AP Physics Summer Assignment 2010

OAKLAND TECHNICAL HIGH SCHOOL ADVANCED ACADEMIC PROGRAMS AP Physics Summer Assignment 2010

I. This packet is a review to brush up on valuable skills, and perhaps a means to assess whether you are correctly placed in Advanced Placement Physics. II. Physics, and AP Physics C in particular, requires an exceptional proficiency in algebra, trigonometry, geometry and calculus. In addition to the science concepts, Physics often seems like a course in applied mathematics. The following assignment includes mathematical problems that are considered routine in AP Physics. This includes knowing several key metric system conversion factors and how to employ them. Another key area in Physics is understanding the geometry of vectors. III. Calculus: Students who have already completed AP Calculus AB will need to remember the skills they have learned. One page of this summer assignment is devoted to a review of the important parts of calculus. Students who will be taking AP Calculus and AP Physics next year will learn these skills then; the calculus review is not required this summer. PROBLEMS

1. Algebra. Often problems on the AP exam are done with variables only. Solve for the variable indicated. Don’t let the different letters confuse you. Manipulate them algebraically as though they were numbers. Many subscripts are used as labels in physics (for example: 1, 2, c, o, i); simply keep the subscript with the variable in your solution.

22 1 a. vv=+002 axx() − , a = b. Ukx= 2 , x = 2

A mm12 c. T = 2π , g = d. FGg = , r = p g r2

1 1 e. mghmv= 2 , v = f. xx=+ vtat + 2 , t = 2 002

μ Ι mLλ g. B =⋅0 , r = h. x = , d = 2π r m d

i. pV= nRT , T = n1 j. sinθc = , θc = n2

1 2 111 k. qV= mv , v = l. = + , si = 2 fsoi s

2. Measurement. Scientists use the mks system (SI system) of units. mks stands for meter-kilogram-second; these are the preferred units for solving physics problems. You must check to be sure all measurements are converted to mks before beginning a solution. This is known as “agreement of units”. In preparation for AP Physics, you must know how to make the following conversions: kilometers (km) to meters (m) centimeters (cm) to meters (m) millimeters (mm) to meters (m) micrometers (μm) to meters (m) grams (g) to kilograms (kg) minutes (min) to seconds (s) hours (h) to seconds (s) days (d) to seconds (s) years (y) to seconds (s)

What if you don’t know the conversion factor for a conversion? Colleges want students who can find missing information for themselves (so do employers!). Hint: try a Google search with “measure” or “measurement”.

Complete each of these conversions. a. 4008 g = kg b. 1.2 km = m c. 823 μm = m d. 298 K = ºC e. 0.77 cm = m f. 8.8 × 10–8 mm = m g. 2.23 × 104 g = kg h. 2.65 cm = m

Write each measurement using the correct mks unit. i. 6.22 grams = j. 105 milligrams = k. 250 milliseconds = l. 32.3 centimeters = m. 18.2 days = n. 27 micrometers = o. 50 micrograms = p. 1000 minutes =

Write each measurement using scientific notation and the correct mks unit. q. 9.2 mm = r. 1040 mg = s. 83 kg = t. 4225 µg = u. 6.33 µg = v. 11,308 µs = w. 11.00 s = x. 40.5 ms = y. 1.00 µs = z. 7.223 kg =

3. Quadratic Equations. Frequently, equations in physics will require the quadratic formula to find a solution. Solve each of the following quadratic equations. a. xx2 +−=820 b. 231xx2 − +=0

c. 34xx+=2 d. xx2 −=53

e. xx( +=512) f. xx22−+=262 xx −− 626

4. Geometry Review. Solve the following geometric problems.

B Line B touches the circle at one point. Line A passes through the center of the circle.

a. Describe line B in relation to the circle:

______

b. What is the angle between A and B?

______

C c. What is the measure of angle C?

30º ______

45º

30º

A d. If A is parallel to B, what is the measure of angle θ? ______

θ B

e. What is the measure of angle θ ?

______

30º

f. The radius of a circle is 5.5 m.

i. What is the circle’s circumference in meters?

______

ii. What is the circle’s area in square meters?

______

3 5. Right Triangle Trigonometry. Use the generic right triangle shown in the figure. Solve the following, using the same units in your answer as are given in the problem

a. θ = 55º and c = 32 m, solve for a and b. b. θ = 45º and a = 15 m/s, solve for b and c.

c. b = 17.8 m and θ = 65º, solve for a and c. d. a = 250 m and b = 180 m, solve for θ and c.

e. a =25 cm and c = 32 cm, solve for b and θ. f. b =104 cm and c = 65 cm, solve for a and θ.

6. Vectors. Most of the quantities that are used in physics are vectors. Therefore, students must be proficient in using vectors. Definitions. Magnitude – size or extent. Magnitude is the numerical portion of a vector’s description. Direction – alignment or orientation of any position with respect to any other position. Direction is often given as an angle. Scalar – a physical quantity that is described by a single number and units. Vector – a physical quantity that is described by a magnitude and a direction. A “directional quantity”. Examples: force, velocity G Notation: A or A Length of the arrow is proportional to the vector’s magnitude. B Direction of the arrow is the vector’s direction. The head of the vector has the arrow; the tail of the vector is the other end. G G A and B are identical vectors because they both have the same magnitude and direction.

Negative Vector – It is possible to have a negative vector. The negative vector has the same magnitude as its positive counterpart, but it is pointing in the opposite direction. A –A

Vector Addition – Add vectors by combining both the magnitude and the direction. The result of adding two vectors is called the resultant. There are four situations to learn: G GG i. Both vectors point in the same direction (parallel). AB+ = R A B R (Add the magnitudes)

G GG A B R ii. The vectors point in opposite directions (anti-parallel). AB+ = R (Subtract the magnitudes. Resultant direction is same as vector with greater magnitude.)

GGG iii. The vectors are perpendicular. AB+= R (Find the resultant magnitude with the Pythagorean Theorem.) R B A R R B B A A

These two vector diagrams show the same vector addition in two different ways.

G GG iv. The vectors are in different directions. Either of two different methods will give the same resultant. AB+ = R

R B A

G G a. Parallelogram Method. The tails of A and B are connected to form adjacent sides of a parallelogram. G The resultant R points from the point where the tails connect to the opposite corner of the parallelogram. B R

G b. Head-to-Tail Method. The vectors are drawn with their correct directions, so that the tail of B is G G G connected to the head of A . The resultant R points from the tail of A to the G R head of B . B A Many vectors can be connected using the head-to-tail method, and the resultant will point from the tail of the first vector in the chain to the head of the last vector.

Vector Subtraction – Vector subtraction is exactly the same as adding the negative of the second vector. GG G G G AB−= A +−=() B R. B A –B R

A R –B

GGG Draw the resultant for the vector addition AB+= R of each of the following. Draw the given vectors using either the parallelogram method or the head-to-tail method.

A B a.

b. A B

c. A B

B A

B e. A

GGG GG f. Draw the resultant for ABCD++ + = R A

C D B

5 7. Calculus. Use these problems for review this summer. Show the solution for each problem. (Not required for students who have not studied Calculus.)

Slope of a line tangent to a curve (derivative) a. yx=−+3212 x8 b. xt=+25 30 − 4.9t2 dy dx = = dx dt

dy dx For x = 10, find y and . For t = 0.005, find x and . dx dt y = x = dy dx = = dx dt

c. xtt=−818 + 2 d. vt=+2.5 9.8 − 12t2 dx dv = = dt dt

dx dv For t = 86,000, find x and . For t = 25, find v and . dt dt x = v = dx dv = = dt dt

Anti-derivative (indefinite integral)

dy dx e. =−531xx3 +5. Write an equation for y as a f. =+20 4t2 . Write an equation for x as a function of t. dx dt function of x. y = y =

When x = 2, y = 4. Write the final equation. When t = 1 , x = 1 . Write the final equation. 2 6

dx dv g. =−74.2tt − 3 . Write an equation for x as a function h. =−2.5t2 + 12t. Write an equation for v as a function dt dt of t. of t.

x = v =

When t = 1, x = 0.45. Write the final equation. When t = 4, x = 0. Write the final equation.