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Chapter 1 Lecture Notes Chapter 1 Lecture Notes Chapter 1 What is science? Science is a body of knowledge that describes the order within nature. What is physics? Physics is the study of basic parts of life like motion, forces, energy, matter, heat, sound, and light. Our studies will take us through classical motion (from Aristotle to Newton). Units There are many things that cannot be measured. For example, we cannot put a quantitative value on how much I want a new car. However, there are many things that can be measured in a quantitative (numerical) way. For example, you can measure the length of a Corvette of the time it takes for a ball to fall to the ground from the top of a building. In order to have a way of sharing our measurements, we need to have a system of measurements (called units) that we can all agree upon. Why? Let’s imagine that I measure the length of an object and I see that it is 10 m. Now someone else measures the length of the same object and says that it is 2 glurgs long. Since we are both measuring the same object, we know that 1 glurg = 5 m. However, it would make things much easier if we both did the measurement in meters. The international or mks system of units is used throughout the majority of the world (with the exception of the United States). Length: The standard unit of length is the meter (1 m). The meter was originally defined so that the distance between the equator and the North Pole along the meridian through Paris was 10,000,000 m. The meter is now defined as the distance light travels in 1 s . 299,729,458 Physics 210 Page 1 Santiago Canyon College Chapter 1 Lecture Notes Time: The standard unit of time is the second (1 s). The second was 111 originally defined as of a mean solar day. Now 60 60 24 the second is defined by looking at photon (light) emission from excited cesium atoms. Mass: The standard unit of mass is the kilogram (1 kg) which is equivalent to 1000 grams. A one kilogram block is kept at the National Institute of Standards and Technology. Other Unit Systems km In most countries, the speed limit signs are posted in . However, in hr mi the United States, speed limit signs are posted in . hr Are these two the same? Yes and no. Both are units of speed (just like meters and glurgs are both units of length) but they are from two different unit systems. We know km mi that are from the international system of units and are from the hr hr English system of units. To be able to compare these two units, we need to convert from one unit system to the other. From appendix A of the text: 1 km = 0.6215 mi mi So let’s imagine that you were driving along at 65.00 . What is your hr km speed in ? hr Physics 210 Page 2 Santiago Canyon College Chapter 1 Lecture Notes mi 1 km km 65.00 * =104.6 hr 0.6215 mi hr m What would your speed be in ? s km 1000 m 1 hr 1 min m 104.6 ∗ ∗ ∗ =29.06 hr km 60 min 60 s s Example 1: The main span of the Golden Gate Bridge is 4200 ft. Express this distance in kilometers. Solution: Example 2: There are 1.057 quarts in a liter and 4 quarts in a gallon. (a) How many liters are there in a gallon? (b) A barrel equals 42 gallons. How many cubic meters are there in a barrel? Solution: Physics 210 Page 3 Santiago Canyon College Chapter 1 Lecture Notes Scientific Notation During this course, we will be dealing with very large and very small numbers. If we write out 27 billion it looks like: 27,000,000,000 This notation can be difficult to work with, so we would like to develop a more compact notation. For example: 470,000 = 4.7 ∗ 100,000 = 4.7∗∗∗∗∗ 10 10 10 10 10 =4.7 × 105 This is called scientific notation. In practice, we don’t want to have to factor out all of the powers of 10. If you look at our original number I have to move the decimal place to the left 5 times for it to be just behind the last digit. Therefore, the exponent on the 10 is 5. Example 3: Convert the following numbers into scientific notation: a) 43,000 b) 425,000,000 c) 982,000,000,000 Solution: Physics 210 Page 4 Santiago Canyon College Chapter 1 Lecture Notes What if our number is less than one? Consider the following number: 0.00034 In order to write this number in scientific notation, the decimal point would have to shift to the right 4 places. Moving the decimal point to the right is the same as dividing by 10; therefore, the exponent in scientific notation is now negative. Therefore, our final result is: 0.00034 = 3.4× 10−4 Example 4: Convert the following decimal numbers into scientific notation: a) 0.00875 b) 0.000053 c) 0.0000000782 d) 0.00000000000643 Solution: Physics 210 Page 5 Santiago Canyon College Chapter 1 Lecture Notes Unit Prefixes As we have already seen: 1 km = 1000 m = 103 m The m above stands for meters (the unit) and the k stands for kilo (which means 1000). The k is called a unit prefix. Another example might be: 3.0GHz = 3.0× 109 Hz In this case Hz is the units (called a Hertz) and G is the prefix (giga = 1,000,000,000). Multiple of 10 Prefix Abbreviation 1012 Tera T 109 Giga G 106 Mega M 103 Kilo k 10−2 centi c 10−3 milli m 10−6 micro µ 10−9 nano n 10−12 pico P 10−15 femto f Physics 210 Page 6 Santiago Canyon College Chapter 1 Lecture Notes Example 5: Write the following in scientific notation: a. 3.1 GW b. 10 pm c. 2.3 fs d. 4s µ Solution: Physics 210 Page 7 Santiago Canyon College Chapter 1 Lecture Notes Coordinate Systems One of our goals is to know the position of our moving object at various times. So far we have restricted ourselves to motion along the x or y axis. The Cartesian coordinate system consists of vertical (y) and horizontal (x) axes which intersect at a point called the origin. These axes are perpendicular to each other and look like: The vector A is defined by two points, the origin and the point (x,y). Our final point (x,y) can be expressed in polar coordinates (r,θ) where: y r= x22 + y and tan θ = (1) x Similarly, our Cartesian coordinates can be expressed in terms of polar coordinates: x= rcosθ and y= rsin θ (2) Physics 210 Page 8 Santiago Canyon College Chapter 1 Lecture Notes Example 6: The polar coordinates of a point are r = 5.50 m and θ=240 . What are the Cartesian coordinates of this point? Solution: Physics 210 Page 9 Santiago Canyon College Chapter 1 Lecture Notes Example 7: If the Cartesian coordinates of a point are given by (2,y) and its polar coordinates are (r,30 ), what are the values of y and r? Solution: Physics 210 Page 10 Santiago Canyon College Chapter 1 Lecture Notes Vectors and Scalars • A scalar quantity is specified by a single value with an appropriate unit and has no direction. • A vector quantity has magnitude and direction (as well as the appropriate unit). A vector quantity is represented as A. The magnitude of the vector can be represented by A or A. Properties of Vectors Equality of Two Vectors Two vectors A and Bare equal if they both have the same magnitude and they point in the same direction. That is: A= B ⇔ A = B&A B Adding Vectors A vector is usually represented by an arrow pointing in its direction and the length of the arrow represents its magnitude. Using this representation of vectors, we are able to add vectors together graphically. To add Bto A : 1. Draw A to scale (for example 1 cm in your drawing could equal 1 km in reality). 2. Now draw B, using the same scale, starting at the tip of A . 3. The resultant vector R= AB + is drawn from the tail of A to the tip of B. Physics 210 Page 11 Santiago Canyon College Chapter 1 Lecture Notes This is known as the triangle method of addition. In the parallelogram rule of addition the tails of the two vectors are joined together and the resultant vector is the diagonal of the parallelogram. Vector addition is commutative. ABBA+=+ (3) If you are adding more than two vectors, the addition obeys the associative law. For three vectors that would look like: A++=( BC) ( AB ++) C Physics 210 Page 12 Santiago Canyon College Chapter 1 Lecture Notes Subtraction of vectors is the same as vector addition but you first need to take the negative of the vector being subtracted. The negative of B has the same magnitude but points in the opposite direction. Multiplying a Vector by a Scalar When multiplying a vector by a scalar (B= sA), the magnitude of B will be B= sA. If s > 0, B will be parallel to A (point in the same direction); however, if s < 0 then B and A will be anti-parallel (point in opposite directions).
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