Page 919
during a measurable time interval, divided by that specific time interval; is measured in m/s2. average power (677): Half the maximum power associated
with an alternating current. Glossary absorption spectrum (751): The characteristic set of wave- average speed (44): How fast an object is moving; is the lengths absorbed by a gas, which can be used to identify that absolute value of the slope of an object’s position-time gas. graph. acceleration (59): The rate at which the velocity of an object average velocity (44): The change in position, divided by the changes. time during which the change occurred; is the slope of an acceleration due to gravity (72): The acceleration of an object’s position-time graph. object in free fall, resulting from the influence of Earth’s gravity; acceleration due to gravity on Earth, g, is 9.80 m/s2 toward the center of Earth. accuracy (13): A characteristic of a measured value that describes how well the results of a measurement agree with the “real” value, which is the accepted value, as measured by competent experimenters. band theory (776): The theory that electric conduction in achromatic lens (499): A combination of two or more lenses solids can be better understood in terms of valance and con- with different indices of refraction (such as a concave lens duction bands separated by forbidden energy gaps. with a convex lens) that is used to minimize a chromatic battery (592): A device made up of several galvanic cells con- aberration. nected together that converts chemical energy to electric activity (810): The number of decays per second of a radioac- energy. tive substance. beat (418): The oscillation of wave amplitude that results from adhesive forces (350): The electromagnetic forces of attrac- the superposition of two sound waves with almost identical tion that particles of different substances exert on one another; frequencies. responsible for capillary action. Bernoulli’s principle (357): States that as the velocity of a alpha decay (806): The radioactive decay process in which fluid increases, the pressure exerted by that fluid decreases. an alpha ( ) particle is emitted from a nucleus. beta decay (806): The radioactive decay process in which a neutron is changed to a proton within the nucleus and a beta alpha particles (748): Massive, positively charged atomic particles that move at high speed; are represented by the ( ) particle and antineutrino are emitted. symbol . binding energy (802): The energy equivalent of the mass ammeter (631): A low-resistance device connected in series defect; is always negative. that is used to measure the electric current in any branch or buoyant force (354): The upward force exerted on an object part of a circuit. immersed in a fluid. amorphous solid (359): A substance having a definite shape and volume, but lacking a regular crystal structure. ampere (593): A flow of electric charge, or electric current, equal to one coulomb per second (1 C/s). amplitude (375): In any periodic motion, the maximum dis- tance an object moves from equilibrium. capacitance (577): The ratio of an object’s stored charge to its angular acceleration (199): The change in angular velocity electric potential difference. divided by the time needed to make the change; is measured capacitor (577): An electric device used to store charge that is in rad/s2. made up of two conductors separated by an insulator. angular displacement (198): The change in the angle as an center of mass (211): The point on the object that moves in object rotates. the same way that a point particle would move. angular impulse–angular momentum theorem (234): centrifugal “force” (216): The apparent force that seems to States that the angular impulse on an object is equal to the pull on a moving object, but does not exert a physical out- change in the object’s angular momentum. ward push on it, and is observed only in rotating frames of angular momentum (233): The product of a rotating object’s reference. moment of inertia and its angular velocity; is measured in centripetal acceleration (153): The center-seeking accelera- kg m2/s. tion of an object moving in a circle at a constant speed. angular velocity (198): The angular displacement of an object centripetal force (154): The net force exerted toward the cen- divided by the time needed to make the displacement. ter of the circle that causes an object to have a centripetal antenna (707): A wire designed to transmit or receive electro- acceleration. magnetic waves. chain reaction (812): Continual process of repeated fission antinode (389): The point with the largest displacement when reactions caused by the release of neutrons from previous fis- two wave pulses meet. sion reactions. apparent weight (98): The force experienced by an object, charging by conduction (547): The process of charging a resulting from all the forces acting on it, giving the object an neutral object by touching it with a charged object. acceleration. charging by induction (548): The process of charging an Archimedes’ principle (354): States that an object immersed object without touching it, which can be accomplished by in a fluid has an upward force on it that equals the weight of bringing a charged object close to a neutral object, causing a the fluid displaced by the object. separation of charges, then separating the object to be armature (656): The wire coil of an electric motor, made up of charged, trapping opposite but equal charges. many loops mounted on an axle or shaft; torque on an arma- chromatic aberration (499): A spherical lens defect in which ture, and the motor’s resultant speed, is controlled by varying light passing through a lens is focused at different points, the current through the motor. causing an object viewed through a lens to seem to be ringed atomic mass unit (800): A unit of mass, u, where u is equal with color. to 1.66 10 27 kg. circuit breaker (627): An automatic switch that acts as a safe- atomic number (800): The number of protons in an atom’s ty device in an electric circuit by opening and stopping the nucleus. current flow when too much current flows through a circuit. average acceleration (59): The change in an object’s velocity closed system (236): A system that does not gain or lose mass.
Glossary 919 919-926 EM GLOSSARY-845813 6/9/04 4:15 PM Page 920
closed-pipe resonator (412): A resonating tube with one end Coulomb’s law (549): States that the force between two closed to air; its resonant frequencies are odd-numbered charges varies directly with the product of their charge and multiples of the fundamental. inversely with the square of the distance between them. coefficient of kinetic friction (127): The slope of a line, k, crest (383): The high point of a wave. between two surfaces, relating frictional force to normal force. critical angle (489): The certain angle of incidence in which coefficient of linear expansion (361): The change in length the refracted light ray lies along the boundary between two divided by the original length and the change in temperature. media. coefficient of static friction (127): A dimensionless constant crystal lattice (359): A fixed, regular pattern formed when the depending on the two surfaces in contact. It is used to calcu- temperature of a liquid is lowered, the average kinetic energy Glossary late the maximum static frictional force that needs to be of its particles decreases and, for many solids, the particles overcome before motion begins. become frozen but do not stop moving and instead, vibrate coefficient of volume expansion (361): The change in vol- around their fixed positions. ume divided by the original volume and the change in temperature; is about three times the coefficient of linear expansion because solids expand in three directions. coherent light (516): Light from two or more sources, whose additive superposition produces smooth wave fronts. (761): Light whose waves are in step, with coinciding maxima and de Broglie wavelength (735): The wavelength associated with minima. a moving particle. cohesive forces (349): The electromagnetic forces of attrac- decibel (406): The unit of measurement for sound level; also tion that like particles exert on one another; responsible for can describe the power and intensity of sound waves. surface tension and viscosity. dependent variable (15): The factor in an experiment that combination series-parallel circuit (629): A complex electric depends on the independent variable. circuit that includes both series and parallel branches. depletion layer (784): The region around a pn-junction diode combined gas law (345): For a fixed amount of an ideal gas, where there are no charge carriers and electricity is poorly the pressure times the volume, divided by the Kelvin temper- conducted. ature equals a constant; reduces to Boyle’s law if temperature dielectrics (707): Nonconducting materials—glass, air, and is constant and to Charles’s law if pressure is constant. water—through which electromagnetic waves move at less complementary color (441): A color of light, which when than the speed of light in a vacuum. combined with another color of light, produces white light. diffraction (439): The bending of light around a barrier. components (122): Projections of the component vectors. diffraction grating (527): A device consisting of large compound machine (269): A machine consisting of two numbers of single slits that are quite close together, diffract or more simple machines that are connected so that the light, and form a diffraction pattern that is an overlap resistance force of one machine becomes the effort force of of single-slit diffraction patterns; can be used to precisely the second machine. measure light wavelength or to separate light of different Compton effect (733): The shift in the energy of scattered wavelengths. photons. diffraction pattern (524): A pattern on a screen of construc- concave lens (493): A diverging lens, thinner at its middle tive and destructive interference of Huygens’ wavelets. than at its edges, that spreads out light rays passing through diffuse reflection (459): A scattered, fuzzy reflection pro- it when surrounded by material with a lower index of refrac- duced by a rough surface. tion; produces a smaller, virtual, upright image. dimensional analysis (6): A method of treating units as concave mirror (464): A mirror that reflects light from its algebraic quantities, which can be cancelled; can be used to inwardly curving surface and can produce either an upright, check that an answer will be in the correct units. virtual image or an inverted, real image. diode (784): The simplest semiconductor device; conducts conduction (315): The process by which kinetic energy is charges in one direction only and consists of a sandwich of transferred when particles collide. p-type and n-type semiconductors. conductor (544): A material, such as copper, through which a charge will move easily. dispersion (491): The separation of white light into a spec- consonance (418): A pleasant set of pitches. trum of colors by such means as a glass prism or water convection (317): A type of thermal energy transfer that occurs droplets in the atmosphere. from the motion of fluid in liquid or gas that is caused by displacement (36): A change in position having both magni- differences in temperature. tude and direction; is equal to the final position minus the conventional current (592): A flow of positive charges that initial position. move from higher potential to lower potential. dissonance (418): An unpleasant, jarring set of pitches. convex lens (493): A converging lens, thicker at its center than distance (34): A scalar quantity that describes how far an at its edges, that refracts parallel light rays so the rays meet at object is from the origin. a point when surrounded by material with a lower index of domain (650): A very small group, usually 10–1000 , that is refraction; can produce a smaller, inverted, real image, or a formed when the magnetic fields of the electrons in a group larger, upright, virtual image. of neighboring atoms are aligned in the same direction. convex mirror (471): A mirror that reflects light from its out- dopants (781): Electron donor or acceptor atoms that can be wardly curving surface and produces an upright, reduced, added in low concentration to intrinsic semiconductors, virtual image. increasing their conductivity by making either extra electrons coordinate system (34): A system used to describe motion or holes available. that gives the zero point location of the variable being stud- Doppler effect (407): The change in the frequency of sound ied and the direction in which the values of the variable caused by the movement of either the source, the detector, or increase. both the detector and the source. Coriolis “force” (217): The apparent force that seems to Doppler shift (446): The difference between the observed deflect a moving object from its path and is observed only in wavelength of light and actual wavelength of light based on rotating frames of reference. the relative speed of the observer and the source of the light. coulomb (549): The SI standard unit of charge; one coulomb, drag force (100): The force exerted by a fluid on an object C, is the magnitude of the charge of 6.24 1018 electrons or moving through the fluid; depends on the object’s motion protons. and properties and the fluid’s properties.
920 Glossary 919-926 EM GLOSSARY-845813 3/31/04 7:47 AM Page 921
equivalent resistance (619): For resistors in a series, is the sum of all the individual resistances. excited state (753): Any energy level of an atom that is high-
er than its ground state. Glossary eddy current (681): A current generated in a piece of metal extrinsic semiconductors (781): Semiconductors with great- that is moving through a changing magnetic field, producing ly enhanced conductivity resulting from the addition of a magnetic field that opposes the motion that caused the dopants. current. efficiency (268): The ratio of output work to input work. effort force (266): The force a person exerts on a machine. elastic collision (298): A type of collision in which the kine- tic energy before and after the collision remains the same. elastic potential energy (291): The potential energy that may be stored in an object, such as a rubber band, as a result of farsightedness (501): A vision defect in which a person can- its change in shape. not see close objects clearly because images are focused electric circuit (592): A closed loop or pathway that allows behind the retina; can be corrected with a convex lens. electric charges to flow. first law of thermodynamics (326): States that the change in electric current (592): A flow of charged particles. thermal energy of an object is equal to the heat that is added electric field (563): The field that exists around any charged to the object, minus the work done by the object. object; produces forces that can do work, transferring energy first right-hand rule (648): A method used to determine the from the field to another charged object. direction of a magnetic field relative to the direction of con- electric field lines (567): Lines that provide a picture of an ventional current. electric field, indicate the field’s strength by the spacing fission (811): The process in which a nucleus is divided into between the lines, never cross, and are directed toward nega- two or more fragments, and neutrons and energy are tive charges and away from positive charges. released. electric generator (675): A device that converts mechanical fluids (342): Materials (liquids and gases) that flow and have energy to electric energy and consists of a number of wire no definite shape of their own. loops placed in a strong magnetic field. focal length (464): The position of the focal point with electric motor (656): An apparatus that converts electric ener- respect to the mirror along the principal axis. gy into rotational kinetic energy. focal point (464): The point where incident light rays that are electric potential difference (569): The change in potential parallel to the principal axis converge after reflecting from energy per unit charge in an electric field. the mirror. electromagnet (649): A magnet created when current flows force (88): A push or pull exerted on an object that causes a through a wire coil. change in motion; has both direction and magnitude and electromagnetic induction (672): The process of generating may be a contact or a field force. a current through a circuit due to the relative motion force carriers (818): Particles that transmit, or carry forces between a wire and a magnetic field when the wire is moved between matter. through the magnetic field or the magnetic field moves past fourth right-hand rule (672): A method used to determine the wire. the direction of the forces on the charges in a conductor that electromagnetic radiation (710): Energy that is carried, or is moving in a magnetic field. radiated, in the form of electromagnetic waves. electromagnetic spectrum (709): The entire range of fre- free-body diagram (89): A physical model that represents the quencies and wavelengths that make up all forms of electro- forces acting on a system. magnetic radiation, including radio waves, microwaves, visible free fall (72): The motion of a body when air resistance is light, and X rays. negligible and the motion can be considered due to the force electromagnetic wave (706): Coupled, changing electric and of gravity alone. magnetic field that travels through space. frequency (384): The number of complete oscillations that a electromotive force (673): The potential difference, measured wave makes each second; is measured in hertz, Hz. in volts, given to the charges by a battery; is abbreviated EMF. fundamental (417): For a musical instrument, the lowest fre- electron cloud (761) The region in which there is a high prob- quency of sound that will resonate. ability of finding an electron. fuse (627): A short piece of metal that acts as a safety device electroscope (546): A device that is used to detect electric in an electric circuit by melting and stopping the current charges and consists of a metal knob connected by a metal from flowing if a dangerously high current passes through stem to two thin metal leaves. the circuit. electrostatics (541): The study of electric charges that can be fusion (813): The process in which nuclei with small masses collected and held in one place. combine to form a nucleus with a larger mass and energy is elementary charge (550): The magnitude of the charge of an released. electron. emission spectrum (724): A plot of the intensity of light emitted from a hot body over a range of frequencies. energy (258): The ability of an object to produce a change in itself or in the world around it. energy level (753): The quantized amount of energy that an atom may have in each level. galvanometer (655): A device that is used to measure very entropy (328): A measure of the disorder in a system. small currents; can be used as a voltmeter or an ammeter. equilibrant (131): A force that places an object in equilibrium; gamma decay (806): The radioactive decay process in which is the same magnitude as the resultant, but opposite in direc- there is a redistribution of energy within the nucleus, but no tion. change in atomic mass or charge. equilibrium (95): The condition in which the net force on an gravitational field (183): The field that surrounds any object object is zero. with mass; equals the universal gravitational constant, times equipotential (570): The electric potential difference of zero the mass of the object, divided by the square of the distance between two or more positions in an electric field. from the object’s center.
Glossary 921 919-926 EM GLOSSARY-845813 3/31/04 7:48 AM Page 922
gravitational force (175): The attractive force between two impulse-momentum theorem (230): States that the impulse objects that is directly proportional to the mass of the on an object equals the object’s final momentum minus the objects. object’s initial momentum. gravitational mass (184): The size of the gravitational force incident wave (387): A wave that strikes a boundary between between two objects. two media. gravitational potential energy (288): The stored energy in a incoherent light (515): Light with unsynchronized wave system resulting from the gravitational force between Earth fronts that illuminates objects with an even, white light. and the object. (761): Light whose waves are out of step, with their maxima ground-fault interrupter (627): A device that contains an and minima not coinciding. Glossary electronic circuit that detects small current differences caused independent variable (15): The factor that is changed or by an extra current path; it opens the circuit, prevents electro- manipulated during an experiment. cution, and often is required as a safety measure for bath- index of refraction (486): For a medium, is the ratio of room, kitchen, and exterior outlets. the speed of light in a vacuum to the speed of light in that grounding (548): The process of removing excess charge by medium. touching an object to Earth. inelastic collision (298): A type of collision in which the ground state (753): State of an atom with the smallest allow- kinetic energy after the collision is less than the kinetic ener- able amount of energy. gy before the collision. inertia (95): The tendency of an object to resist change. inertial mass (183): A measure of an object’s resistance to any type of force. instantaneous acceleration (59): The change in an object’s velocity at a specific instant of time. instantaneous position (40): The position of an object at any half-life (809): The time required for half the atoms in a given particular instant in time. quantity of a radioactive isotope to decay. instantaneous velocity (46): A measure of motion that tells harmonics (417): Higher frequencies, which are odd-numbered the speed and direction of an object at a specific instant in multiples of the fundamental frequency; give certain musical time. instruments their own unique timbre. insulator (544): A material, such as glass, through which a heat (317): Energy transferred between two objects in contact charge will not move easily. with one another and always flows from the hotter object to interaction pair (102): A pair of forces that are equal in the cooler object. strength, but opposite in direction. heat engine (326): A device that continuously converts thermal interference (388): Results from the superposition of two or energy to mechanical energy; requires a high-temperature more waves; can be constructive (wave displacements in the thermal energy source, a low-temperature receptacle (a sink), same direction) or destructive (waves with equal but oppo- and a way to convert the thermal energy into work. site amplitudes). heat of fusion (324): The amount of heat required to change interference fringes (516): A pattern of light and dark bands 1 kg of a substance from a solid state to a liquid state at its on a screen, resulting from the constructive and destructive melting point. interference of light waves passing through two narrow, heat of vaporization (324): The amount of heat required to closely spaced slits in a barrier. change 1 kg of a substance from a liquid state to a gaseous intrinsic semiconductors (780): Pure semiconductors that state at its boiling point. conduct charge as a result of thermally freed electrons and Heisenberg uncertainty principle (737): States that it is holes. impossible to simultaneously measure the exact position inverse relationship (18): A hyperbolic relationship that and momentum of a particle of light or matter. exists when one variable depends on the inverse of the other Hooke’s law (376): States that the force acting on a spring is variable. directly proportional to the amount that the spring is isolated system (237): A closed system on which the net exter- stretched. nal force is zero. hypothesis (8): An educated, testable guess about how vari- isotope (701): Each of the differing forms of the same atom ables are related. that have different masses, but have the same chemical properties.
ideal gas law (345): For an ideal gas, the pressure times the volume is equal to the number of moles, times the con- joule (259): Unit of energy, J; 1 J of work is done when a force stant, R, and the Kelvin temperature; predicts the behavior of 1 N acts on an object over a displacement of 1 m. of gases remarkably well unless under high-pressure or low- temperature conditions. ideal mechanical advantage (267): For an ideal machine, is equal to the displacement of the effort force, divided by dis- placement of the load. illuminance (433): The rate at which light strikes a surface, or falls on a unit area; is measured in lumens per square meter, Kepler’s first law (172): States that the planets move in ellip- lm/m2, or lux, lx. tical paths, with the Sun at one focus. illuminated source (432): An object, such as the Moon, that Kepler’s second law (173): States that an imaginary line from becomes visible as a result of the light reflecting off it. the Sun to a planet sweeps out equal areas in equal time image (461): The combination of image points in a plane mir- intervals. ror from which the reflected object seems to originate. Kepler’s third law (173): States that the square of the ratio of impulse (230): The product of the average net force on an the periods of any two planets is equal to the cube of the object and the time interval over which the force acts. ratio of their average distances from the Sun.
922 Glossary 919-926 EM GLOSSARY-845813 6/9/04 4:16 PM Page 923
kilowatt-hour (604): An energy unit used by electric compa- magnetic flux (646): The number of magnetic field lines that nies to measure energy sales; 1 kWh is equal to 1000 watts, pass through a surface. W, delivered continuously for 3600 s (1 h). magnification (468): The amount that an image is enlarged or
kinetic energy (258): The energy of an object, resulting from reduced in size, relative to the object. Glossary its motion. magnitude (35): A measure of size. kinetic friction (126): The force exerted on one surface by a Malus’s law (444): States that the intensity of light coming out second surface when the two surfaces rub against one anoth- of a second polarizing filter equals the intensity of polarized er because one or both of the surfaces are moving. light coming out of a first polarizing filter, times the cosine, squared, of the angle between the polarizing axes of the two filters. mass defect (802): The difference between the sum of the masses of individual nucleons and the actual mass. mass number (800): The sum of the numbers of neutrons and laser (762): A device that produces powerful, coherent, direc- protons in an atom’s nucleus. tional, monochromatic light that can be used to excite other mass spectrometer (701): Device that uses both electric and atoms; the acronym stands for light amplification by stimu- magnetic fields to measure the masses of ionized atoms lated emission of radiation. and molecules and can determine the charge-to-mass ratio of law of conservation of angular momentum (243): States an ion. that if there are no net external torques on an object, then its measurement (11): A comparison between an unknown angular momentum is conserved. quantity and a standard. law of conservation of energy (293): States that in a closed, mechanical advantage (266): The ratio of resistance force to isolated system, energy is not created or destroyed, but rather, effort force. is conserved. mechanical energy (293): The sum of kinetic and gravitation- law of conservation of momentum (237): States that the al potential energy of a system. momentum of any closed, isolated system does not change. microchip (788): An integrated circuit consisting of thousands law of reflection (391): States that the angle of incidence is of diodes, transistors, resistors, and conductors. equal to the angle of reflection. (458): States that the angle mirror equation (467): Relates the focal length, the object a reflected ray makes, as measured from the normal to a position, and the image position of a spherical mirror. reflective surface, equals the angle the incident ray makes, as moment of inertia (205): The resistance to rotation. measured from the same normal. momentum (230): The product of the object’s mass and the law of universal gravitation (175): States that gravitational force between any two objects is directly proportional to the object’s velocity; is measured in kg m/s. product of their masses and inversely proportional to the monochromatic light (516): Light having only one wave- square of the distance between their centers. length. lens (493): A piece of transparent material, such as glass or motion diagram (33): A series of images showing the positions plastic, that is used to focus light and form an image. of a moving object taken at regular (equal) time intervals. Lenz’s law (679): States that an induced current always is pro- mutual inductance (682): Effect in which a changing current duced in a direction such that the magnetic field resulting through a transformer’s primary coil creates a changing from the induced current opposes the change in the magnet- magnetic field, which is carried through the core to the trans- ic field that is causing the induced current. former’s secondary coil, where the changing field induces a leptons (818): Any of a family of particles like electrons and varying EMF. neutrinos. lever arm (201): The perpendicular distance from the axis of rotation to the point where force is exerted. linear relationship (16): A type of relationship that exists between two variables whose graphed data points lie on a straight line. line of best fit (15): A line that best passes through or near nearsightedness (501): A vision defect in which a person graphed data; used to describe data and predict where new cannot see distant objects clearly because images are focused data will appear on the graph. in front of the retina; can be corrected with a concave lens. longitudinal wave (381): A mechanical wave in which the dis- net force (92): The vector sum of all the forces on an object. turbance is in the same direction, or parallel to, the direction neutral (543): An atom whose positively charged nucleus of wave motion. exactly balances the negative charge of the surrounding loudness (406): Sound intensity as sensed by the ear and electrons. interpreted by the brain; depends mainly on the pressure Newton’s first law (94): States that an object at rest will wave’s amplitude. remain at rest, and a moving object will continue moving in luminous flux (433): The rate at which light energy is emitted a straight line with constant speed, if and only if the net force from a luminous source; is measured in lumens, lm. acting on that object is zero. luminous source (432): An object, such as the Sun or an Newton’s second law (93): States that the acceleration of an incandescent lamp, that emits light. object is proportional to the net force and inversely propor- tional to the mass of the object being accelerated. Newton’s second law for rotational motion (208): States that the angular acceleration of an object is directly propor- tional to the net torque and inversely proportional to the moment of inertia. machine (266): A tool that makes work easier (but does not Newton’s third law (102): States that all forces come in pairs change the amount of work) by changing the magnitude or and that the two forces in a pair act on different objects and the direction of the force exerted to do work. are equal in strength and opposite in direction. magnetic field (645): The area around a magnet, or around node (389): The stationary point where two equal wave puls- any current-carrying wire or coil of wire, where a magnetic es meet and are in the same location, having a displacement force exists. of zero.
Glossary 923 919-926 EM GLOSSARY-845813 6/9/04 4:16 PM Page 924
normal (391): The line in a ray diagram that shows the direc- physics (3): The study of matter and energy and their relation- tion of the barrier and is drawn at a right angle, or perpendi- ships. cular, to the barrier. piezoelectricity (711): The property of a crystal that causes it normal force (107): The perpendicular contact force exerted to bend or deform, producing electric vibrations, when a by a surface on another object. voltage is applied across it. nuclear reaction (807): Occurs when the number of neutrons pitch (406): The highness or lowness of a sound wave, which or protons in a nucleus changes; can be produced by bom- depends on the frequency of vibration. bardment of nuclei by gamma rays, other nuclei, protons, plane mirror (461): A flat, smooth surface from which light is neutrons, alpha particles, or electrons. reflected by regular reflection, producing a virtual image that Glossary nucleons (802): Protons and neutrons. is the same size as the object, has the same orientation, and nucleus (749): The tiny, massive, positively charged central is the same distance from the mirror as the object. core of an atom. plasma (348): A gaslike, fluid state of matter made up of neg- nuclide (801): The nucleus of an isotope. atively charged electrons and positively charged ions that can conduct electricity; makes up most of the matter in the uni- verse, such as stars. polarization (443): Light whose waves oscillate only in a single plane. (644): For a magnet, describes the property of having two distinct, opposite ends, one of which is a north- seeking pole and the other of which is a south-seeking pole. object (461): A luminous or illuminated source of light rays position (34): The separation between an object and the that are to be reflected by a mirrored surface. origin; it can be either positive or negative. observed light frequency (446): The frequency of light as position-time graph (38): A graph that can be used to deter- seen by an observer. mine an object’s velocity and position, as well as where and opaque (433): A medium that absorbs light and reflects some when two objects meet, by plotting the time data on a hori- light rather than transmitting it, preventing objects from zontal axis and the position data on a vertical axis. being seen through it. power (263): The work done, divided by the time needed to open-pipe resonator (412): A resonating tube with both ends do the work. open that also will resonate with a sound source; its resonant precision (12): A characteristic of a measured value describing frequencies are whole-number multiples of the fundamental. the degree of exactness of a measurement. origin (34): The point at which both variables in a coordinate pressure (342): The force on a surface, divided by the surface’s system have the value zero. area. primary coil (682): An electrically insulated transformer coil, which, when connected to an AC voltage source, induces an alternating EMF in the secondary coil. primary color (440): Red, green, and blue, which can be com- bined to form white light and mixed in pairs to produce the pair production (820): The conversion of energy into a matter- secondary colors: yellow, cyan, and magenta. antimatter pair of particles. primary pigment (441): Cyan, magenta, and yellow, each of parallel circuit (623): A type of electric circuit in which there which absorbs one primary color from white light and are several current paths; its total current is equal to the sum reflects two primary colors; can be mixed in pairs to produce of the currents in the individual branches, and if any branch the secondary pigments: red, green, and blue. is opened, the current in the other branches remains principal axis (464): A straight line perpendicular to the unchanged. surface of a mirror that divides the mirror in half. parallel connection (600): A type of connection in which the principle of superposition (388): States that the displacement circuit component and the voltmeter are aligned parallel to of a medium caused by two or more waves is the algebraic one another in the circuit, the potential difference across the sum of the displacements of the individual waves. voltmeter equals the potential difference across the circuit principal quantum number (755): The integer, n, that deter- element, and there are two or more current paths to follow. mines the quantized values of r and E for an electron’s particle model (33): A simplified version of a motion diagram orbital radius in hydrogen and the energy of a hydrogen in which the moving object is replaced by a series of single atom—the radius, r, increases as the square of n, whereas points. the energy, E, depends on 1/n2. pascal (342): The SI unit of pressure. projectile (147): An object shot through the air, such as a foot- Pascal’s principle (352): States that any change in pressure ball, that has independent vertical and horizontal motions applied at any point on a confined fluid is transmitted undi- and, after receiving an initial thrust, travels through the air minished throughout the fluid. only under the force of gravity. pendulum (378): A device that can demonstrate simple har- monic motion when its bob (a massive ball or weight), sus- pended by a string or light rod, is pulled to one side and released, causing it to swing back and forth. period (375): In any periodic motion, the amount of time required for an object to repeat one complete cycle of motion. quadratic relationship (17): A parabolic relationship that periodic motion (375): Any motion that repeats in a regular results when one variable depends on the square of another cycle. variable. periodic wave (381): A mechanical wave that moves up and quantized (725): Energy exists only in bundles of specific down at the same rate. amounts. photoelectric effect (726): The emission of electrons by cer- quantum mechanics (761): The study of the properties of tain metals that is produced when they are exposed to elec- matter, using its wave properties. tromagnetic radiation. quantum model (760): A model that predicts only the proba- photon (727): A discrete, quantized bundle of radiation that bility that an electron is in a particular region. travels at the speed of light, has zero mass, and has energy quarks (818): Tiny particles that make up protons, neutrons, and momentum. and pions.
924 Glossary 919-926 EM GLOSSARY-845813 3/31/04 8:00 AM Page 925
second law of thermodynamics (330): States that natural processes go in a direction that maintains or increases the total entropy of the universe.
second right-hand rule (649): A method used to determine Glossary radian (197): 1 of a revolution; abbreviated “rad.” the direction of the field produced by an electromagnet, 2 radiation (317): The thermal transfer of energy by electromag- relative to the flow of conventional current. netic waves through the vacuum of space. self-inductance (682): The inductance of EMF in a wire carry- radioactive (806): Materials that undergo radioactive decay ing a changing current. and emit penetrating rays. semiconductors (775): Conductive materials, such as silicon ray (390): A line that can show the direction a wave is travel- or germanium, which, when made into solid-state devices, ing and is drawn at a right angle to a wave’s crest. can amplify and control weak electric signals through elec- tron movement within a tiny crystalline space. ray model of light (432): A model that represents light as a series circuit (618): A type of electric circuit in which all cur- ray that travels in a straight path, whose direction can be rent travels through each device and is the same everywhere; changed only by putting an obstruction in the path. its current is equal to the potential difference divided by the Rayleigh criterion (530): States that if the central bright spot equivalent resistance. of one image falls on the first dark ring of the second image, series connection (600): A type of connection in which there the images are at the limit of resolution. is only a single current path. real image (465): An inverted optical image that is smaller short circuit (627): Occurs when a very low resistance circuit than the object and is formed by the converging of light rays. is formed, causing a very large current that could easily start receiver (712): A device used to obtain information from elec- a fire from overheated wires. tromagnetic waves; consists of an antenna, a coil-and-capacitor significant digits (7): All the valid digits in a measurement, circuit, a detector to decode the signal, and an amplifier. the number of which indicates the measurement’s precision. reference level (288): The position where gravitational poten- simple harmonic motion (375): A motion that occurs when tial energy is defined as zero. the restoring force on an object is directly proportional to the reflected wave (387): An erect or inverted returning wave that object’s displacement from equilibrium. results from some of the energy of the incident wave’s pulse Snell’s law of refraction (486): States that the product of the being reflected backward. index of refraction of a medium and the sine of the angle of refraction (391): The change in direction of waves at the incidence equals the product of the index of refraction of a boundary between two different media. second medium and the sine of the angle of refraction. resistance (595): A property that determines how much cur- solenoid (649): A long coil of wire with many loops; fields rent will flow; is equal to voltage divided by current. from each loop add to the fields of the other loops, creating resistance force (266): The force exerted by a machine. a greater total field strength. resistor (596): A device with a specific resistance; may be sound level (406): A logarithmic scale that measures ampli- made of long, thin wires; graphite; or semiconductors tudes; depends on the ratio of the pressure variation of a and often is used to control the current in circuits or parts of particular sound wave to the pressure variation in the most circuits. faintly heard sound; unit of measurement is the decibel, dB. resonance (380): A special form of simple harmonic motion sound wave (404): A pressure variation transmitted through that occurs when small forces are applied at regular intervals matter as a longitudinal wave; it reflects and interferes and to an oscillating or vibrating object and the amplitude of the has frequency, wavelength, speed, and amplitude. vibration increases. specific heat (318): The amount of energy that must be added resultant (35): A vector that results from the sum of two to a material to raise the temperature of a unit mass by one other vectors; it always points from the first vector’s tail to the temperature unit; is measured in J/kg K. last vector’s tip. specular reflection (459): A reflection produced by a smooth rotational kinetic energy (287): The kinetic energy of an surface in which parallel light rays are reflected in parallel. object, proportional to the object’s moment of inertia and spherical aberration (467): The image defect of a spherical the square of its angular velocity. mirror that does not allow parallel light rays far from the principal axis to converge at the focal point, and produces an image that is fuzzy, not sharp. Standard Model (818): A model of the building blocks of matter in which all particles can be grouped into three fami- lies: quarks, leptons, and force carriers. standing wave (389): A wave that appears to be standing still, scalars (35): Quantities, such as temperature or distance, that produced by the interference of two traveling waves moving are just numbers without any direction. in opposite directions. scientific law (9): A well-established rule about the natural static friction (126): The force exerted on one surface by a world that sums up, but doesn’t explain, a pattern in nature. second surface when there is no motion between the two scientific method (8): A systematic method of observing, surfaces. experimenting, and analyzing to answer questions about the step-down transformer (682): A type of transformer in natural world. which the voltage coming out of the transformer is smaller scientific theory (10): An explanation based on numerous than the voltage put into the transformer. observations, supported by experimental results, that may step-up transformer (682): A type of transformer in which explain why things work the way they do. the secondary voltage coming out of the transformer is larg- secondary coil (682): An electrically insulated transformer er than the primary voltage going into the transformer. coil in which an alternating EMF is induced by an AC current stimulated emission (762): The process that occurs when an through the primary coil. excited atom is struck by a photon having energy equal to the secondary color (440): Yellow, cyan, and magenta, each of energy difference between the excited state and the ground which is produced by combining two primary colors. state—the atom drops to the ground state and emits a secondary pigment (441): Red, green, and blue, each of photon with energy equal to the energy difference between which absorbs two primary colors from white light and the two states. reflects one primary color; can be produced by mixing pairs streamlines (358): Lines representing the flow of fluids of cyan, magenta, and yellow pigments. around objects.
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strong nuclear force (802): An attractive force that binds the nucleus together; is of the same strength between protons and protons, protons and neutrons, and neutrons and neutrons. superconductor (603): A material with zero resistance that vector resolution (122): The process of breaking a vector into can conduct electricity without a loss of energy. its components. surface wave (382): A mechanical wave in which the particles vectors (35): Quantities, such as position, that have both mag- move both parallel and perpendicular to the direction of nitude and direction. wave motion. velocity-time graph (58): A graph that can be used to plot the Glossary velocity of an object versus time and to determine the sign of an object’s acceleration. virtual image (461): The image formed of diverging light rays; is always on the opposite side of the mirror from the object. volt (569): The unit equal to one joule per coulomb, 1 J/C. voltage divider (620): A series circuit that is used to produce tension (105): The specific name for the force exerted by a a voltage source of desired magnitude from a higher-voltage rope or a string. battery; often is used with sensors such as photoresistors. terminal velocity (101): The constant velocity of an object that voltmeter (631): A high-resistance device used to measure the is reached when the drag force equals the force of gravity. voltage drop across any portion or a combination of portions thermal energy (295): A measure of the internal motion of an of a circuit and is connected in parallel with the part of the object’s particles. circuit being measured. thermal equilibrium (315): The state in which the rate of energy flow between two objects is equal and the objects are at the same temperature. thermal expansion (347): A property of all forms of matter that causes the matter to expand, becoming less dense, when heated. watt (263): Unit of power, W; 1 J of energy transferred in 1 s. thin-film interference (520): A phenomenon in which a wave (381): A disturbance that carries energy through matter spectrum of colors is produced due to the constructive and or space; transfers energy without transferring matter. destructive interference of light waves reflected in a thin film. wave front (390): A line representing the crest of a wave in two thin lens equation (493): States that the inverse of the focal dimensions that can show the wavelength, but not the length of a sperical lens equals the sum of the inverses of the amplitude, of the wave when drawn to scale. image position and the object position. wavelength (383): The shortest distance between points where third right-hand rule (652): A method that can be used to the wave pattern repeats itself, such as from crest to crest or determine the direction of the force on a current-carrying from trough to trough. wire in a magnetic field. wave pulse (381): A single disturbance or pulse that travels threshold frequency (726): The certain minimum value at or through a medium. above which the frequency of radiation causes the ejection of weak nuclear force (821): A weak force acting in the nucleus electrons from a metal. in beta, , decay. time interval (36): The difference between two times. weightlessness (98): An object’s apparent weight of zero that torque (202): A measure of how effectively a force causes rota- results when there are no contact forces pushing up on the tion; is equal to the force times the lever arm. object. total internal reflection (489): Occurs when light traveling work (258): The transfer of energy by mechanical means; is through an area with a higher index of refraction to an area done when a constant force is exerted on an object in the with a lower index of refraction hits a boundary at an angle direction of motion, times the object’s displacement. that exceeds the critical angle and all light reflects back into work-energy theorem (258): States that when work is done the area with the higher index of refraction. on an object, a change in kinetic energy occurs. trajectory (147): The path of a projectile through space. work function (731): The energy required to free the most transformer (682): A device that can decrease or increase the weakly bound electron from a metal; measured by the voltages in AC circuits with relatively little energy loss. threshold frequency in the photoelectric effect. transistor (787): A simple device made of doped semicon- ducting material that can act as an amplifier, converting a weak signal to a much stronger one. translucent (433): A medium that transmits light and also can reflect a fraction of the light, but does not allow objects to be seen clearly through it. transparent (433): A medium that transmits light and also X ray (713): High-frequency electromagnetic wave emitted by can reflect a fraction of the light, allowing objects to be seen rapidly accelerated electrons. clearly through it. transverse wave (381): A mechanical wave that vibrates per- pendicular to the direction of the wave’s motion. trough (383): The low point of a wave.
uniform circular motion (153): The movement of an object or particle trajectory at a constant speed around a circle with a fixed radius.
926 Glossary 927-942 EM INDEX-845813 6/10/04 9:15 PM Page 927
acceleration of free-fall rides, 74; Armatures, 656 centrifugal “force” and, 216; Arsenic, semiconductors and, 781 confusion of body’s systems by, Artificial intelligence, 792 138; conservation of mechanical Artificial radioactivity, 811 Aberration, chromatic, 499; in energy by, 294 Artificial satellites, Kepler’s laws and Hubble Space Telescope, 467; Analyzers, 444 orbit of, 173; Landsat 7, 180; limits on spherical, 467, 498 Angle of incidence, 486, 488; critical, mass of, 180; orbital speed and period Absolute value, 841 489; law of reflection and, 458, 459, of, 180, 181 prob. Absolute zero, 316 460 prob.; total internal reflection Astrolabe, 172 illus. Absorption spectrum, 751–752 and, 489; two-dimensional waves Astronauts, weightlessness of in Acceleration, 59–64; angular, 199, 199 and, 391 space, 182 table; average (a), 59–64, 63 prob., Angle of reflection, 391 Astronomy, expansion of the universe, 65, 68; centripetal, 153, 154–155; Angle of refraction, 486, 487 prob.; 447; Hubble Space Telescope, 467; use of constant, 57 lab, 65–71, 68 table; total internal reflection and, 489–490; Doppler effect by, 410 direction of, 63; of Earth, 104 prob.; wave model of light and, 488 Atmosphere, convection in, 317 force and, 88, 90–91; gravity and free Angle of revolution, 198 Atmospheric pressure, 343, 343 table fall and, 72–75; instantaneous, 59; Angle of the resultant vector, 123 Atom laser, 768 linear vs. angular, 199 table; motion Angular acceleration, 199 Atom smashing, 799 diagrams and, 60, 60 prob.; Newton’s Angular displacement, 198 Atomic clocks, 50, 445
second law and. See Newton’s second Index Angular frequency, 200 Atomic mass unit, 800 law; positive and negative, 61–62; Atomic number (Z), 800 Angular impulse-angular momentum velocity-time graphs and, 62; Atomic particles, 748 theorem, 234–235 velocity vs., 64 Atomic spectra, absorption spectrum, Acceleration due to gravity (g), 72–75, Angular momentum, 233–235; 751–752; Balmer series and, 756 illus.; 74 prob., 76–77 lab; amusement park conservation of, 243–245; of determining atomic structure from, rides, 74; ball thrown upwards, 72–73; electrons, 755 752; emission spectra, 749–750, pendulums and, 378–379, 379 prob., Angular velocity, 198–199; affect of 752, 755 lab 392–393 lab; from universal force on, 201; conservation of angular Atomic structure, Bohr model of, gravitation and Newton’s second momentum and, 243–245 752–756, 757 prob., 758 prob., 759, law of motion, 182; weightlessness Animals, body temperature of, 322 759 prob.; nuclear model of, 748–752, of water in falling cup and, 182 lab Annihilation, positron/electron, 766–767 lab; quantum model of, Accelerators, linear, 815; 819–820 760–761 synchrotrons, 816 Anodes, 726 Atomizers, Bernoulli’s principle and, Accommodation, 500 Antenna, 707–708, 712 357 Accuracy, 13–14 Antimatter, 819–820; pair production Atoms, 747–765; absorption spectrum Achromatic lenses, 499, 502 and, 820; particle conservation and, 751–752; charge of, 543–544; Activities. See Launch Labs; MiniLabs; and, 820 electron orbital radius, 755; Physics Labs Antineutrino, 818, 822 emission spectra from, 749–750, Activity, 810 Antineutrons, 820 752, 755 lab; energy of emitted Adaptive optical system (AOS), 476 Antinodes, 389 photons from, 753–754; energy Additive color process, 440 Antiparticles, 819 of, total, 755, 757 prob.; energy of Adhesive forces, 350 Antiprotons, 820 vibration of (E), 725; excitation of, Agent, 88 Aperture, 530 761–762; lasers from excited. See Air bags, 231 Apparent weight, 98, 99 prob., 182 Lasers; mass of, 749; neutral, 543; Air columns, resonance in, 412–414 Applying Physics, carbon conductors, quantized energy levels in, 753–754; Air, conduction by, 545 544; contact lenses, 501; dragster relative size of potential energy of, Air resistance, drag force and, 100–101; records, 68; electromagnets, 649; 289; spinning coins as model projectile motion and, 152; streamlines Fosbury-Flop, 212; friction, causes of, of, 747 lab and, 358 130; geosynchronous orbits, 180; hear- Audiocassette recorders, 651 Aircraft, streamlining of, 358 ing and frequency, 413; illuminance of Auditory canal, 405 Alcohol molecules, evaporation of, desktops, 435; nonreflective eyeglasses, Automobile carburetors, 351, 364–365 lab 520; ohmmeters, 624; potential energy Bernoulli’s principle and, 357 Algorithms, 22 of an atom, 289; power output of Automobile engines, first law of ALNICO V, 645 Tour de France racer, 265; relative size thermodynamics and, 326–327; Alpha decay, 806, 808 prob. of potential energy of atom, 289; spark plugs in, 662 Alpha particles, 748, 806, 807 table resistance, 597; running shoes, 231; Automobile transmissions, ideal Alpha radiation, 806 speed records, 44; spherical aberration mechanical advantage (IMA) of, Alternating current (AC), 677, 682, on Hubble Space Telescope, 467; static 272 707–708, 709 electricity, damage to electronic devices Automobiles, collisions of, 231; elastic Alternating current (AC) generators, by, 570; steam heat, 317; transformer potential energy of bumpers, 378; 677–678 ratings, 683 hybrid cars, 608; speed of, 20–21 lab; AM radio waves, 697 lab streamlining of, 358 Arago, Jean, 519 Ammeter, 595, 599, 600, 631, 655, Average acceleration (a), 59–64, 63 Archimedes, 354 729 illus. prob., 65, 68 Amorphous solid, 359 Archimedes’ principle, 354–355, Average power, 677 Ampere (A), 5 table, 593 356 prob. Average speed, 44, 45 prob. Ampère, André-Marie, 650 Arcs, electric, 556 Average velocity, 44, 45 prob.; equation Amplifier, 788 Area, force and pressure and, for, 44; motion diagrams and, 46–47 Amplitude, 375, 382–383, 392–393 lab, 342, 343 prob. Avogadro, Amedeo, 345 405–407 Aristotle, 3 lab Avogadro’s number, 345 Amusement-park rides, accelerated Arithmetic, significant digits and, Axis, principle, 464 frames of reference and, 216; 7, 8 prob. Axles, 269
Index 927 927-942 EM INDEX-845813 6/10/04 9:16 PM Page 928
Bottom quarks, 819 illus. Cerenkov effect, 812 illus. Bow and arrow, elastic potential Cesium clocks, 50 energy and, 291 Chadwick, James, 800 Boyle, Robert, 344 Chain reactions, 812 Back-EMF, 680–681 Boyle’s law (volume and pressure of Challenge Problems, Bohr model of Balanced electric circuits, 628 prob. a gas), 344, 346 prob. the atom, 759 prob.; capacitance (C), Balances, Lenz’s law and, 680–681 Brahe, Tycho, 171, 172 579 prob.; coiled springs, 380 prob.; Balloons, charging of, 563 lab Brass instruments, source of sound collisions and conservation of energy, Balls, acceleration of one thrown from, 411 300 prob.; concave mirror, locating upward, 72–73; change in momentum Bridges, earthquake-proof, 394 image on, 470 prob.; Coulomb’s law of after collision, 231; energy change Bright-line emission spectra, and electric force, 552 prob.; current- from throwing and catching (work- 750, 755 lab voltage curve of a diode, 786 prob.; energy theorem), 286–287; flight Brushes, 656 distribution transformers, 685 prob.; of one thrown at an initial angle, Bubble chambers, 817 electric circuits, balanced, 628 prob.; 151 prob.; momentum of two Buildings, earthquake-proof, 394 entropy, 329 prob.; force and motion colliding, 236 Buoyant force, 341 lab, 354–355, 356 in one dimension, 100 prob.; free-fall Balmer series, 756 illus. prob. objects, 75 prob.; graphing, 18 prob.; Band theory of solids, 776–777 Butterflies, thin-film interference kinetic energy of photoelectron, 731 Bands, conduction, 776–777; on wing of, 523, 530 prob.; lenses and human vision, 501 valence, 776–777 prob.; linear expansion and, 363 prob.; Base, transistor, 787 moment of inertia (I), 208 prob.; Base units, SI, 5, 5 table motion on inclined planes, 132 prob.; Bathroom scales, 96, 98, 110 physics of music, 417 prob.; planetary Index Bats, Doppler effect and, 410 motion, 176 prob.; power and efficiency, Batteries, 592 Cadmium, nuclear reactors and, 813 268 prob.; reduction of light intensity Beats, 418 Callisto, distance of from Jupiter, when passed through second filter BEC. See Bose-Einstein condensates 174 prob. (Malus’s law), 444 prob.; relative-velocity, Becquerel, Henri, 799, 806 Calorimeter, 319, 321 prob. 157 prob.; single-slit diffraction, 526 Bernoulli, Daniel, 357, 546 Calorimetry, 319–320, 321 prob. prob.; torque of electric motors, 656 Bernoulli’s principle (velocity and Cameras, lenses in, 503 prob.; two-dimensional collisions and, pressure of moving fluid), 357 Cancer, from cellular phones, 716; 244 prob.; uniform straight-line motion Beta decay, 806, 808 prob. See also radiation treatments for, 811 of multiple objects, 40 prob.; voltage Radioactive decay; weak interactions Candela (cd), 5 table, 434 across a capacitor, 604 prob. and, 821–822 Capacitance (C), 577; charging of Chandra X-ray Observatory, 188 Beta particles, 806, 807 table capacitors, 580–581 lab; determining, Changes of state, 323–324; boiling Beta radiation, 806. See also Radiation; 577, 578, 578 prob.; unit of (farad), 578 point, 323–324; heat of fusion, 324, distance and intensity of, 824–825 lab Capacitors, 577–579; capacitance (C) 324 table, 325 prob.; heat of vaporiza- Bicycle gears, ideal mechanical advan- of, 577, 578, 578 prob.; charging of, tion, 324, 324 table; melting point, tage (IMA), 270, 270 lab, 271 prob., 580–581 lab; controlling capacitance, 323, 324 lab 272, 276 579; electromagnetic waves from, Charge, atomic, 543–544; electrostatic. Bicycles, 270, 276; ideal mechanical 709–710; types of, 577 illus., 579 See Electrostatic charge; elementary, advantage (IMA) of, 270, 270 lab, 271 Capillary action, 350 550; neutral, 543 prob., 272; mechanical advantage (MA) Carbon, 544 Charge pumps, 592 of, 270, 272; multi-gear, 272; power Carbon-14 dating, 11, 810 Charge-to-mass ratio, of electrons, output of Tour de France racer, 265 Carburetors, Bernoulli’s principle 698–699; of ion in a mass spectrome- Big Bang Theory, 9 illus. and, 357 ter, 702, 703 prob.; of protons, 699–700 Billiard ball collisions, 301 Careers, physics-related, 3 Charged objects, 542–544, 554–555 Bimetallic strips, 363 Carnot, Sadi, 328 lab. See also Neutral objects; charging Binary numbers, 22 Carriers, force, 818 by conduction, 547; charging by Binding energy, nuclear, 799 lab, Cars. See Automobiles induction, 548; forces on, 546–548; 802–804, 804 prob. Cassette tapes, 651 like charges, 542; opposite charges, Binoculars, lenses in, 502 Cathode-ray tube, 657; charge-to-mass 542–543 Black holes, 185, 188 ratio of electrons and, 698–699; Charges, 542–544. See also Electric Blood pressure, 343 table charge-to-mass ratio of protons and, currents; Electrostatics; elementary, Blue-shifted light, 446 699–700 550; like, 542; neutral, 543; opposite, Bob, pendulum, 378 Cathodes, 726 542–543; separation of, 544, 547; Body temperature, regulation of, 322 Cavendish, Henry, 177–178, 546 sharing of, 575–576; storing of, 577; Bohr model of the atom, 752–756, CD players, 764 unit of (C), 549, 578 759; energy of emitted photons, Cells, photovoltaic, 592 Charging by conduction, 547, 549 lab 753–754, 758 prob.; ionization energy Cellular phones, 716 Charging by induction, 548, 549 lab and, 759; Newton’s second law and, Celsius, Anders, 316 Charles, Jacques, 344 754–755; orbital energy values, 756, Celsius scale, 316 Charles’s law (volume and tempera- 757 prob.; orbital radius and, 755, 760; Center of mass, 211–212; of human ture of a gas), 344 problems with, 754, 759 prob.; quan- body, 212; locating, 211, 213 lab; Charm quarks, 819 illus. tized energy levels in, 753–754 stability and, 212–213 Chips, 22, 789 Bohr, Niels, 752–753, 754–755, 759 Centi-, 6 table Chlorophyll, 442 Bohr radius, 755 Centrifugal “force”, 156, 216 Chromatic aberration, 499 Boiling point, 323–324 Centripetal acceleration, 153, Circuit breakers, 627–628 Boltzmann’s constant (k), 345 154–155, 216 Circuits. See Electric circuits Bose-Einstein condensates, 366, 768 Centripetal force, 154, 155 Circular motion, uniform. See Uniform Bose, Satyendra Nath, 366, 768 Centripetal motion, space station circular motion Bosons, 768 design and, 162 Circular waves, 390–391
928 Index 927-942 EM INDEX-845813 6/10/04 9:17 PM Page 929
Clarinets, sound from, 411, 414, 417 Compound machines, 269–270; Convex lenses, 493; focal length and, Clocks, cesium, 50; light, 78 bicycles, 270, 271 prob., 272, 276; ideal 495, 504–505 lab; masking of, 495 lab; Closed-pipe resonators, 412, 413, 414, mechanical advantage (IMA) of, 270, properties of, 494, 494 table; real 416 prob., 420–421 lab 271 prob., 272; mechanical advantage images and, 494–495, 496 prob.; Closed systems, 236 (MA) of, 270, 271 prob. virtual images and, 494, 497 Cloud chamber, Wilson, 817 Compton, Arthur Holly, 733, 734 Convex mirrors, 471; field of view of, Cochlea, 405 Compton effect, 733–734 471; location of image on, 471, 472 Coefficient of friction ( ), 127, Computer animation, 19 illus. prob.; vs. other single-mirror systems, 129–130, 136–137 lab; kinetic ( ), Computer storage disks, 659 473 table; virtual images formed by, k 127, 129 table, 136–137 lab; static ( s), Computers, 22, 659 471 127, 129 table, 136–137 lab; Concave lenses, 493, 498; properties Coordinate systems, 34–35, 122, 135, typical values, 129 table of, 494, 494 table; thin lens equation 155, 848 Coefficient of kinetic friction ( k), and, 494, 498 Copernicus, Nicholas, 171 127, 129 table, 136–137 lab Concave mirrors, 464–468, 470; locat- Copper, ductility of, 360 Coefficient of linear expansion, 361, ing image on, 465–468, 469 prob., 470 Coriolis “force”, 216–217 361 table prob.; vs. other single-mirror systems, Cornell, Eric, 366, 768 Coefficient of static friction ( s), 127, 473 table; Problem-Solving Strategies, Cosines, law of, 120 129 table, 136–137 lab 466; real image defects on, 467; real COSTAR, 467 Coefficient of volume expansion, 361, image formed by, 466, 474–475 lab; Coulomb (C), 549–550
361 table virtual image formed by, 470, Coulomb, Charles, 549 Index Coefficients of thermal expansion, 474–475 lab Coulomb’s law, 549–550, 551 prob., 361, 361 table Condensation, 351 552, 552 prob.; direction of magnitude Coherent light, 516–519, 761; from Condensation trails, 817 of force and, 550; equation for, 550; incoherent with double-slit experi- Conduction, 315; band theory of Problem-Solving Strategies, 550 ment, 517; interference of, 516–519; solids and, 776–777; charging by, Credit card readers, 688 from lasers, 763. See also Lasers 547, 549 lab; electrical, 777; heat Crest, wave, 383 Cohesive forces, 349; in plants, 350; transfer by, 315, 317; in solids, Critical angle ( c), 489 surface tension and, 349, 350 illus.; 775–783 Crystal lasers, 764 viscosity and, 349 Conduction bands, 776–777 Crystal lattice, 359 Coil-and-capacitor circuit, electro- Conductivity, 777 Cube roots, 840 magnetic waves from, 709–710 Conductors, electrical, 544–545; air as, Curie, Marie, 3, 799 Coiled springs. See Springs 545; electric fields near, 576–577; free Curie, Pierre, 799 Coils, primary, 682; secondary, 682 electrons in solid, 777, 778 prob. Currents. See Electric currents Cold-blooded animals, 322 Connecting Math to Physics, 47, 68, Curved mirrors, comparing, 473, 473 Collider Detector at Fermilab (CDF), 123, 521, 728; adding and subtracting table; concave, 464–470; convex, 471, 817 fractions, 468; direct and inverse rela- 472 prob.; mathematical method to Collisions, baseballs, 231; billiard balls, tionships, 175, 435; inequalities, 683; locate image on, 467, 469 prob.; 301; car crashes, 231; conservation reducing equations, 408 magnification by, 468; parabolic, 467; of energy and, 297–298, 299 prob., Conservation of angular momentum, ray tracing to locate images formed 300 prob., 300–301; conservation of 243–245; angular velocity and, by, 465–467 momentum and, 300; elastic, 298, 243–244; tops and gyroscopes Cymbals, source of sound from, 411 301 lab; ice skating and, 301; impulse and, 244–245 and momentum and, 230–231, 232 Conservation of energy, 285 lab, prob.; inelastic, 298; superelastic 293–301; in a calorimeter, 319–320; (explosive), 298; two-dimensional, collisions between two objects and, 241, 242 prob.; two-particle, 236, 297–298, 299 prob., 300–301; 246–247 lab conservation of mechanical energy Dalziel, Harles, 634 Color printers, additive pigment and, 293–295, 296 prob.; loss of Dams, 676–677 process, 442 mechanical energy and, 295; Problem- Dark matter, 823 Color television tubes, additive color Solving Strategies, 295; transfer of Davisson, Clinton, 735 process and, 440 potential energy to kinetic energy de Broglie, Louis, 735, 760, 768 Colors, 440–442; additive color process, and, 301 lab, 302–303 lab de Broglie wavelength, 735, 736 prob., 440–441, 442; complementary, 441; Conservation of momentum, law of, 760 green plants and chlorophyll, 442; hot 237. See also Momentum Dead spots, 405 and cool, 441 lab; Newton’s study of, Consonance, 418 Decay. See also Radioactive decay; alpha, 440; primary, 440; secondary, 440; Constant acceleration, 65–71; displace- 806, 808 prob.; beta, 806, 808 prob.; subtractive color process, 441–442; ment and, 67 prob.; equations for, 68 gamma, 806; nuclear reactions and, thin-film interference and reinforce- table; position and, 66, 68, 68 table; 807–808, 809 prob. ment of, 520–521 velocity and, 65, 68, 68 table Deci-, 6 table Combination series-parallel circuits, Constructive interference, 516; from Decibel (dB), 406 629, 630 prob. diffraction gratings, 528; double-slit Deep Space 1, 239 Combined gas law, 345 interference and, 516, 517, 518; Deflection of light, Einstein’s theory Comets, 172 mechanical waves and, 389; thin-film of relativity, 185 Commutators, 656 interference and, 520 Density, free-electron, 777, 778 prob. Compact discs (CDs), lasers in CD Contact forces, 88 Dependent variables, 15, 16, 848 players, 764; as reflection gratings, Contact lenses, 501 Depletion layer, 784 515 lab, 527 Control rods, 813 Derived units, SI, 5 Compasses, 648 Controlled chain reactions, 812–813 Descartes, Réne, 486 Complementary colors, 441 Convection, 317 Destructive interference, 516; double- Complementary pigments, 442 Conventional currents, 592 slit interference and, 516, 517, 518; Components, vector, 122. Converging lenses. See Convex lenses mechanical waves and, 389; thin-film See also Vectors Conversion factors, 6, 847 interference and, 520
Index 929 927-942 EM INDEX-845813 6/10/04 9:17 PM Page 930
Diagrams, coordinate systems, 34–35, DVDs, lasers in DVD players, 764; 632–633 lab; series-parallel, 629, 630 122, 135, 155; electric circuit, as reflection gratings, 515 lab, 527, prob.; short, 627; voltage divider, 620, 597–599, 599 lab; free-body, 89; 529 prob. 622 prob. motion, 32–33; ray. See Ray tracing Dyes, absorption and reflection Electric conduction, 777 Diamonds, 544 of light by, 441 Electric currents (I), 592; ammeters Dielectrics, 707 and, 631, 655; from changing magnetic Diffraction, 524–528, 530–531; double- fields, 671 lab, 671–673, 674–675 prob.; slit, 516–519, 532–533 lab; in the eye, controlling in a circuit with resistors, 531, 531 lab; resolving power of lenses 596–597, 598 prob.; effective, 677; and, 530–531; single-slit, 524–526, from electric generators, 675–678; 526 prob.; wave model of light energy carried by, 592, 593, 594 prob.; Ear, as closed-pipe resonator, 413; and, 439 forces on in magnetic fields, 652–653, damage to from loud sounds, 406–407; Diffraction gratings, 527–528, 530, 654 prob.; galvanometers and, 628 detection of sound by, 405; frequencies 531 lab; DVDs, spacing between rows prob., 655; in parallel circuits, detected by, 413; sensitivity to ampli- of, 529 prob.; grating spectroscopes, 623–624, 625–626 prob.; power of, tude of sound waves, 406 528; holographic, 527; reflection, 593, 594 prob.; producing, 591 lab, 592; Earth, acceleration of, 104 prob.; acceler- 515 lab, 527, 529 prob.; replica, 527; resistance-current relationships, 4 lab, ation of objects due to gravity of. See retinal projection screens, 531 lab; 18, 606–607 lab; in series circuits, Acceleration due to gravity; continents, transmission, 527; wavelength of light 618–620, 621–623 prob.; in series- floating of and Archimedes’ principle, from, 528, 529 prob. parallel circuits, 629, 630 prob.; trans- 355; Coriolis “force”, 217; gravitational Diffraction patterns, 524–526 mitting over long distances, 603–604; field, strength of, 183; heating of by Diffuse reflections, 459 unit of (ampere), 5 table, 593; voltage- radiation, 317; magnetic field of, 651; Digital virtual discs (DVDs), lasers current relationships, 606–607 lab
Index mass of, determination of, 178; in DVD players, 764; as reflection Electric field lines, 567 Newton’s thought experiments on gratings, 515 lab, 527, 529 prob. Electric fields (E), 563–579. See also satellite orbits and, 179; period of Digits, significant. See Significant digits Electric forces; affect of on charged satellite orbiting, 180, 181 prob.; Dimensional analysis, 6–7, 847 object, 563 lab; capacitors and, positive/negative rotation of, 198; Diodes, 784–786. See also Transistors; 577–579, 578 prob., 579 prob.; conduc- pressure at center of, 343 table; radius, current and voltage of, 785, 785 prob., tors and, 576–577; electric potential mass, and distance from the Sun, 173 786 prob., 790–791 lab; light-emitting, and, 569–571, 572 prob.; generating table; speed of object on equator, 199; 450, 786, 788 lab with Van de Graaff generator, 567 illus., speed of satellite orbiting, 180, 181 Direct relationships, 175, 435, 851 568; Millikan’s oil-drop experiment prob.; the Sun as source of light for, Dispersion, 491–492 and, 573, 574 prob.; sharing of charges 432; weight (F ) on, 96 Displacement ( d), 36–37; angular, g and, 575–576; strength of, 564, 564 Earthquakes, building 198; equation for, 36; length and table, 565 prob., 566 prob., 567, 573 lab; construction and, 394 direction of, 37; from a v-t graph, 67 typical values, 564 table; visualizing, Echolocation, 410 illus. prob., 68 564, 567–568 Eclipses, lunar, 487 Dissonance, 418 Electric forces, 541 lab, 546–553. See Eddy currents, 681 Distance, coordinate system, 34 also Electric fields; applications of, Effective current, 677 Divers, angular momentum (L) and, 552–553; charging by conduction, Effective voltage, 677, 678 235; pressure of water on a body, 353; 547, 549 lab; charging by induction, Efficiency, 268 rotational kinetic energy (KE ) 548, 549 lab; Coulomb’s law and, rot Effort force (Fe), 266 and, 287 549–550, 551 prob., 552; Problem- Einstein, Albert, 10 illus.; Bose-Einstein Dividers, voltage. See Voltage Solving Strategies, 550; separation of condensates and, 366, 768; energy divider circuits charges on neutral objects, 547 equivalent of mass (E mc2), 802, Dogs, hearing of, 413 Electric generators, 675–678 820; general theory of relativity, 10 Domains, magnetic, 650 Electric guitars, 411 illus., 184–185; gravitational lenses Dopants, 781, 782 prob. Electric heaters, thermal energy and, 506; photoelectric theory of, Doped semiconductors, 781; conduc- released by, 601–602, 602 prob. 727–729; photon momentum and, tivity, 782 prob.; diodes, 784–786, Electric motors, 656, 656 prob., 680 733; rest energy (E mc2), 292; 785 prob., 786 prob.; light meters and, 0 Electric potential, 569–571, 572 prob. stimulated emission of atoms 783; microchips (integrated circuits) Electric potential difference ( V), 4 and, 762 and, 788–789; n-type, 781; p-type, prob., 569–571, 572 prob.; capacitors Ejected electron, kinetic energy of, 781; thermistors, 782; transistors and, 577–579, 578 prob., 579 prob.; 728–729, 730 prob., 732 prob. and, 787–788 conductors and, 576–577; Millikan’s Elastic collisions, 298, 299 prob., Doppler effect, 407–408, 410; equation oil-drop experiment and, 573, 574 301 lab for, 408; frequency and, 409 prob.; prob.; sharing of charges and, 575–576; Elastic potential energy, 291–292 light waves and, 445–446; measuring in a uniform field, 571, 572 prob., 573, Elasticity, 360 motion on surface of the Sun by, 574 prob.; unit of (volt), 569; of zero Electric arcs, 556 422; reducing equation for, 408; uses (equipotential positions), 570 Electric bills, 604 of, 410 Electric power transmission, 603–605 Electric circuits, 592–593; applications Double-image quasars, Electric transmission lines, 604 of, 620, 627–628; balanced, 628 prob.; gravitational lenses and, 506 Electrical conduction in solids, diagramming, 591 lab, 597, 599 lab, Double-slit interference, 516–519; 775–783 599–600; fuses and, 617 lab; measur- interference patterns, 516; wavelength Electricity, static. See Static electricity; ing current and voltage, 631; parallel, of light from, 518–519, 519 prob., transmission of, 603–605 623–624, 623 lab, 625 prob., 626, 532–533 lab Electromagnetic force, 802 632–633 lab; rates of charge flow and Down quark, 819 illus. Electromagnetic induction, 671 lab, energy transfer, 593, 594 prob.; release Drag force, 100–101 672; electric generators and, 675–678; of thermal energy by, 601–602; resist- Drums, source of sound from, 411 electromotive force (EMF) and, 673, ance and Ohm’s law, 595–597, 598 Dry cells, 592 674–675 prob.; Lenz’s law and, prob.; series, 618–620, 621–623 prob., Ductility, 360 679–681; self-inductance and,
930 Index 927-942 EM INDEX-845813 6/10/04 9:18 PM Page 931
681–682; transformers and, 682–683, Electrostatic charge, 541 lab, 541–545. calorimeter, 319; cosines, law of, 120; 684 prob., 685 See also Electric force; charged objects, Coulomb’s law, 550; critical angle for Electromagnetic receivers, 712 542–543, 554–555 lab; conductors and total internal reflection, 489; current Electromagnetic spectrum, 708 illus., insulators and, 544–545; microscopic in series circuit, 619; de Broglie 709 view of, 543–544; separation of, 544, wavelength, 735; displacement, 36; Electromagnetic wave theory, 706, 592–593; unit of (C), 549–550 Doppler effect, 408; Doppler shift, 723; problems with, 723, 724, 725, Electrostatic generator, 568 446; effective current, 677; efficiency, 726 Electrostatics, 541–553; applications of, 268; electric field strength, 564; electric Electromagnetic waves, 706–713; from 552–553; charged objects, 542–543, potential difference, 569, 571; electro- AC sources, 707–708, 709; from a coil 554–555 lab; charging by conduction, motive force (EMF), 673; electron and capacitor, 709–710; de Broglie wave- 547, 549 lab; charging by induction, orbital radius, 755; energy equivalent length and, 735, 736 prob.; discovery 548, 549 lab; conductors and insula- of mass (E mc2), 802; energy of a of, 705–706; electromagnetic spectrum, tors and, 544–545; Coulomb’s law photon, 727; energy of an atom, 755; 708 illus., 709; emission spectra from, and, 549–550, 551 prob., 552, 552 prob.; energy of an emitted photon, 754; 724–725; energy of (photoelectric forces on charged bodies, 546–548; energy of vibration, 725; equivalent for theory), 726–729, 730 prob., 731, 732 grounding and, 548; microscopic view resistors in parallel, 624; equivalent prob., 738–739 lab; materials that shield, of charge, 543–544; separation of resistance for resistors in series, 619; 714–715 lab; momentum of (Compton charge on neutral objects, 547 final velocity with average acceleration, effect), 733–734; from piezoelectricity, Electroweak force, 823 65; first law of thermodynamics, 326;
711; power of, 725; receiving, 697 lab, Elementary charge, 550 force of magnetic field on charged par- Index 712; from a resonant cavity, 711; speed Elevators, 98, 99 prob., 108–109 lab ticles, 657; force on current-carrying of, 706; travel of through matter and Elliptical orbits, Kepler’s first law wire in a magnetic field, 653; frequen- space, 707–708; velocity of through and, 172 cy of a wave, 384; gravitational field dielectric, 707; wavelength-frequency EM wave. See Electromagnetic wave strength, 183; gravitational mass, 184; relationship for, 706 EMF. See Electromotive force (EMF) gravitational potential energy, 289; Electromagnetism, 648–649; charge-to- Emission spectra, 724; of atoms, half-life, 810; heat required to melt a mass ratio of electrons and, 698–699; 749–750, 752, 755 lab; of light from solid, 324; heat required to vaporize a charge-to-mass ratio of protons and, hot bodies, 724 lab, 724; photoelectric liquid, 324; heat transfer, 318; Hooke’s 699–700; determination of path of effect and, 726–729, 730 prob., 731, law, 376; hydraulic lift, force exerted electron and, 699, 700 prob.; electro- 732 prob.; shape of, 725 by, 352; ideal gas law, 345; ideal magnetic waves and, 714–715 lab; mag- Emissions, spontaneous, 762; mechanical advantage (IMA), 267; netic field near current-carrying wires, stimulated, 762 impulse-momentum theorem, 230; 648–649; mass spectrometers and, Energy, 258–259, 285; conduction and, index of refraction, 489; inertial mass, 701–702, 703 prob., 704 315; conservation of. See Conservation 183; inverse relationship between two Electromagnets, 649; of energy; direction of force and, 257 lab; variables, 18; Kepler’s third law, 173; audiocassette/videocassette recorders elastic potential, 291–292; of electric kinetic energy, 258; kinetic friction and, 651; computer storage disks and, currents, 592, 593, 594 prob.; gravita- force, 127; linear relationship between 659; creating, 660–661 lab; magnetic tional potential (PE), 288–289, 290 two variables, 16; magnification by a domains and, 650 prob.; kinetic (KE), 258–259, 287, 289; spherical mirror, 468; Malus’s law, 444; Electromotive force (EMF), 673, mechanical, 293–295; quantized, 725; mechanical advantage (MA), 266; mir- 2 674–675 prob.; back-EMF, 680–682; rest (E0 mc ), 292; thermal. See Ther- ror equation, 467; moment of inertia induced in electric generators, mal energy; unit of (Joule), 259; work of a point of mass, 205; motion for 675–677; transformers and, 682–683 and change in (work-energy theorem), average velocity, 47; Newton’s second Electron clouds, 761 258–259, 261 prob., 286–287 law for linear motion, 93; Newton’s Electron diffraction pattern, wave Energy crisis, 331 second law for rotational motion, 208; properties of particles and, 735 Energy equivalent of mass (E mc2), Newton’s third law, 102; observed light Electron neutrino, 819 illus. 802–803, 820 frequency, 446; order of operation in, Electron volt, energy of an electron Energy levels, electron, 753; energies 843; period of a pendulum, 379; peri- and, 727 of, 757 prob.; frequency and wave- od of satellite orbiting Earth, 180; pho- Electronic devices, diodes, 784–786, length of emitted photons and, 758 ton momentum, 733; plane-mirror 785 prob., 786 prob., 788 lab; transistors prob.; transitions in, 756 image height, 462; plane-mirror image and integrated devices, 787–789 Engines, heat, 326–327; internal- position, 462; point source of illumi- Electrons, angular momentum of, 755; combustion, 326–327 nance, 435; position with average charge-to-mass ratio of, 698–699; dis- Entropy, 328–331, 329 prob.; equation acceleration, 68; potential energy in a covery of, 747; electromagnetic force in for change in, 329; second law of spring, 376; power, 263; power dissipat- nucleus and, 802; force of magnetic thermodynamics and, 330–331 ed by a resistor, 601; power of electric fields on, 657, 658 prob.; free in semi- Equations, angle of resultant vector, circuit, 593; pressure, 342; pressure of conductors, 779–780, 780 prob., 782 123; angular acceleration, 199; angular water on a body, 353; Pythagorean the- prob.; frequency and wavelength of impulse-angular momentum theorem, orem, 120; quadratic relationship emitted, 758 prob.; kinetic energy of 234; angular momentum, 233; angular between two variables, 17; Rayleigh cri- ejected due to photoelectric effect, velocity, 198; average acceleration, 62; terion, 530; reducing form of, 408; 728–729, 730 prob., 732 prob.; magni- average velocity, 44; buoyant force, reflection, law of, 458; resistance, 595; 2 tude of charge of, 550; mass of from 354; capacitance, 577; centripetal rest energy (E0 mc ), 292; sines, law charge-to-mass ratio, 698, 699; meas- acceleration, 154; charge-to-mass of, 120; slope of a straight line, 17; urement of charge of in Millikan’s ratio in a Thomson tube, 699; Snell’s law of refraction, 486; solving, oil-drop experiment, 573, 574 prob.; charge-to-mass ratio of an ion in mass 843–845; speed of a satellite orbiting orbital energy values, 755–756, 757 spectrometer, 702; coefficient of linear Earth, 180; static friction force, 127; prob.; orbital radius of, 755, 760; path expansion, 361; coefficient of volume thermal energy dissipated by a resistor, of, determining, 699, 700 prob. expansion, 361; combined gas law 602; thin lens, 493; time interval, 36; Electroscope, 546, 548; charging by (pressure, volume, and temperature), torque, 202; transformer, 683; velocity conduction, 547, 549 lab; charging by 345; conservation of angular momen- with constant acceleration, 68; wave- induction, 548, 549 lab tum, 243; conservation of energy in a length-frequency relationship for a
Index 931 927-942 EM INDEX-845813 6/10/04 9:18 PM Page 932
wave, 706; wavelength of light from ment), 574 prob.; orbital sizes of Fermi National Accelerator double-slit experiment, 518; wave- Jupiter’s moons, 174 prob.; orbital laboratory, 816 length of light from diffraction grating, speed and period of satellite orbiting Ferromagnetism, 650 528; width of bright bands on single- Earth, 181 prob.; pendulum, accelera- Fiber-optic communications, lasers slit diffraction pattern, 525; work, 258, tion due to gravity, 379 prob.; photo- and, 764 260; work-energy theorem, 259 electron kinetic energy, 730 prob.; Field coils, 656 Equator, speed of object on, 199 power, 264 prob.; power and energy Field forces, contact forces vs., 88 Equilibrant, 131 released by a heater, 602 prob.; pressure, Field lines, electric, 567; magnetic, 646 Equilibrium, 95, 211–217; center of 343 prob.; real and apparent weight, 99 Fields, electric. See Electric fields; mass and, 211–213; force and motion prob.; reflection and angle of incidence, gravitational, 182–183; magnetic. in two dimensions and, 131; rotational, 460 prob.; relative-velocity, 158 prob.; See Magnetic fields 213, 218–219 lab; static, 213, 214–215 resistance-current relationships, 4 prob.; Filtering, polarization by, 443 prob.; translational, 213, 218–219 lab series-parallel circuits, 630 prob.; space Final time (tf), 36 Equipotential positions, 570 propulsion, 240 prob.; speed of sound First law of thermodynamics, Equivalent resistance, in parallel using resonance, 416 prob.; spring con- 326–328; heat engines and, 326–327; circuits, 624, 625–626 prob., 628; stant and energy of a spring, 377 prob.; heat pumps and, 328, 334; refrigera- in series circuits, 619–620 step-up transformers, 684 prob.; thin- tors and, 327–328 Error, measurement, 11–12, 13 film interference, 522 prob.; torque, 204 First right-hand rule, 649 Evaporation, 350–351, 364–365 lab prob., 209 prob.; two-dimensional colli- Fish, swim bladders and Archimedes’ Evaporative cooling, 351; of alcohols, sions, 242 prob.; two-part motion, 70 principle, 355 364–365 lab; production of prob.; two-particle collisions, 237 prob.; Fission, nuclear, 811–812 Bose-Einstein condensates, 366 uniform circular motion, 155 prob.; Fluids, 342. See also Gases; Liquids; Example Problems, acceleration, direc- uniform straight-line motion of multiple Archimedes’ principle and, 354–355, Index tion and magnitude of, 63 prob.; accel- objects, 41 prob.; uniform straight-line 356 prob.; Bernoulli’s principle and, eration on motion diagram, 60 prob.; motion of single object, 39 prob.; vector 357–358; buoyancy and, 341 lab, alpha and beta decay, 808 prob.; angle addition/subtraction, 121 prob., 124 354–355, 356 prob.; hydraulic systems of refraction, 487 prob.; Archimedes’ prob.; voltage dividers and, 622 prob.; and, 352; ideal, 342; Pascal’s principle principle, 356 prob.; average velocity voltage drops in series circuits, 621 and, 352; plasma, 348; pressure in, and speed, 45 prob.; balanced friction prob.; wavelength of light from double- 342; pressure of on a body, 353; forces, 128 prob.; calorimeter, transfer slit experiment, 519 prob.; wavelength velocity of moving, 357 of heat in, 321 prob.; capacitance, 578 of light from diffraction grating, 529 Fluorescein, 724 lab prob.; coefficient of linear expansion, prob.; work and energy, 261 prob.; work Fluorescent lamps, 432, 450 362 prob.; collisions, kinetic energy lost function and kinetic energy, 732 prob. Flutes, 411, 412 in, 299 prob.; concave mirror, locating Excimer lasers, 764, 765 Flux, luminous, 433; magnetic, 646 image on, 469 prob.; conductivity of Excited state, 753 Focal length ( f ), 464; of concave doped silicon, 782 prob.; conservation Expansion joints, 360 mirror, 464; of convex lenses and, of mechanical energy, 296 prob.; convex Experiments. See also Launch Labs; 494–495, 504–505 lab; of thin lens, lens, image formed by, 496 prob.; convex MiniLabs; Physics Labs; comparing 494 mirror, locating image on, 472 prob.; results of, 11–12; scientific method Focal point, 464; of lenses, 494; Coulomb’s law and electric force, 551 and, 8 of mirrors, 464 prob.; current through a resistor, 598 Explosive collisions, 298 Foci, 172 prob.; de Broglie wavelength, 736 prob.; Exponential growth, 18 Fog, 351 diode in a single circuit, 785 prob.; Exponents, 839, 840 Forbidden energy regions, 776 displacement from a motion diagram, External world, 88 Force, 88. See also Force in one dimen- 69 prob.; displacement from a v-t Extrapolation, 849 sion; Force in two dimensions; adhe- graph, 67 prob.; Doppler effect, 409 Extreme Physics, artificial intelligence, sive, 350; angular velocity and, 201; prob.; electric potential difference in a 792; black holes, 188; Bose-Einstein area and pressure and, 342, 343 prob.; uniform field, 572 prob.; electric power condensates, 366; cesium clocks, 50; buoyant, 341 lab, 354–355, 356 prob.; and energy, 594 prob.; electron, path of gravitational lenses, 506; Hall voltage, centrifugal, 156, 216; centripetal, 154, 700 prob.; energy levels, 757 prob.; force 662; sound waves in the Sun, 422; 155; on charged bodies, 546–550, 551 and displacement at an angle, 262 time dilation, 78 prob.; cohesive, 349; contact, 88; drag, prob.; force, average, 232 prob.; force of Extrinsic semiconductors, 781, 782, 783 100–101; effort, 266; electric. See magnetic field on charged particles, Eye, 500–501; diffraction on retina, 531, Electric forces; field, 88; friction. See 658 prob.; free-electron density in a 531 lab; focusing of images, 500; near- Friction; gravitational. See Gravitation- conductor, 778 prob.; free electrons in sightedness and farsightedness, 501; al force; interaction, 102–103, 104 intrinsic semiconductor, 780 prob.; gas refraction from, 501 prob.; resolving prob.; magnitude of common, 91 table; laws, 346 prob.; gravitational potential power of, 531 net. See Net force; normal, 107; resist- energy, 290 prob.; heat transfer, 318 Eye surgery, lasers and, 764, 765 ance, 266; strong nuclear, 802; types prob.; horizontal acceleration, 97 prob.; Eyeglasses, 501, 520 of, 94 table; unit of (N), 91; weak illumination of a surface, 436 prob.; nuclear, 821, 823; work and (angle inclined planes, 133 prob., 134 prob.; between force and displacement), 260, induced electromotive force, 674 prob.; 262 prob. inertia, moment of, 207 prob.; lever Force-acceleration graphs, 90–91 arm and torque, 202 prob.; magnetic Force carriers, 818 fields, strength of, 654 prob.; mass Force in one dimension, 87–95. See defect and nuclear binding energy, 804 Fahrenheit scale, 316 also Force; Force in two dimensions; prob.; mass spectrometer, mass of a Farad (F), 578 acceleration and, 88, 90–93; combin- neon atom from, 703 prob.; mechanical Faraday, Michael, 183, 578, 652, 675, 705 ing forces, 92; contact vs. field forces, advantage (MA)/ideal mechanical Farsightedness, 501 88; drag force and terminal velocity, advantage (IMA), 271 prob.; nuclear Fast neutrons, 812 100–101; elevators and, 98, 108–109 equations, 808 prob., 809 prob.; oil Fermato-, 6 table lab; free-body diagrams of, 89; interac- drop, charge on (Millikan’s experi- Fermi, Enrico, 811, 818 tion pairs and, 102–103, 104 prob.;
932 Index 927-942 EM INDEX-845813 6/10/04 9:19 PM Page 933
Newton’s first law and, 94–95; New- Gamma particles, 818 of, 10 illus.; Einstein’s general theory ton’s second law and, 96, 97 prob., Gamma radiation, 806, 807 table, 811, of relativity and, 184–185 98; Newton’s third law and, 102–103, 824–825 lab Gravity waves (g waves), 422 103 lab, 104 prob.; normal force and, Gas-discharge lamps, 450 Grimaldi, Francesco Maria, 439 107; Problem-Solving Strategies, 98; Gas lasers, 764 Ground-fault interrupters, 627, 634 real and apparent weight and, 98, 99 Gas laws, 344–345, 347 prob.; Boyle’s Ground faults, 634 prob.; ropes and strings and, 87 lab, law (volume and pressure of a gas), Ground state, 753 105, 106 prob.; tension and, 105, 344, 346 prob.; Charles’s law (volume Grounding, 548 106 prob. and temperature of a gas), 344; com- Guitars, sound from, 411 Force in two dimensions, 131–135. bined gas law, 345; ideal gas law, 345 Gyroscopes, 245 See also Force; Force in one dimension; Gases, 323; absorption spectrum of, equilibrium and, 119 lab, 131; inclined 751–752; convection currents and, planes, 132, 133 prob., 134 prob., 135, 347; emission spectra from, 750, 752, 135 lab 755 lab; gas laws and. See Gas laws; Fosbury-Flop, 212 pressure exerted by, 342 Fossil fuels, energy crisis and, 331 Geiger, Hans, 748 Foucault, Jean, 457 Geiger counters, 817, 824–825 lab Hahn, Otto, 811 Fourth right-hand rule, 672 Geiger-Mueller tubes, 817 Hale-Bopp comet, 172 Fractions, 468, 837 General theory of relativity, Half-life, 809–810, 810 table, 813 lab
Fractions of revolutions (radians), Einstein’s, 184–185 Hall, E. H., 662 Index 197, 198 illus. Generators, 675–678; alternating- Hall voltage, 662 Frames of reference, rotating, 216 current, 677–678; electric, 592 illus., Halley’s comet, 172 Franklin, Benjamin, 541, 577, 582 675–677 Harmonic motion. See Simple harmonic Fraunhofer, Josef von, 751 Geometric optics, 432 motion Fraunhofer lines, 751 Geometry, 853–856 Harmonics, 417. See also Simple Free-body diagrams, 89 Germanium, 777, 779 harmonic motion Free-electron density, 777, 778 prob. Germer, Lessmer, 735 hc, units of and photon energy, 727, Free-fall objects, 72–75; acceleration Giga-, 6 table 728 of due to gravity, 72, 182; amusement Glasses, eye. See Eyeglasses Hearing, damage to from loud sounds, park rides, 74; balls thrown upwards, Global Positioning System (GPS), 14 406–407; sensitivity to amplitude of 72–73 Gluons, 818, 819 illus., 820 sound waves, 406; sound detection Frequency ( f ), 384, 385 prob.; funda- Gold foil experiment, Rutherford’s, and, 405 mental, 417; threshold, 726–727, 728, 748, 766–767 lab, 799 Heat, 317; calorimetry and, 319–320, 731, 732 prob.; unit of (Hz), 384; wave- Gold, malleability of, 360 321 prob.; conduction, 317; convection, length-frequency relationship, 706; of Gongs, source of sound from, 411 317; radiation, 317; release by resistors, waves from a pendulum, 392–393 lab GPS systems. See Global Positioning 601–602; specific, 317–318, 319–320, Fresnel, Jean, 519 System (GPS) 321 prob.; transfer of, 317–318, 318 Friction (Ff ), 94 table, 126–130; Graduated cylinder, precision of prob., 319 prob. balanced friction forces, 127, 128 measurements in, 12 illus. Heat engines, 326–327 prob.; causes of, 130; coefficients of, Graphite, 544, 777 Heat of fusion, 324, 324 table, 325 prob. 127, 129 table; kinetic, 126, 127; Graphs, 15–19, 18 prob., 848–852; Heat of vaporization, 324, 324 table model for, 126–127; static, 126, force-acceleration, 90–91; line, 15–17; Heat pumps, 328, 334 127; unbalanced friction forces, 127; non-linear relationships on, 17–18; Heisenberg uncertainty principle, 129 prob. position-time, 38–42, 58; predicting 737, 760 Fringes, interference, 516 values from, 19; slope of lines on. See Heisenberg, Werner, 737 Frisch, Otto, 811 Slope of a line; variables on, 15, 16; Helioseismology, 422 Fuel efficiency, 327 velocity-time, 58–59; of waves, 384, 390 Helium, nuclear fusion and, 814 Fundamental frequency, 417 Grass, green color of, 442 Helmholtz, Hermann, 411 Fuses, 617 lab, 627, 628 Grass seeds, visualizing electric Henry, John, 671 Fusion, nuclear, 813–814, 826 field lines and, 568 Hertz (Hz), 384 Future Technology, adaptive optical Grating spectroscopes, 528 Hertz, Heinrich, 723 systems, 476; atom lasers, 768; Gratings, diffraction. Holes, 779–780 computers, 22; rotating space stations, See Diffraction gratings Holograms, 534, 765 162; solar sails, 248; spacecraft and Gravitational field (g), 182–183 Holographic diffraction gratings, 527 static electricity, 556; thermonuclear Gravitational force (Fg), 175; Newton’s Holography, 534 fusion, 826 law of universal gravitation and, Home electric bills, 604 175–178; orbital speed and period of Home thermostats, 363 satellite orbiting Earth and, 180, 181 Home wiring, 627–628 prob.; planetary motion and, 176, 178; Hooke’s law, 376, 377 prob. universal gravitation constant (G) and, Horns, 712 176, 177–178; weightlessness and, 182 Hot bodies, radiation from, Gravitational lenses, 506 723 lab, 724 lab, 724–725 Gabor, Dennis, 534 Gravitational mass (mgrav), 184 Hot plates, release of thermal Gadolinium, 645 Gravitational potential energy (PE), energy by, 601 Galilei, Galileo, 10 illus., 72, 174 prob., 288–289, 290 prob.; of an atom, 289; Household appliances, equivalent 405, 437 kinetic energy and potential energy of resistance and, 628; kilowatt power of, Gallium, 781 a system and, 289; mechanical energy 605; thermal energy released by, 601 Gallium aluminum, 764 and, 293–294; reference level and, How It Works, bathroom scales, 110; Gallium arsenide, 764 288, 289; work and, 288 bicycles, 276; credit card readers, 688; Galvanic cells, 592 Graviton, 819, 820 ground-fault interrupters (GFCI), 634; Galvanometers, 628 prob., 655, 671 lab Gravity, acceleration due to, 72–75, heat pumps, 334; lightning rods, 582; Gamma decay, 806 76–77 lab, 88; development of theory scanning tunneling microscope, 740
Index 933 927-942 EM INDEX-845813 6/10/04 9:19 PM Page 934
Hubble, Edwin, 447 234–235; baseballs and, 231; car Ions, charge-to-mass ratio of, 702, 703 Hubble Space Telescope, 467 crashes and, 231, 232 prob. prob.; sources of, 704 Human body, body temperature of, 322; In-line skaters, recoil of, 238–239 Isolated systems, 237 center of mass of, 212; hearing and. Incandescent bodies, radiation from, Isotopes, 701, 801. See also Radioactive See Hearing; as simple machine, 273; 723 lab, 724–725 isotopes; activity of, 810; analysis of speech and, 411; as a variable resistor, Incandescent bulbs, 432, 531 lab, with mass spectrometer, 701, 704; 597; vision and. See Vision 723 lab artificial, 811; half-life of, 809–810, Hunter, John H., 110 Incidence, angle of. See Angle of 810 table, 813 lab Huygens, Christiaan, 439 incidence Huygen’s wavelets, 439, 490, 524–525 Incident wave, 387 Hybrid cars, 608 Inclined planes, 135 lab; ideal mechani- Hydraulic lift systems, 352 cal advantage (IMA) of, 269; motion Hydroelectric electricity, 603 along, 132, 133 prob., 134 prob., 135; Hydrogen, atomic spectra, 752; electron as simple machines, 269 cloud, 761 illus.; electron orbital radius, Incoherent light, 515, 761 755; ionization energy, 759; orbital Independent variables, 15, 16, 848 Jodrell Bank Observatory, 506 energy values, 756, 757 prob. Index of refraction, 486, 486 table, 489 Joule (J), 259 Hyperbola, 18 Induced electromotive force, 673, 674 Joule heating loss, 603, 604 Hyperopia, 501 prob., 676 Joule, James Prescott, 259 Hypothesis, 8 Inductance, mutual, 682; self, 681–682 Junction, diode, 784 Induction, charging by, 548, 549 lab, Jupiter, determination of speed of light 554–555 lab, 705 and, 437–438; orbital sizes of Jupiter’s Inelastic collision, 298 moons, 174 prob.; radius, mass, and Index Inequalities, 683 distance from the Sun, 173 table Inertia, 95; moment of (I), 205–206, 206 table, 207 prob., 208 prob. Inertial mass (minertial), 183 Ice, floating of, 347, 355; pressure and Initial time (ti), 36 freezing of, 359–360 Instantaneous acceleration, 59 Ice skaters, angular momentum (L) Instantaneous angular acceleration, and, 235; collisions between two, 301 199 Ideal fluids, 342 Kelvin (K), 5 table, 316 Instantaneous angular velocity, 199 Kelvin scale, 316 Ideal gas law, 345 Instantaneous position (d), 40 Kepler, Johannes, 172–173 Ideal machines, efficiency of, 268; ideal Instantaneous velocity, 46, 46 lab Keplerian telescope, 502 mechanical advantage (IMA) of, 267 Instruments, accuracy of, 13 Kepler’s first law, 172 Ideal mechanical advantage (IMA), Insulators, 544, 778–779 Kepler’s second law, 173, 174 prob. 267; of automobile transmissions, Intensity, luminous. See Luminous Kepler’s third law, 173, 176 272; of bicycle gears, 270, 271 prob., intensity Ketterle, Wolfgang, 768 272, 276; of compound machines, Interaction pairs, 102; Earth’s accelera- Kilo-, 6 table 270, 271 prob.; efficiency and, 268; of tion and, 104 prob.; normal force and, Kilogram (kg), 5 table simple machines, 269 107; Problem-Solving Strategies, 103; Kilopascal (kPa), 342 Illuminance (E), 433–434; equation tension forces and, 105, 106 prob. Kilowatt-hour (kWh), 605 for point source, 435; inverse-square Interference, 388–389, 516–521; Kinetic energy (KE), 258–259, 287; relationship and, 434; of a surface, double-slit, 516, 517–519, 519 prob., collision between two objects and, 435, 436 prob., 437 532–533 lab; thin-film, 520–521, 522 297–298, 299 prob., 300; mechanical Illuminated source, 432 prob., 523 energy and, 293–294; of photoelec- Illumination, from illuminated sources, Interference fringes, 516 trons, 728–729, 730 prob.; potential 432; luminous flux (P) and, 433, 434; Interference patterns, double-slit, 516; energy and, 289; rotational (KErot), luminous intensity and, 434; from single-slit, 525 287; work and change in (work-energy luminous sources, 432; of a surface Internal-combustion engine, 326–327 theorem), 258–259, 261 prob. (illuminance, E), 433–434, 435, 436 Internal reflection, total, 489–490 Kinetic friction (F ), 126–127, prob., 437 International Bureau of Weights and f , kinetic 129; balanced friction forces and, 128 IMA. See Ideal mechanical advantage Measures, 6 prob; coefficient of, 127, 136–137 lab; (IMA) International Prototype Meter, 6 illus. unbalanced friction forces and, 129 Images, 461; from concave lenses, 498; International Space Station (ISS), prob. from concave mirrors, 465–468, 469 162, 556 prob., 470, 474–475 lab; from convex International System of Units. See SI lenses and, 494–495, 496 prob., 497; Internet Physics Labs, forces in an from convex mirrors, 465–468, 470 elevator, 108–109 lab; measurement of prob., 471, 472 prob.; mirror, 461; from speeding objects, 20–21 lab; momentum plane mirrors, 461–463, 462 lab; real, in a collision, 246–247 lab 465, 474–475 lab, 494–495, 496 prob.; Interpolation, 849 spherical thin lenses and, 494; virtual. Intrinsic semiconductors, 780, 782 Labs. See Launch Labs; MiniLabs; Physics See Virtual images Inverse relationships, 18, 175, 851 Labs Impulse (F t), 230; impulse-momentum Inverse square law, 175 Lamps, types of, 450 theorem and, 230–231, 232 prob.; Inverse square relationship, illumi- Landsat 7, 180 of two particles in closed, isolated nance and, 434 Lascaux cave, radiocarbon dating system, 236 Io (Jupiter’s moon), 174 prob., 437 and, 11 Impulse-momentum theorem, Iodine, radioactive, 811 Lasers, 445, 762–765; atom, 768; CD 230–231, 232 prob.; angular impulse- Ion engines, 239 and DVD players and, 764; eye surgery angular momentum theorem, Ionization energy, 759 with, 764, 765; fiber-optic communi-
934 Index 927-942 EM INDEX-845813 6/10/04 9:20 PM Page 935
cations and, 764; holograms and, 765; 502; resolving power, 530–531; spheri- Luminous source, 432; rate of light inefficiency of, 764; production of cal aberration on, 498 from (luminous flux (P)), 433, 434 Bose-Einstein condensates and, 366; Lenz’s law, 679–681 Lunar eclipses, refraction and, 487 production of coherent light by, 763; Leptons, 818, 819 illus., 820, 822 Lux (lx), 433 spectroscopy with, 765 Lever arm, 201, 202 prob. Lyman series, 756 illus. Launch Labs. See also Mini Labs; Physics Levers, 269 Labs; atoms, spinning penny model of, Leyden jar, 577 747 lab; balloons, charging of, 563 lab; Light. See also Illumination; blue-shifted, buoyancy of objects, 341 lab; conserva- 446; coherent, 516, 761; color and, tion of momentum, 285 lab; currents 440–442; diffraction, 439, 515 lab, and circuits, 591 lab; electric current 524–528, 529 prob., 530–531, 531 lab; from changing magnetic fields, 671 lab; dispersion, 491–492; Doppler effect for, electric fields and charged objects, 563 446–447; Einstein’s general theory of m (slope). See Slope of a line lab; electromagnetic (radio) waves, 697 relativity and, 185; incoherent, 515, MA. See Mechanical advantage (MA) lab; energy, factors affecting, 257 lab; 761; interference, 515–521, 522 prob., Machines, 266–273; compound, force on suspended object, 87 lab; fus- 523; lasers and. See Lasers; luminous 269–270, 271 prob., 272; efficiency of, es and electric circuits, 617 lab; graphs flux (P) and, 433, 434; luminous 268; effort force on (Fe), 266; human of constant speed and acceleration, 57 intensity and, 434; monochromatic, body as, 273; ideal mechanical advan- lab; LED lights through stroboscope, 516; observed light frequency, 446; tage (IMA), 267, 269, 270, 271 prob., 272; mechanical advantage (MA), 775 lab; light, path of through air, 431 opaque media and, 433; path of Index lab; light reflected off a compact disc, through air, 431 lab; polarization, 266–267, 270, 271 prob.; resistance 515 lab; magnetic fields, direction of, 443–444, 448–449 lab; ray model of, force of (Fr), 266; simple, 269 643 lab; modeling nucleus, 799 lab; 432–434; red-shifted, 446; reflection. Magnetic domains, 650 momentum, 229 lab; music, production See Reflection; refraction. See Refrac- Magnetic field lines, 646 of, 403 lab; planetary orbits, 171 lab; tion; rope model of, 443; speed of, Magnetic fields, 645–647; audio- projectile motion, 147 lab; rate of fall 437–438, 445–447; translucent media cassette/videocassette recorders and, of objects, 3 lab; reflection of image and, 433; transparent media and, 433; 651; direction of, 643 lab, 646; Earth’s, onto screen, 457 lab; rotational wave nature of, 439–447, 441 lab; 651; electric current from changing. See motion, 197 lab; spectrum of incandes- wavelength of, 518–519, 519 prob., Electromagnetic induction; electric cent light bulb, 723 lab; static electricity 528, 532–533 lab motors and, 656; forces on charged and electric force, 541 lab; straight-line particles, 657, 658 prob.; forces on elec- Light clock, 78 motion, 31 lab; sum of forces, 119 lab; tric currents in, 652–653; forces Light-emitting diodes (LEDs), 432, temperature changes, 313 lab; waves in on objects in, 647; galvanometers and, 450, 785 lab, 786, 788 lab, 790–791 lab a coiled spring, 375 lab 655; loudspeakers and, 653; magnetic Light meters, 620, 783 Lava, viscosity of, 349 domains and, 650; near a coil, 649; Light spectrum, 440 Law of conservation of energy, near current-carrying wires, 648–649; Light bulbs, lighting with an electric 293–301, 301 lab; mechanical energy strength of, 653, 654 prob., 660–661 current, 591 lab; parallel circuits and, and, 293–295, 296 prob.; Problem- lab; three-dimensional, 650 lab 626; radiation from incandescent, 723 Solving Strategies, 295; two-object Magnetic flux, 646 lab, 724–725; resistance of, 595 collisions and, 297–298, 299 prob., Magnetic poles, 644 Lighting, advances in, 450 300–301 Magnetic storage media, 651, 659 Lightning, 545, 547, 577, 582 Law of conservation of momentum, Lightning rods, 577, 582 Magnetic strips, credit card, 688 237, 241, 242 prob. Like charges, 542 Magnets, 644–647; electromagnets, 649, Law of Cosines, 120, 855 Line graphs, 15–17, 849–851 660–661 lab; Hall voltage and, 662; Law of inertia. See Newton’s first law Linear accelerators, 815 magnetic fields around, 645–647, 647 Law of reflection, 391, 458–459; angle Linear expansion of a solid, 361, 361 prob.; permanent, 645; poles of, 644; of incidence and, 458, 459, 460 prob.; table, 362 prob., 363 temporary, 645, 650 rough surfaces and, 459; two- Linear relationships, 16–17, 850 Magnification, 468, 472 prob.; convex dimensional waves and, 391 Liquid-crystal thermometers, 315 mirrors and, 471; spherical concave Law of Sines, 120, 856 Liquid mercury, 349 mirrors and, 468; spherical thin lenses Law of universal gravitation, 175–178, Liquids, 323. See also Fluids; adhesive and, 493, 494 182; gravitational mass (mgrav) and, 184; forces in, 350; boiling point of, Magnitude, 35 inverse square law and, 175; Kepler’s 323–324; buoyancy and, 341 lab, Malleability, 360 third law and, 176; universal gravitation 354–355, 356 prob.; cohesive forces in, Malus’s law, 444, 444 prob. constant (G), 176, 177–178 349; condensation of, 351; evaporation Marianas Trench, 353 illus. Laws, 9. See also specific laws of, 350–351, 364–365 lab; heat of Marimbas, 414 Laws of thermodynamics, 326–331 vaporization of, 324, 324 table; pres- Mars, hypothesis of canals on, 9; radius, LEDs. See Light-emitting diodes (LEDs) sure and freezing of water, 342, mass, and distance from the Sun, 173 Length, SI base quantity (m), 5 table 359–360; pressure of water on a body, table; surface of, 9 illus. Lenses, 493–499, 494 table, 500–503; 353; surface tension of, 349, 350 illus.; Marsden, Ernest, 748 achromatic, 499, 502; binoculars thermal expansion of, 347; viscosity of, Mass (m), affect of on space (Einstein’s and, 502; camera, 503; chromatic 349; volatile, 351 theory of relativity), 184–185; of an aberration on, 499; concave, 493, 494 Logarithms, 857 atom, 800, 801; of Earth, 178; energy table, 498; convex, 493, 494–495, 496 Long-period comets, 172 of (rest energy, E ), 292; gravitational Longitudinal wave, 381 0 prob., 497, 504–505 lab; focal length (f) (mgrav), 184; inertial (minertial), 183; and, 494; focal point, 494; gravitation- Loudness, 406 kinetic energy (KE) of an object and, al, 506; human eye and vision and, Loudspeakers, 653 287; projectile motion and, 148 lab; 500–501, 501 prob.; magnification, Lumen (lm), 433 on a spring. See Springs; unit of (kg), 493, 494; masking of, 495 lab; Luminous flux (P), 433 5 table Luminous intensity, 434; unit of microscope, 503; path of rays passing Mass defect, 802–803, 804 prob. (candela), 5 table, 434 through, 493; refracting telescopes and, Mass number, 800, 801
Index 935 927-942 EM INDEX-845813 6/10/04 9:20 PM Page 936
Mass spectrometers, 701–702, 704; Millikan’s oil-drop experiment, 573, motion; rotational. See Rotational identification of trace materials with, 574 prob., 698 motion; two-dimensional. See 704; ions charge-to-mass ratio from, Mini Labs. See also Launch Labs; Physics Two-dimensional motion; uniform 702; isotope analysis with, 704; mass Labs; bright-line emission spectra, 755 straight line. See Straight-line motion of an atom from, 703 prob.; modeling lab; change, measuring, 8 lab; changing Motion diagrams, 32–33, 48–49 lab; of, 702 lab; purification of samples velocity and, 58 lab; convex lenses, acceleration on, 60, 60 prob.; average with, 704 masking of, 495 lab; diffraction on the velocity, 46–47; changing velocity and, Math, 4–7, 833–857. See also Connect- human retina, 531 lab; electric field 58; coordinate systems and, 34–35; ing Math to Physics; absolute value, strength, 573 lab; emission spectrum particle model, 33; time intervals and 841; dimensional analysis, 6–7, 847; from hot body, 724 lab; energy, displacement on, 36–37 equations, solving, 843–847; expo- exchange, 301 lab; hot and cool Motor oil, viscosity of, 349 nents, 839–840; fractions, 837; geome- colors, 441 lab; inclined plane, 135 lab; Motors, electric, 656, 656 prob. try, 853–855; logarithms, 857; propor- induction and conduction, 549 lab; MRI magnets, 603 tions, 838; rates, 838; rounding, 835; instantaneous velocity vectors, 46 lab; Multi-gear bicycles, 272, 276 scientific notation, 841–843; signifi- light-emitting diodes, 788 lab; Multiple objects, straight-line motion cant digits, 7, 833–834, 835; square magnetic fields, three-dimensional, of, 40, 41 prob., 42 and cube roots, 839–840; symbols, 650 lab; mass spectrometer, modeling Multipliers, 655 833; trigonometry, 855–856 of, 702 lab; melting point, 324 lab; Muon neutrinos, 819 illus. Matter, energy contained in (E mc2), parallel resistance, 623 lab; pressure Muons, 818, 819 illus. 802; propagation of waves through, of a solid, 345 lab; projectile motion, Musical intervals, 418 707; states of. See States of matter; 148 lab; rebound heights, 239 lab; Music, hearing loss from loud, wavelength of, 735, 736 prob. retinal projection screen, 531 lab; 406–407 Matter waves, 735, 736 prob. schematic diagrams, 599 lab; spinning Music, physics of, 411–419; beats, 418, Index Maximum static friction force tops, 213 lab; virtual image position, 419 illus.; consonance and dissonance, (Ff, static), 127, 129 462 lab; weightlessness of water, 182 418; fundamental frequency, 417; har- Maxwell, James, 706, 723 lab; wheels and axles on bicycle monics, 417; loudness of notes, 414; Measurement error, 11–12, 13 gears, 270 lab; wind instruments, musical intervals, 418; percussion Measurements, 8 lab, 11 ; accuracy of, 418 lab instruments, 411; reed instruments, 411; 13; comparing, 11–12; errors in read- Mirages, 490 reproduction of music and noise, 419; ing, 13; margin of error, 11–12; preci- Mirror equation, 467 resonance in air columns, 412–414, sion of, 8 lab, 12; SI units, 5; signifi- Mirror image, 461 446 prob.; resonance on strings, cant digits and, 7 Mirrors, comparison of types, 473, 473 414–415; sound spectrum and, 417; Mechanical advantage (MA), 266–267; table; concave, 464–468, 469 prob., sources of sound, 403 lab, 411; stringed of compound machines, 270, 271 prob.; 470, 474–475 lab; convex, 471, 472 instruments, 411, 414–415, 417 prob.; ideal. See Ideal mechanical advantage prob., 473 table; focal length (f ), 464; timbre (tone quality or color), 415; (IMA) focal point, 464; in lasers, 763; locat- wind instruments, 418 lab Mechanical energy (E), 293–295; con- ing image on curved, 465–468, 469 Mutual inductance, 682 servation of, 293–295, 296 prob.; loss prob.; magnification by spherical, 468; Myopia, 501 of, 295 mirror equation, 467; plane, 460 prob., Mechanical waves, 381–382; amplitude 461–463, 462 lab; production of, 457; of, 382–383; behavior of at bound- reflection of image onto screen by, aries, 387–388; depicting on graphs, 457 lab 384; frequency of, 384; interference Models, 19 between, 388–389, 389 lab; period Moderator, 812 of, 383, 385 prob.; phase of, 383; Mole (mol), 5 table, 345 resonance and, 389; speed of, 382, Moment of inertia (I), 205–206, 207 n-type semiconductors, 781. 384, 385 prob., 387; superposition of, prob., 208 prob.; equation for, 205; of See also Diodes; Transistors 388–389; two-dimensional, 390–391; various objects, 206 table Nano-, 6 table wavelength of, 383, 385 prob. Momentum (p), 230; angular, 233–235, National Institute of Science and Mega-, 6 table 243–245; conservation of, 237, Technology (NIST), 6 Meitner, Lise, 811 243–244; impulse-momentum theo- Natural gas, 331 Melting point, 323, 324 lab rem and, 230–231, 232 prob.; of a par- Nearsightedness, 501 Memory, computer, 22 ticle, 737; rebound heights, 239 lab; Negative acceleration, 61–62 Mercury (element), 350 recoil and, 238–239; space propulsion Negative exponents, 842 Mercury (planet), radius, mass, and and, 239, 240 prob.; two-dimensional Negative position, 35 distance from the Sun, 173 table; shape collisions and, 241, 242 prob., two-par- Neodymium, 645 of orbit of, 171 lab ticle collisions and, 229 lab, 236–237, Neon signs, plasma in, 348 Mesons, 818 237 prob., 246–247 lab Neptune, discovery of, 179; radius, mass, and distance from the Sun, 173 table Metals, kinetic energies of electron Monochromatic light, 516 Net force, 92; centripetal force and, 155; ejected from, 731; work function of, Moon (Earth’s), distance to, 13; as of a coiled spring, 376–378; of a 731, 732 prob. illuminated source, 432; lunar eclipses and, 487 pendulum, 378–379 Meter (m), 5 table Moonlight, 432 Net torque, 203 Michelson, Albert, 438 Moons, orbital sizes of Jupiter’s, Neutral objects, 543–544, 547. See also Micro-, 6 table 174 prob. Charged objects Microchips, 788–789 Moore, Gordon, 22 Neutrinos, 818, 822 Microphones, 673 Morpho butterfly, thin-film interfer- Neutrons, mass of nucleus and, 800; Microscopes, lenses in, 503; scanning ence on wing of, 523, 530 strong nuclear forces and, 802 tunneling microscope (STM), 740 Motion, accelerated. See Acceleration; Newton (N), 91 Microwaves, 711, 712 circular. See Circular motion; force Newton, Sir Isaac, 10 illus., 175, 179, Milli-, 6 table and. See Force; periodic. See Periodic 440 Millikan, Robert A., 573, 698, 731 motion; planetary. See Planetary Newton’s first law, 94–95
936 Index 927-942 EM INDEX-845813 7/29/04 4:32 PM Page 937
Newton’s second law, 93; acceleration Optical systems, adaptive, 476 Pendulums, 378–379; acceleration due to Earth’s gravitation and, 182; Optics. See Lenses; Mirrors of due to gravity, 378–379, 379 prob., apparent weight and weightlessness, Orbital energy values, 755–756, 392–393 lab; conservation of 98; bathroom scales and, 96; Bohr 757 prob. mechanical energy and, 294–295; model of the atom and, 754–755; cen- Orbital periods, 172; Kepler’s first law examining wave characteristics with, tripetal force and, 155; drag force and and, 172; Kepler’s second law and, 392–393 lab; period of, 379 terminal velocity and, 100–101; hori- 173; Kepler’s third law and, 173, 174 Penzias, Arno, 9 illus. zontal acceleration and, 97 prob.; prob.; Newton’s law of universal gravi- Percussion instruments, source Problem-Solving Strategies, 98 tation and, 176; of a planet orbiting of sound from, 411 Newton’s second law for rotational the Sun, 173, 176; of satellite orbiting Period (T), 375; of a coiled spring, 378; motion, 208, 209 prob. Earth, 180, 181 prob. harmonic, 375; of a pendulum, 379, Newton’s third law, 102–103, 104 prob. Orbital radius, 755, 760 392–393 lab; of a wave, 383, 385 prob. NIST-F1 cesium clock, 50 Orbits, early studies of, 171; geosynchro- Periodic motion, 375–380, 392–393 Node, 389 nous, 180; Kepler’s laws and, 172–173, lab Noise, 419 174 prob.; Newton’s law of universal Periodic wave, 381, 383 Nonideal fluids, viscosity of, 349 gravitation and, 175–178; Newton’s Permanent magnets, 645; magnetic Nonlinear relationships, 17–18; thought experiments on, 179; orbital fields around, 645–647 inverse relationship between two speed and period of a planet orbiting Perspiration, evaporative cooling variables, 18, 851; quadratic relation- Earth, 180, 181 prob.; period of a plan- by, 351
ship between two variables, 17, 852 et orbiting the Sun, 176; shape of, 171 Phase, mechanical wave, 383 Index Nonreflective eyeglasses, 520 lab, 172 Phosphor, 657 Normal, 391 Order of operations, 843 Photocells, 726; photoelectron kinetic Normal force (FN ), 94 table, 107, 127 Organ pipes, source of sound from, energy, 728–729, 730 prob., npn-transistor, 787 411 732 prob.; threshold frequency, Nuclear equations, 807, 808 prob., 809 Origin, coordinate system, 34 726–727; work function of a metal prob. Oscillation cycle, coil and capacitor and, 731, 732 prob. Nuclear fission, 811–812 circuit, 709–710 Photocopiers, 553 Nuclear fusion, 813–814, 826 Outward force. See Centrifugal force Photoelectric effect, 726; Einstein’s Nuclear model of the atom, 748–752; Ovenproof glass, 360 theory of, 727–729; energy of a absorption spectrum and, 751–752; photon and, 727–728, 731 prob.; emission spectra and, 749–750, 752; kinetic energy of an ejected electron, problems with, 752; Rutherford’s gold 728–729, 730 prob.; Millikan’s foil experiments and, 748–749 experiments proving, 731; modeling, Nuclear reactions, 807; equations for, 738–739 lab; threshold frequency and, 807, 808 prob., 809 prob.; nuclear 726–727; work function of a metal fission and, 811–812; spontaneity and, 731, 732 prob. of, 803–804 p-type semiconductors, 781. See also Photon energy (E), 727, 753–754; Nuclear reactors, 812–813 Diodes; Transistors kinetic energy of electron, 728–729, Nucleons, 802, 819 Pair production, 820 730 prob.; Problem-Solving Strategies, Nucleus, 749, 799–805; binding energy Parabola, 17 illus., 147 728; work function of a metal and, of, 799 lab, 802–804, 804 prob.; charge Parabolic dish antennas, 712 731, 732 prob. of, 800; discovery of, 799; mass defect Parabolic mirrors, 467 Photons, 727, 820; energy of, 727–729, of, 802–803, 804 prob.; mass of (mass Parallax, 13 731 prob., 753–754; frequency and number), 800, 801; Rutherford’s exper- Parallel circuits, 623–624, 624 lab, wavelength of, 758 prob.; momentum iments on. See Gold foil experiment, 625–626 prob., 626, 632–633 lab. of, 733–734 Rutherford’s; size of, 800; strong See also Series circuits; Series-parallel Photoresistors, 620 nuclear forces and, 802 circuits Photosynthesis, chlorophyll and, 442 Nuclides, 801 Parallel connections, 600 Photovoltaic cells, 592 Paraxial ray simplification, 467 Physicists, 3 Particle accelerators, 815–816 Physics, 3–4. See also Extreme Physics Particle detectors, 816–817 Physics Labs, acceleration due to gravity, Particle model of light, 737; Compton 76–77 lab; capacitors, charging of, effect and, 733–734; photoelectric the- 580–581 lab; charged objects, 554–555 ory and, 726–729, 730 prob., 731, 732 lab; coefficient of friction, 136–137 lab; prob., 738–739 lab; radiation from, 724 concave mirror images, 474–475 lab; Object, 461 lab; incandescent bodies and, 724–725 conservation of energy, 302–303 lab; Oboe, 417 Particle model of motion, 33 chang- convex lenses and focal length, Observed light frequency (fobs), 446 ing velocity and, 58; uniform motion 504–505 lab; double-slit interference, Ocean trench, pressure at deepest, and, 33 532–533 lab; electric circuits, 632–633 343 table Particles, Compton effect and, 733–734; lab; electromagnetic wave shielding, Oersted, Hans Christian, 648, 671, 705 de Broglie wavelength and, 735, 736 714–715 lab; electromagnet, creating, Ohm (Ω), 595 prob.; Heisenberg uncertainty principle 660–661 lab; evaporative cooling of Ohm, George Simon, 596 and, 737; location of, 737; magnetic alcohols, 364–365 lab; forces in an Ohm’s law, 595–597 forces on, 657, 658 prob.; momentum elevator, 108–109 lab; measurement of Oil-drop experiment, Millikan’s, of, 735, 737; photoelectric theory of, speeding objects, 20–21 lab; motion 573, 574 prob., 698 726–729, 730 prob., 731, 732 prob.; diagrams, creating, 48–49 lab; orbits of Oil, thin-film interference and, 522 prob. wave properties of, 735, 736 prob., 737 planets and satellites, 186–187 lab; Opaque media, 433, 458 Pascal (Pa), 342 pendulums and waves, 392–393 lab; Open-pipe resonators, 412, 414 Pascal, Blaise, 352 photoelectric effect, 738–739 lab; Opposite charges, 542–543 Pascal’s principle, 352 polarization of light, 448–449 lab; Optical fibers, total internal reflec- Paschen series, 756 illus. power (P) on a stair climber, 274–275 tion and, 490 Pauli, Wolfgang, 818 lab; projectile motion, 160–161 lab;
Index 937 927-942 EM INDEX-845813 6/10/04 9:22 PM Page 938
radiation intensity and distance, Positron Emission Tomography prob., 325 prob., 328 prob.; vibration 824–825 lab; speed of sound, 420–421 (PET), 811 and waves (Chapter 14), 379 prob., 386 lab; thermal energy and water tempera- Positrons, 819 prob.; work, energy, and simple ture, 332–333 lab; transformers, Potential energy, of an atom, 289; elas- machines (Chapter 10), 261 prob., 262 induced voltage of, 686–687 lab; tic, 291–292; gravitational, 288–289, prob., 264 prob., 272 prob. translational and rotational equilibrium, 290 prob., 293–294; in a spring Precision, 8 lab, 12, 13–14 218–219 lab; two-particle collisions, 376–378, work and, 288 Predictions, graphs and, 19 246–247 lab; voltage, current, and Potentiometer, 596 illus., 597 Prefixes, SI, 6 table resistance relationships, 606–607 lab Power (P), 263, 265, 268 prob.; average, Pressure (P), 342; atmospheric, 343; Physics of music. See Music, physics of 677; of electric currents, 593, 594 prob., Boyle’s law (volume and pressure of a Piano, 411, 417 illus. 677; of an electric motor, 264 prob.; of gas) and, 344, 346 prob.; calculation of, Pico-, 6 table electromagnetic waves, 725; from a 342, 343 prob., 345 lab; combined gas Piezoelectricity, 711 resistor, 601–602, 602 prob.; on a stair law (pressure, volume, and tempera- Pigments, 441–442; chlorophyll, 442; climber, 274–275 lab; unit for (W), ture), 345; of fluids, 342, 352, 353, complementary, 442; primary, 441, 263 357–358; Pascal’s principle and, 352; 442; secondary, 441 Power (mathematics), 840 relationship with force and area, 342; Pion, 818 Power companies, 604–605 typical values, 343 table; unit of (Pa), Pitch, 406; Doppler effect and, 407 Practice Problems, acceleration 342 Planck, Max, 725, 728 (Chapter 3), 61 prob., 64 prob., 65 prob., Pressure waves, damage to human ear Planck’s constant (h), 725, 727 67 prob., 69 prob., 71 prob., 74 prob.; by, 406–407; detection of by human Plane mirrors, 460 prob., 461–463, 462 atoms (Chapter 28), 757 prob., 758 ear, 405; loudness and, 406–407; lab, 473 table prob.; conservation of energy (Chapter pitch and, 406; resonance length Planetary model of the atom. 11), 287 prob., 291 prob., 297 prob., 300 and, 412–414; sensitivity of human Index See Nuclear model of the atom prob.; current electricity (Chapter 22), ear to, 406; sound as, 404–405 Planetary motion, angular momentum 594 prob., 598 prob., 600 prob., 603 Pressurized water reactors, 813 (L) and, 234; Brahe’s study of, 171, prob., 605 prob.; electric fields (Chapter Primary coils, 682 172; Copernicus’s study of, 171; Ein- 21), 565 prob., 566 prob., 571 prob., 572 Primary colors, 440 stein’s general theory of relativity and, prob., 574 prob., 578 prob.; electromag- Primary pigments, 441, 442 185; gravitational fields and, 182–183; netic induction (Chapter 25), 675 prob., Principle axis, 464 Kepler’s laws and, 172–173, 174 prob.; 678 prob., 684 prob.; electromagnetism Principle of superposition, 388 modeling, 186–187 lab; Newton’s law (Chapter 26), 700 prob., 703 prob., 706 Principle quantum number, 755 of universal gravitation and, 175–178; prob., 707 prob.; force and motion Prism, dispersion of light and, 491 Newton’s thought experiments on (Chapter 4), 89 prob., 93 prob., 97 prob., Problem-Solving Strategies, conserva- satellites and, 179; orbital period, 176, 100 prob., 104 prob., 106 prob.; force in tion of energy, 295; electric force, 550; 180, 181 prob.; orbital shape, 171 lab, two-dimensions (Chapter 5), 121 prob., force and motion, 98; interaction pairs, 172; orbital size, 174 prob.; orbital 125 prob., 128 prob., 130 prob., 133 103; line-graphs, plotting, 16; motion speed, 180, 181 prob. prob., 135 prob.; fundamentals of light in two dimensions (projectile motion), Planets, motion; radius, mass, and dis- (Chapter 16), 436 prob., 447 prob.; illu- 149; ray tracing to locate images tance of from the Sun, 173 table; See mination (Chapter 16), 436 prob., 447 formed by curved mirrors, 466; also Planetary motion prob.; interference and diffraction schematic diagrams, 599; series-parallel Plants, capillary action and, 350; chloro- (Chapter 19), 519 prob., 522 prob., 526 circuits, 629; thin-film interference, phyll in, 442; cohesive forces in, 350 prob., 529 prob.; magnetic fields (Chap- 521; units of hc and photon energy, Plasma, 348, 545, 556 ter 24), 647 prob., 650 prob., 654 prob., 728; vector addition/subtraction, 123; Plasma contactor, 556 658 prob.; momentum (Chapter 9), work, 260 Pluto, 173 table 233 prob., 238 prob., 240 prob.; motion Projectile launcher, designing, pn-junction diode, 784–786, 785 prob., in two dimensions (Chapter 6), 150 160–161 lab 786 prob. prob., 152 prob., 156 prob., 159 prob.; Projectile motion, 147 lab, 147–152; pnp-transistor, 787 the nucleus (Chapter 30), 801 prob., air resistance and, 152; factors affecting Point source, illuminance of, 435, 436 805 prob., 808 prob., 809 prob., 810 path of, 160–161 lab; mass and, 148 prob.; luminous intensity of, 434 prob.; physics toolkit (Chapter 1), 5 prob., lab; Problem-Solving Strategies, 149; Poisson, Simeon Denis, 519 7 prob., 8 prob., 18 prob.; planetary of projectiles launched at an angle, Polarization of light, 443–444, 444 motion (Chapter 7), 174 prob., 181 150, 151 prob., 152 prob. prob., 448–449 lab prob.; quantum theory (Chapter 27), Projectiles, 147 Polarized, 644, 645 730 prob., 732 prob., 736 prob.; reflec- Proportions, 838 Polarized light, 443 tion and mirrors (Chapter 17), 460 Protons, atomic number (Z) and, 800; Polarizing filters, 443–444, 444 prob., prob., 469 prob., 472 prob.; refraction charge-to-mass ratio of, 699–700; 448–449 lab and lenses (Chapter 18), 487 prob., electromagnetic force in nucleus and, Pole-vaulting, elastic potential energy 496 prob., 497 prob.; representing 802; mass of from charge-to-mass and, 291–292 motion (Chapter 2), 39 prob., 41 prob., ratio, 700; mass of nucleus and, 800; Polonium, 799 45 prob.; rotational motion (Chapter 8), strong nuclear forces and, 802 Position (d), 34; constant acceleration 200 prob., 203 prob., 205 prob., 208 prob., Pulleys, 269; ideal mechanical and, 66, 68, 68 table; instantaneous, 210 prob., 215 prob.; series and parallel advantage (IMA) of, 269; mechanical 40; negative, 35 circuits (Chapter 23), 619 prob., 622 advantage (MA) of, 267; Position-time graphs, 38–42; average prob., 623 prob., 626 prob., 630 prob.; Pythagorean theorem, 120 speed and, 44; constant acceleration solid-state electronics (Chapter 29), and, 66; motion of multiple objects, 778 prob., 780 prob., 783 prob., 786 40, 40 prob., 41 prob., 42; motion of prob.; sound (Chapter 15), 405 prob., single object, 38, 39 prob., 40; object 409 prob., 416 prob.; states of matter velocity and, 43–44; straight-line (Chapter 13), 344 prob., 356 prob., 362 formula vs., 46, 47 table prob.; static electricity and electric force Positive acceleration, 61–62 (Chapter 20), 552 prob.; thermal energy Quadratic equations, 846 Positive exponents, 841 (Chapter 12), 317 prob., 319 prob., 321 Quadratic formula, 846
938 Index 927-942 EM INDEX-845813 6/10/04 9:22 PM Page 939
Quadratic graphs, 852 Real image, 465; concave mirrors and, Right-hand rules, first, 649; fourth, Quadratic relationships, 17, 850 465–467, 474–475 lab; convex lenses 672; second, 649; third, 652 Quantized energy, 725 and, 494–495, 496 prob. Ripple tanks, 390–391 Quantum mechanics, 761 Real weight, 98, 99 prob. Rise, 17 Quantum number, principle, 755 Receivers, 712 Rockets, affect of Coriolis force on, 217; Quantum theory of the atom, Recoil, 238–239 space propulsion and, 239, 240 prob. 760–761 Red-shifted light, 446 Rocks, history of Earth’s magnetic Quarks, 818, 819 table, 820, 822 Reducing equations, 408 field in, 651 Quartz crystal, piezoelectricity and, Reed instruments, 411 Rod, pendulum, 378 711 Reeds, 411 Roemer, Ole, 437–438 Quartz-halogen lamps, 450 Reference level, 288, 289, 290 prob. Roentgen, Wilhelm, 713 Quasars, double-image, 506 Reflected wave, 387 Roller coasters, confusion of body’s Reflection, 457–473; angle of, 391; systems by, 138; conservation of concave mirrors and, 464–468, 469 mechanical energy and, 294 prob., 470; convex mirrors, 471, 472 Rope model of light waves, 443 prob.; diffuse, 459; of image onto Ropes, forces of, 105, 106 prob. movie screen, 457 lab; law of, 391, Rossi X-ray Timing Explorer, 188 458–459, 460 prob.; plane mirrors and, Rotating frames of reference, 216 Radar detectors, 410 461–463; polarization of light by, Rotational equilibrium,
Radian (rad), 197, 198 illus. 443; regular, 459; total internal, 213, 218–219 lab Index Radiation, 317; alpha, 806, 807 table; 489–490 Rotational kinetic energy (KErot), 287 beta, 806, 807 table; distance and Reflection gratings, 515 lab, 527, 529 Rotational motion, 197–217; effect of intensity of, 824–825 lab; gamma, 806, prob. force on angular velocity, 201; angle of 807 table; from incandescent bodies, Refracting telescopes, 502 revolution, 198; angular acceleration, 723 lab, 724–725; medical uses Refraction, 391, 485 lab, 485–492; 199; angular displacement, 198; angular of, 811 angle of, 486, 487 prob., 488; disper- frequency, 200; angular momentum Radiation detectors, 817, 824–825 lab sion of light by, 491–492; index of, (L), 233–235; angular velocity, Radio waves, receiving, 697 lab, 712; 486, 486 table, 489; lenses and. See 198–199; center of mass and, 211–213, shielding from, 714–715 lab Lenses; lunar eclipses and, 487; 213 lab; centrifugal “force” and, 216; Radioactive, 806 mirages and, 490; Snell’s law of, Coriolis “force” and, 216–217; distance Radioactive dating, 11, 810 486–487, 488; total internal reflection of a point on a rotating object, 198; Radioactive decay, 18, 799, 806; activity and, 489–490; two-dimensional waves equilibrium and, 213, 214–215 prob., and, 810; alpha, 806, 808 prob.; beta, and, 391; wave model of, 488–489 218–219 lab; lever arms, 201–202, 202 806, 808 prob.; gamma, 806; half-life Refrigerators, 327–328 prob.; measurement of (radians), 197, and, 809–810, 813 lab; nuclear Relative velocity, 157–159 198 illus.; moment of inertia (I) and, equations showing, 807, 808 prob., Relativity, Einstein’s theory of, 184–185 205–206, 207 prob., 208 prob.; New- 809 prob. Replica gratings, 527 ton’s second law of, 208, 209 prob.; Radioactive iodine, 811 Resistance (R), 595–597; factors rotating frames of reference, 216; rota- Radioactive isotopes, activity of, 810; affecting, 595 table; in parallel circuits, tional kinetic energy (KErot), 287; sign analysis with mass spectrometer, 701, 624, 625–626 prob.; reducing loss of and direction of, 198; stability of 704; artificial, 811; half-life of, energy by, 604; resistance-current objects and, 213; torque and, 202–203, 809–810, 810 table, 813 lab; medical relationships, 4 lab, 18, 606–607 lab; 204 prob. uses of, 811; nuclear equations and, in series circuits, 619–620, 621 prob. Rounding, 835 807, 808 prob., 809 prob. 622 prob.; in series-parallel circuits and, Rubbing alcohol, evaporation of, Radioactive waste, 813 629, 630 prob.; zero in superconductors, 351, 364–365 lab Radioactivity, activity and, 810; artificial, 603 Run, 17 Resistance force (F ), 266 811; cancer treatment with, 811; discov- r Running shoes, physics of, 231, 304 ery of, 799; distance and intensity of, Resistivity, 777 Rutherford, Ernest, 543, 748, 800; dis- 824–825 lab; half-life and, 809–810, Resistors, 596–597, 598 prob.; current- covery of three types of radiation, 806; 810 table, 813 lab; nuclear equations voltage characteristics, 790–791 lab; gold foil experiments of, 748–749, and, 807, 808 prob., 809 prob.; types of in parallel circuits, 623–624, 625–626 766–767 lab, 799 radiation, 806, 807 table prob.; release of thermal energy by, Radiocarbon dating, margin 601–602; in series circuits, 619–620, of error, 11 621 prob. Rainbows, 491–492 Resonance, 380; in air columns, Rates, 838 412–414; hearing and, 414; speed of Ratios, 838 sound from, 413, 416 prob., 420–421 Ray model of light, 432–434; illumina- lab; on strings, 414–415 Satellites, mass of, 180; orbits of, 173, tion of a surface and, 435, 436 prob., Resonance length, 412–413, 416 prob. 180, 181 prob., 186–187 lab; speed of, 437; luminous flux (P) and, 433; lumi- Resonant cavities, 711 180, 181 prob. nous intensity and, 434; speed of light Resonators, 412–414; closed-pipe, 412; Saturn, 173 table and, 437–438 open-pipe, 412; resonance length and, Saxophone, 411, 412, 414 Ray optics, 432 412–413; standing pressure waves and, Scalars, 35 Ray tracing, concave mirrors and, 412 Scales, weight (Fg) and, 96, 98, 99 prob., 110 465–467, 470 prob.; convex lenses and, Rest energy (E0), 292 495, 496 prob., 497; convex mirrors Resultant force, 131 Scanning tunneling microscope and, 471, 472 prob.; plane mirrors and, Resultants, 35 (STM), 737, 740 462; two-dimensional waves and, 391 Retinal projection screen, 531 lab Schematic diagrams, 597, 597 table, Rayleigh criterion, 530–531 Reversible air conditioners. 598 prob., 599, 599 lab Rayleigh, Lord, 530 See Heat pumps Schrödinger, Erwin, 760 Reactions, chain, 812; fusion, 813–814, Revolution, angle of ( ), 198; fractions Schwarzschild radius, 188 826 of (radians), 197, 198 illus. Scientific law, 9
Index 939 927-942 EM INDEX-845813 6/10/04 9:23 PM Page 940
Scientific method, 8–10 Snell, Willebrord, 486 Speed of light, ray model of light and, Scientific notation, 841–843 Snell’s law of refraction, 486–487, 437–438; wave model of light and, Scientific theory, 10 501 prob. 445–447; wavelength-frequency Scuba diving, regulation of pressure, Soap, spectrum produced by, 520 relationship and, 706 344 illus. Soddy, Frederick, 799 Speed of sound, 404–405, 405 table, Seafloor spreading, 651 Solar and Heliospheric Observatory 413, 416 prob., 420–421 lab Second (s), 5 table (SOHO), 422 Speedometers, 662 Second law of thermodynamics, Solar breeze, 248 Spherical aberration, 467, 498 329 prob., 330–331 Solar cells, 592 Spherical mirrors, 464; aberration on, Second right-hand rules, 649 Solar collectors, 327 467; locating image on, 467, 469 prob.; Secondary coils, 682 Solar sails, 248 magnification by, 468; mirror equation Secondary colors, 440 Solenoids, 649 for, 467; ray tracing and, 465–467 Secondary pigments, 441 Solid-state electronics, 775–789; con- Spiderwebs, surface tension and, 349 Segré, Emilio, 811 ductors and, 777, 778 prob.; diodes, Spontaneous emissions, 762 Self-inductance, 681–682 784–786, 785 prob., 786 prob., 790–791 Sport utility vehicles, stability of, 220 Semiconductors, 775, 779–783; lab; insulators, 778–779; semiconduc- Spring constant (k), 376, 377 prob. diodes, 784–786, 785 prob., 786 prob., tors, 775, 779–783; transistors and Spring force (Fsp ), 94 table 788 lab, 790–791 lab; doped, 781–782, integrated devices, 787–789 Springs, elastic, 375 lab, 376–378, 380 782 prob.; extrinsic, 781; free electrons Solids, 323; amorphous, 359; band prob.; graphing elongation of, 17 prob.; in, 779–780, 780 prob., 782 prob.; theory of, 776–777; conduction of mass on (Hooke’s law), 376, 377 prob.; intrinsic, 780, 780 prob.; light meters electricity by, 775–783; crystalline, potential energy of, 376–378, 377 using, 783; n-type, 781; p-type, 781; 359; elasticity of, 360; heat of fusion prob.; waves in, 375 lab, 381, 389, 389 thermistors, 782; in transistors and of, 324, 324 table, 325 prob.; insulating, lab Index integrated devices, 787–789 778–779; melting point of, 323, 324 Square root property, 845 Separation of charges, 547 lab; pressure and, 342, 343 prob., Square roots, 839 Series circuits, 618–620, 619 prob., 359–360; thermal expansion of, Stability, 212–213, 213 lab, 220 632–633 lab. See also Parallel circuits; 347, 360–361, 362 prob., 363, Stair climbers, work and power and, Series-parallel circuits; current in, 363 prob. 274–275 lab 619; equivalent resistance and, 619; Songbird migration, relative velocity Standard model of matter, 818–823; voltage drops in, 620, 621 prob. and, 159 antimatter and, 819–820; leptons and Series connections, 600 Sound. See also Sound waves; music. quarks, 818–819, 819 table; protons Series-parallel circuits, 629, 630 prob. See Music, physics of; properties and and neutrons, 819; testing of, Sextant, 172 illus. detection of, 403–407 822–823; weak nuclear force Sharing of charges, 575–576 Sound detectors, 405 and, 821–822 Ships, floating of, 355 Sound level, 406 Standardized Test Practice, 29, 55, 85, Shock absorbers, running shoes Sound quality, 415, 417–418 117, 145, 169, 227, 283, 311, 339, 373, as, 304 Sound spectra, 417 401, 429, 455, 483, 513, 539, 561, 589, Shock, electric, 597 Sound waves, 387, 403, 404–410; 615, 641, 669, 695, 721, 745, Short circuits, 627, 628 detection of by human ear, 405; 773, 797, 831 Short-period comets, 172 Doppler effect and, 407–408, 409 Standing waves, 389, 412–413 SI units, 5–6; base units, 5, 5 table; prob., 410; loudness and, 406–407; Stars, plasma in, 348 converting between, 6; prefixes, 6 table from musical instruments. See Music, States of matter, Bose-Einstein Significant digits, 7, 8 prob., 12, physics of; pitch and, 406; properties condensates, 366, 768; changes in, 833–834, 835–836 of, 404–405; reproduction of, 419; 323–324, 324 lab, 325 prob.; fluids. Silicon, semiconductors and, 779, 781, sound detectors and, 405; speed of, See Fluids; gases. See Gases; solids. 782 prob. 404–405, 405 table, 413, 416 prob., See Solids Simple circuits. See Series circuits 420–421 lab; in the Sun, 422; Static electricity, applications of, Simple harmonic motion, 375; wavelength of, 404 552–553; charging by conduction, amplitude of, 375; pendulums and, Space, affect of mass on (Einstein’s 547, 549 lab; charging by induction, 378–379, 379 prob., 392–393 lab; theory of relativity), 184–185 548, 549 lab; conductors and period of (T), 375; resonance and, Space heaters, release of thermal insulators and, 544–545; Coulomb’s 380; springs and, 376–378, 377 prob., energy by, 601, 602 prob. law, 549–550, 551 prob., 552, 552 380 prob. Space stations, rotating, 162 prob.; damage to electronic devices by, Simple machines, 269; human body as, Space telescopes, 476 570; electric charge and, 541–544, 273; ideal mechanical advantage Space travel, affect on humans, 162; 554–555 lab; electric force and, 541 (IMA), 269; six types of, 269 solar sails and, 248; space propulsion, lab, 546–550, 551 prob., 552 prob.; Sine waves, resonance length and, 239, 240 prob.; static electricity and, separation of charge on neutral 412–414 556; time dilation and, 78; weightless- objects, 547; spacecraft and, Sines, law of, 120, 856 ness and, 182 556 Single-slit diffraction, 524–526; index Specific heat, 318; of common sub- of refraction of unknown substance, stances, 318 table; measuring by Static equilibrium, 213, 214–215 prob. 526 prob.; width of bright bands on calorimetry, 319–320, 321 prob. Static friction (Ff , static), 126, 127, diffraction pattern, 525 Spectra, 440; absorption, 751–752; 129; coefficient of, 127, 136–137 lab Sinusoids, 18 electromagnetic, 708 illus., 709; Steam heat, 317 Skiing, conservation of mechanical emission. See Emission spectra; Step-down transformers, 682, 683 energy and, 294 of incandescent body, 723 lab; Step-up transformers, 682, 683, 684 Skin, resistance of, 597 rainbows and, 491–492 prob. Sky, color of, 442 Spectroscopes, 750, 752, 765 Stimulated emission, 762 Slope of a line (m), 17, 850; on force- Spectroscopy, 752, 765 STM. See Scanning tunneling microscope acceleration graphs, 91; motion Specular reflection, 459 Stored energy. See Potential energy diagrams and, 46; position-time graphs Speech, 411 Straight line equation, 16–17, 46, 47 and, 43–44 Speed, average, 20–21 lab, 44, 45 prob. table, 850
940 Index 927-942 EM INDEX-845813 6/10/04 9:23 PM Page 941
Straight-line motion, 31–47, 31 lab; (kelvin), 5 table; speed of sound and, and, 152; of projectiles launched at average speed and, 44, 45 prob.; average 404, 405 table; thermal energy and, angles, 150, 151 prob. velocity and, 43–44, 45 prob., 46–47; 314–315; thermometers and, 315; of the Transformers, 682–683; relationship coordinate systems analyzing, 34–35; universe, 725 between voltages in two coils of, displacement from, 36–37; instanta- Temperature scales, 316, 317 prob. 686–687 lab; step-down, 682, 683; neous velocity and, 46; motion diagrams Tension (F ), 94 table, 105, 106 prob. step-up, 682, 683, 684 prob.; uses of, for, 32–33, 48–49 lab; of multiple T 685 objects, 40, 40 prob., 41 prob., 42; Tera-, 6 table Transistors, 787–789; computers and, nonuniform vs. uniform, 58; Terminal velocity, 101 22; npn, 787; pnp, 787 particle model of, 33; position-time Teslas (T), 653 Translational equilibrium, 213, graphs of, 38–42; of single objects, 38, Test-Taking Tips, 29, 55, 85, 117, 218–219 lab 39 prob., 40 145, 169, 227, 283, 311, 339, 373, Translucent media, 433 Strange quarks, 819 illus. 401, 429, 455, 483, 513, 539, 561, Transmission gratings, 527 Strassmann, Fritz, 811 589, 615, 641, 669, 695, 721, 745, Transparent media, 433 Streamlines, 358 773, 797, 831 Transverse wave, 381 Stringed instruments, 411, 414–415 Theories, 10 Trigonometry, 855–856 Strings, forces of, 105, 106 prob. Thermal energy, 295; calorimetry and, Trombone, 412 Stroboscope, 775 lab 319–320, 321 prob.; changes of state Trough, wave, 383 Strong nuclear forces, 802 and, 323–324, 324 lab, 325 prob.; Trumpet, 411 entropy and the second law of thermo-
Submersibles, Archimedes’ principle Tuba, 411 Index and, 355; pressure of water on, 353 dynamics, 328–331, 329 prob.; first law Tug-of-war, 103 lab, 105 Subtractive color process, 441 of thermodynamics and, 326–328; Turbines, 676–677 Sun, color of, 442; fusion in, 814; joule heating loss, 603, 604; kinetic Twin paradox, 78 Kepler’s laws of planetary motion and, and potential energy and, 314; release Two-dimensional collisions, 241, 242 172–173; as luminous source, 432; by resistors, 601–602, 602 prob.; tem- prob., 244 prob. mass of, 173 table; period of a planet perature and, 314–315, 332–333 lab; Two-dimensional motion, Problem- orbiting, 176; power of waves from, thermometers and thermal equilibri- Solving Strategies, 149; projectile 725; pressure at center of, 343 table; um, 315; transfer of, 313 lab, 317, 318 motion, 147 lab, 147–152, 160–161 radiation from, 317, 432; radius of, prob., 319 prob. lab; relative velocity and, 157–159, 158 173 table; sound waves in, 422 Thermal equilibrium, 315 prob.; uniform circular motion and, Superconductors, 603 Thermal expansion, 347; coefficients 153–156 Superelastic collisions, 298 of, 361, 361 table; of gases, 347; of Two-dimensional waves, 390–391; Superior mirages, 490 liquids, 347; of solids, 360–361, 362 graphing, 390; reflection and, Surface gravity waves, 422 prob., 363, 363 prob. 390–391; refraction and, 391 Surface tension, 349, 350 illus. Thermistors, 782 Two-particle collisions, 236, 237 prob., Surface waves, 382. See also Mechanical Thermodynamics, 313. See also Thermal 246–247 lab waves energy; first law of, 326–328; second Two-point calibration, 13 Swim bladders, 355 law of, 329 prob., 330–331 Two-slit interference. See Double-slit Swimming, pressure and, 353 Thermometers, 315 interference Symbols, 833 Thermonuclear fusion, 826 Tympanic membrane, 405 Synchrotrons, 816 Thermostats, 363 Systemé Internationale d’Unites. Thin-film interference, 520–521, 522 See SI units prob., 523; applications of, 521; on Systems, 88; closed, 236; hydraulic, 352; butterfly wings, 523, 530; Problem- isolated, 236 Solving Strategies, 521 Thin lens equation, 493, 498 Third right-hand rule, 652 Thomson, George, 735 Ultrasound, 410 Thomson, J. J., 543, 698–699, 747, 748 Ultraviolet waves, 711 Thomson tube, charge-to-mass ratio of Uniform circular motion, 153–156; electrons, 698–699; charge-to-mass centripetal acceleration, 153, 154–155, ratio of protons, 699–700 155 prob.; centripetal force, 155 Tape players, 788 Thorium-234, 807 illus. Uniform field, electric potential Tau neutrino, 819 illus. Threshold frequency, 726–727; Einstein’s difference in, 571, 572 prob.; equation Technology. See Extreme Physics; Future photoelectric-effect theory and, 728; for, 571; Millikan’s oil-drop experiment Technology; Technology and Society work function of a metal and, 731, and, 573, 574 prob. Technology and Society, amusement 732 prob. Units, converting, 847 Thrust (F ), 94 table park rides, 138; cellular phones, 716; thrust Universal gravitation, 175–178; hybrid cars, 608; lighting, advances in, Timbre, 415 gravitational mass (mgrav) and, 184; 450; running shoes, 304; sport utility Time dilation, 78 Kepler’sthird law and, 176; Newton’s vehicles, 220 Time interval, 36 discovery of, 175; orbital period Telescopes, adaptive optical systems Time, SI base quantity (s), 5 table and, 176, 180, 181 prob.; orbital (AOSs) on, 476; refracting, 502; Tone color, 415 speed and, 180, 181 prob.; universal resolving power, 530, 531 Tone quality, 415 gravitation constant (G), 176, Television, 579, 657, 712 Top quarks, 819 illus. 177–178 Temperature, Charles’s law (volume Tops, 213 lab, 244 Universal gravitation constant (G), and temperature of a gas) and, 344; Torque, 202–203; applying to a steel 176, 177–178 combined gas law (pressure, volume, wheel, 209 prob.; balancing, 204 prob.; of Universe, expansion of, 446–447; and temperature), 345, 346 prob.; electric motors, 656, 656 prob.; net, 203 origins of, 823; temperature of, 725 limits of, 316; power of incandescent Total internal reflection, 489–490 Up quark, 819 illus. bodies and, 724; regulation of internal Trajectory, 147, 148; factors affecting, Uranium, 799, 807 illus., 812–813 by animals, 322; SI base quantity 160–161 lab; perspective of the viewer Uranus, 173 table, 179
Index 941 927-942 EM INDEX-845813 6/10/04 9:24 PM Page 942
Voltaic cells, 592 mechanical advantage of, 269, Voltmeter, 599, 600, 631, 655 271 prob. Volume, combined gas law and, 345 White light, 440–441 Wieman, Carl, 366, 768 v-t graph. See Velocity-time graph Wilson cloud chamber, 817 Vacuum, pressure in, 343 table; speed Wind instruments, 418 lab of light in (c), 438, 445 Wire loops, magnetic field near, 649 Vacuum tubes, 775 Wires, force on from magnetic field, Valence bands, 776–777 653, 654 prob.; power dissipated in, Van de Graaff generator, 567 illus., 568 W boson, 822 604; resistance of, 596, 604 Van de Graaff, Robert, 568 W bosons, 822 Work (W), 258; calculating, 259–260, Van Musschenbroek, Pieter, 577 Warm-blooded animals, 322 261 prob.; efficiency and, 268; energy Variable resistors, 597 Water, capillary action of, 350; heat of change and (work-energy theorem), Variable Specific Impulse Magneto- fusion, 324; heat of vaporization, 324; 258–259, 286–287; equation for, 258; plasma Rocket (VASIMR), 556 pressure and freezing of, 359–360; force and displacement at an angle, Variables, 15, 16; dependent, 15, 16; pressure of column of on a body, 353; 259–260, 262 prob.; gravitational independent, 15, 16; isolating in specific heat of, 318; surface tension of, potential energy (PE) and, 288; ideal equations, 845; linear relationships 349, 350 illus.; thermal energy and mechanical advantage (IMA) from, between, 16–17, 850; quadratic temperature of, 332–333 lab; waves, 267; kinetic energy and, 258–259; relationships between, 17, 852 381, 382, 387, 390–391 power (P) and, 263, 264 prob., 265, Vector components, 122 Watt (W), 263 274–275 lab; Problem-Solving Strate- Vector resolution, 122 Watt-hour meters, 604 illus. gies, 260; wheels and axles on bicycle Vectors, 35, 119–125; adding single- Watt-second, 604–605 gears, 270 lab Index dimensional, 35; adding two- Wave fronts, 390 Work-energy theorem, 258–259, 261 dimensional, 120, 121 prob., Wave model of light, 439–447, 737; prob., 286–287 123, 124 prob.; components of color and, 440–442, 441 lab; de Work function of a metal, 731, 732 (vector resolution), 122; equilibrant Broglie wavelength and, 735, 736 prob.; prob. of, 131; length and direction of Doppler effect and, 445–446; expan- displacement, 37; subtracting single- sion of the universe and, 446–447; dimensional, 37 interference and, 515–521; observed Velocity, 43–47; acceleration vs., 64; light frequency, 446; polarization of angular, 198–199; average, 44, 45 prob., light, 442–444, 444 prob., 448–449 lab; 46–47; with average acceleration, 65; reflection and, 458–459; refraction X rays, 713, 733–734 changing, 58, 58 lab; with constant and, 488–489 acceleration, 68; instantaneous, 46; Wave pulse, 381 position and constant acceleration Wavelength, 383; of light waves, 445, and, 68, 68 table; relative, 157–159; 518, 519 prob., 528, 532–533 lab; of time dilation at high, 78 mechanical waves, 383–384, 385 prob.; Velocity-time graphs, 58–59; accelera- refraction and, 488–489; of sound tion and, 62, 63 prob.; displacement waves, 404; wavelength-frequency y-intercept (b), 17, 848 from, 66, 67 prob., 68 relationship, 706 Young, Thomas, 516 Venus, 173 table Waves, 381–386; amplitude of, Yukawa, Hideki, 818 Vibrating atom, energy of, 725 382–383; behavior of at boundaries, Vibrational motion. See Periodic 387–388; crest of, 383; depicting on motion graphs, 384; electromagnetic. See Elec- Videotape recorders, 651 tromagnetic waves; frequency of, 384; Violin, 411, 417 illus. incident, 387; interference between, Virtual images, 461, 473, 473 table; 388–389, 389 lab; longitudinal, from concave lenses, 494; from Z boson, 822 381–382; mechanical, 381–382; period 0 concave mirrors, 470, 474–475 lab; Zero-g, 182 of, 383, 385 prob.; periodic, 381; phase from convex lenses, 494, 497; from Zeros, significant, 7 of, 383; reflected, 387; resonance and, convex mirrors, 471; from plane 389; sound. See Sound waves; speed of, mirrors, 462, 462 lab Viscosity, 349 382, 385 prob., 387; springs and. See Vision, 500–501, 501 prob.; focusing Springs, elastic; standing, 389; super- of images, 500; nearsightedness and position of, 388–389; transverse, 381; farsightedness, 501; resolving trough of, 383; two-dimensional, power of eye and Rayleigh criterion, 390–391; wavelength of. See Wavelength 531 Weak bosons, 818, 820 Voice, human, 411 Weak nuclear forces, 821 Volatile liquids, 351 Weather, Coriolis force and, 217 Volt (V), 569 Wedge, 269 Voltage, 570, 606–607 lab; effective, 677, “Weighing Earth” experiment, 678; Hall, 662; measurement with Cavendish’s, 177–178 voltmeter, 631; in parallel circuits, Weight (Fg), 94 table; of astronauts in 624; in series circuits, 618–619, space, 182; determination of, 96; real 621–623 prob.; of transformers, 683, and apparent, 98, 99 prob.; unit for 684 prob.; voltage dividers and, 620, (newton), 96 621 prob. Weightlessness, 98, 182, 182 lab Voltage divider circuits, 620, 621 prob., Wheel-and-axle machines, 269–270; 622 prob. bicycle gears, 270 lab; ideal mechanical Voltage drops, 620, 621 prob., 631 advantage (IMA) of, 269, 271 prob.;
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