AP B Summer Assignment Combined

DR. Malik’s AP Physics I Summer Assignment 2017

Assignment is due September 6, 2017 Assessment will be on 9/7 & 9/8

Late Penalty: 10% numerical grade reduction for each day late.

Welcome to AP Physics I! It is a college level physics course that is fun, interesting, and challenging on a level you have not yet experienced. This assignment will review all of the prerequisite knowledge expected of you.

There are six parts to this assignment. It is the quantity not the difficulty of the problems that has the potential to overwhelm, so do it over an extended period of time. By taking the time to review and understand all parts of this assignment, you will help yourself acclimate to the rigor and pacing of AP Physics.

Use online resources if you need to, but really this is all stuff you already know how to do (basic math skills). It is VERY important that this assignment be completed individually. It will be a total waste of your time to copy the assignment from a friend. The summer assignment will be due the first day of class. Good luck!

I: Scientific Notation and Dimensional Analysis

Many numbers in physics will be provided in scientific notation. You need to be able read and simplify scientific notation. (This section is to be completed without calculators…all work should be done by hand.) Get used to no calculator! Express the following the numbers in scientific notation. Keep the same unit as provided. ALL answers in physics need their appropriate unit to be correct.

1. 7640000 kg = ______2. 0.000000003 m = ______

3. 8327.2 s = ______4. 0.0093 km/s = ______

Often times multiple numbers in a problem contain scientific notation and will need to be reduced by hand. Before you practice this, remember the rules for exponents you learned in algebra: Complete the following statements.

5. When numbers with exponents are multiplied together, you ______the exponents and

the bases.

6. When numbers are divided, you the exponents and the bases.

7. When an exponent is raised to another exponent, you the exponents and the base.

Using the three rules from above, simplify the following numbers in proper scientific notation: 6 4 8. (3x10 ) · (2x10 ) = ______4 -2 9. (1.2x10 ) / (6x10 ) = ______10. (4x108) · (5x10-3) = 11. (7x103)2 = ______13. (2x10-3)3 = ______12. (8x103) / (2x105) = ______Fill in the power and the symbol for the following unit prefixes. Look them up as necessary. These should be memorized for next year. Kilo- has been completed as an example. Complete the rest.

14. Prefix Power Symbol Giga- Mega- Kilo- 103 k Centi- Milli- Micro- Pico-

Not only is it important to know what the prefixes mean, it is also vital that you can convert between metric units. If there is no prefix in front of a unit, it is the base unit which has 100 for its power, or just simply “1”. Remember if there is an exponent on the original unit, the converted unit should be raised to the same exponent.

Convert the following numbers into the specified unit. Use scientific notation when appropriate.

15. 24 g = kg 2 2 19. 3.2 m = cm

16. 94.1 MHz = Hz 20. 40 mm3 = m3

17. 6 Gb = kb 21. 1 g/cm3 = kg/m3

18. 640 nm = m 22. 20 m/s = km/hr

For the remaining scientific notation problems, you may use your calculator. It is important that you know how to use your calculator for scientific notation. The easiest method is to use the “EE” button. An example is included below to show you how to use the “EE” button. Ex: 7.8x10-6 would be entered as 7.8 E -6

23. (3.67x103)(8.91x10-6) = ______

24. (5.32x10-2)(4.87x10-4) = ______

25. (9.2x106) / (3.6x1012) = ______

26. (6.12x10-3)3 = ______II: Geometry Calculate the area of the following shapes. It may be necessary to break up the figure into common shapes.

1. 7 m 2.

22 m 12 m 16 m 6 m

15 m 18 m

Area = Area =

Calculate the unknown angle values for questions 3-6.

A B m C D E F H n G

Lines m and n are parallel.

A = 75° B = C = D =

E = F = G = H =

θ =____ 1

θ 2 =______

θ 3 =______A = B =

θ = 4 θ = C = D = 5

III: Trigonometry

Write the formulas for each one of the following trigonometric functions?

1. sinθ = ______2. cosθ = ______3. tanθ = ______

Calculate the following unknowns using trigonometry. Use a calculator, but show all of your work. Please include appropriate units with all answers. (Watch the unit prefixes!)

y d x 4. 5. d 6. θ y x θ = 30° θ = 17° θ = 60° y = d = x = x x = d = y = y

39.8 m 2.3 mm 8. 9. 7.

1.4 m c = R = d =

θ = θ = θ =

13.7 m d 12. 10. 11. θ = 26° 6.7 m θ 21.6 km x

y = x = R =

θ = d = θ =

You will need to be familiar with trigonometric values for a few common angles. Memorizing this diagram in degrees or the chart below will be very beneficial for next year (in math and physics!). In the diagram, the cosine of the angle is the x-coordinate and the sine of the angle is the y-coordinate (in other words, each radius of the circle shown is the hypotenuse of a right triangle). Write the ordered pair (in fraction form) in the table below for each of the angles shown on the quarter-circle.

90° 60°

Refer to your completed chart to answer the following questions?

14. At what angle is sine at a maximum?

15. At what angle is sine at a minimum?

16. At what angle is cosine at a minimum?

17. At what angle is cosine at a maximum?

18. At what angle are the sine and cosine equivalent?

19. As the angle increases in the first quadrant, what happens to the cosine of the angle?

20. As the angle increases in the first quadrant, what happens to the sine of the angle?

Use the figure at right to answer problems 21 and 22. l θ

h 21. Find an expression for h in terms of l and θ?

22. What is the value of h if l = 6 m and θ = 40°?

IV: Algebra

Solve the following (almost all of these are extremely easy – it is important for you to work independently). Units on the numbers are included because they are essential to the concepts, however they do not have any effect on the actual numbers you are putting into the equations. In other words, the units do not change how you do the algebra. Show every step for every problem, including writing the original equation, all algebraic manipulations, and substitution!

Section A: For problems, 1-4, use the three equations below:

Using the first equation to solve for t given that = 5 m/s, = 25 m/s, and a = 10 m/s2? 1. v0 vf

Given = 0 m/s, = 0 m and t = 10 s, use the second and third equations together to find ? 2. v0 x0 xf If a = 10 m/s2, = 0 m, = 120 m, and = 20 m/s. Use the second equation to find 3. x0 xf v0 t ?

How does each equation simplify when a = 0 m/s2 and = 0 m? 4. x0

Section B: For problems, 5 – 11, use the four equations below.

ΣF = ma

f = µ N

f ≤ µ N

s s F = −kx

5. If ΣF = 10 N and a = 1 m/s2, find m using the first equation?

6. Given ΣF = f , m = 250 kg, µ = 0.2, and N = 10m, find a?

7. ΣF = T – 10m, but a = 0 m/s2. Use the first equation to find m in terms of T?

8. Given the following values, determine if the third equation is valid? (Given: ΣF = f , m = 90 kg, and a = 2 m/s2.

Also, µ = 0.1, and N = 5 N).

s 9. Use the first equation in Section A, the first equation in Section B and the following givens and find ΣF? (given: m = 12

kg, v = 15 m/s, v = 5 m/s, and t = 12 s) 0 f

10. Use the first equation in Section I, the first equation in Section II and the following givens to find ΣF? (given:

m = 12 kg, v = 15 m/s, v = 5 m/s, and t = 12 s) 0 f

11. Use the last equation to solve for F if k = 900 N/m and x = 0.15 m? s Section C: For problems 12, 13, and 14 use the two equations below.

2 a =v

τ = rFsinθ

12. Given that v is 5 m/s and r is 2 meters, find a?

13. Originally, a = 12 m/s2, then r is doubled. Find the new value for a?

14. Use the second equation to find θ when τ = 4 Nm, r = 2 m, and F = 10N?

Section D: For problems 15 – 23, use the equations below.

K = 1/2mv2

ΔUg = mgh W = F(Δx)cosθ

2 Us = 1/2kx P = W/t

P=Fvavgcosθ

15. Use the first equation to solve for K if m = 12 kg and v = 2 m/s?

If ∆U = 10 J, m = 10 kg, and g = 9.8 m/s2, find h using the second equation? 16. g

If K = ∆U , g = 9.8 m/s2, and h = 10 m. Find 17. g v? 18. The third equation can be used to find W if you know that F is 10 N, ∆x is 12 m, and θ is 180°? 19. Use the value for W you found in the previous question to find P if t = 2 s. Which equation do you need?

Given U = 12 joules, and x = 0.5 m, find k using the fourth equation? 20. s

21. For the same value of x as given in problem 20 and the k value you just found, use the last equation in Section B to find F ? s

22. Assuming θ = 0° and F = F , use the third equation listed above along with the numbers found and s given in the previous two questions to find W?

23. For P = 2100 W, F = 30 N, and θ = 0°, find v using the last equation in this section? avg

Section E: For problems 24 – 26, use the equations below.

p = mv

J = FΔt = Δp Δp = mΔv

24. If p is 12 kgm/s and m is 25 kg. Find v using the first equation?

The symbol “∆” means “final state minus initial state”. So, ∆v means v – v and ∆p means p – p . Find 25. f i f i v using the third equation if p = 50 kgm/s, m = 12 kg, and v and p are both zero? f f i i

Use the second and third equation together to find v if v = 0 m/s, m = 95 kg, F = 6000 N, and 26. i f ∆t = 0.2 s?

Section F: For problems 27 – 29 use the three equations below.

T is 1 second and g is 9.8 m/s2. Find l using the second equation? 27. p

m = 8 kg and T = 0.75 s. Solve for k? 28. s

Given that T = T, g = 9.8 m/s2, and that l = 2 m, find f (the units for f are Hertz)? 29. p Section G: For problems 30 – 33, use the equations below.

30. Find F if G = 6.67 × 10-11 m3 kg-1 s-2, M = 2.6 × 1023 kg, m = 1200 kg, and r = 2000 m? g

31. What is r if U = -7200 J, G = 6.67 × 10-11 m3 kg-1 s-2, M = 2.6 × 1023 kg, and m = 1200 kg? g Use the first equation in Section IV for this problem. K = U , G = 6.67 × 10-11 m3 kg-1 s-2, and 32. g M = 3.2 × 1023 kg. Find v?

Using the first equation above, describe how F changes if r doubles? 33. g

Section H: For problems 34 – 38, use the equations below.

34. If P = 100,000 Pa, ρ = 1.2 kg/m3, g =9.8 m/s2, and h = 75 m, calculate the value of P? 0 35. If m doubles but V is halved, how does F change if g is constant? b

36. Using the first equation, third equation, and the first equation from Section B, determine the value of a if

3 3 2 ρ = 1000 kg/m , V = 2 m , and g = 9.8 m/s . Assume F = ΣF? b

37. If y is constant, how does P change if v is tripled (use the fifth equation, here)?

38. Find v if v =300 m/s and A equals 2.5 A ? 2 1 2 1

Section I: For problems 39 – 43, use the equations below.

PV = nRT Q = mc∆T

W = −P∆V

∆U = Q + W

39. What is T, if V = 2x10-3 m3, n = 1 mol, R = 8.31 J/kg·K, and P = 7x106 Pa? 40. Assuming n and R are both held constant, what happens to T if P is doubled and V is tripled?

41. Calculate m if c = 4000 J/kg°C, Q = 6.2 kJ, and T = 12 °C. To do this correctly kJ needs to be converted into units of J?

42. If U doubles and k , R, and M remain the same values, how does v change? B rms

43. If ΔV is positive and ΔU is zero, what is the sign of Q? Justify your answer using the last two equations?

Section J: For problems, 44 – 47, use the equations below. 44. If v is constant, how does f change if λ quadruples?

45. If c is equal to 3x108 m/s. What is the value of n if v equals 2.25 x 108 m/s?

46. If n is greater than n , is θ greater than, less than, or equal to θ ? Justify your answer using 2 1 1 2 the third equation?

47. Assuming θ is 90°, write an expression for θ in terms of n and n . 2 1 1 2

Section K: For problems 48-52, use the equations below.

= 48. If s = -5 cm and s = 2 cm, calculate the value of i 0 f (units are cm for f )?

R is known to be -3.2 cm. Find s if s = 4 cm? 49. i 0

What is the numerical value of M if s = 2f (M has no units)? 50. 0

51. What is θ if d = 8.5x10-4 m, m = 2, and λ = 6.3x10-7 m?

52. Using the last two equations, calculate x if θ is 1.2°, m is 1, λ is 400 nm, and L is 1.4 m. To solve this correctly, λ m

should be converted from units of nm to m?

Section L: For problems 53– 58, use the equations below. = qV

53. k is a constant and is always equal to 9.0 × 109 Nm2/C2. If q = 1.2 × 10-13 coulombs, Q = -q, and F = -10 Newton’s then find r using the first equation?

54. Another way of writing k is . Using k = 9.0 × 109 Nm2/C2, solve for E ? o 55. Find E using the fourth equation if V = 120 volts and d = 0.2 meters?

56. Use the second and fourth equations together to find V if r = d, Q = 1.6 × 10-19 C and k is 9.0 × 109 Nm2/C2. Can you find the fifth equation in your algebraic steps?

If I have a U of 12 joules and I double Q and q then what is my new value of 57. E U ? E 58. 58. If F is 0.2 N, d = 2.0 × 10-4 m, and q is 8.0 × 10-19 C, find V?

Section M: For problems 59 – 64, use the equations below.

i 59. If C is 12× 10-6 farads and V is 12 volts, find Q using the first equation?

60. The relationship between E and k is described in problem number 35. Use that relationship to re-write the

second equation listed in this section in terms of k instead of E ?

O 61. E is a constant and always equals 8.85× 10-12 C2/Nm2. If A = 0.3 m2 and d = 0.012 m, find C?

62. Given Q = 3.0 × 10-6 C, and C = 7× 10-6 F, find U ? C

Use the fourth equation to find C if C = 2× 10-6 F, C = 4× 10-6 F, and C = 6× 10-6 F? 63. P 1 2 3

Use the fifth equation to find C if C = 2× 10-6 F, C = 4× 10-6 F, and C = 6× 10-6 F? 64. S 1 2 3

Section N: For problems 65 – 70 use the equations below. V = IR

65. Given V = 220 volts, and I = 0.2 amps, find R (the units are ohms, Ω)?

66. If ∆Q = 0.2 C, t = 1s, and R = 100 Ω, find V using the first two equations?

67. R = 60 Ω and I = 0.1 A. Use these values to find P using the first and third equations?

Let R = R. If R = 50 Ω and R = 25 Ω and I = 0.15 A, find V? 68. S 1 2

Let R = R. If R = 50 Ω and R = 25 Ω and I = 0.15 A, find V? 69. P 1 2

70. Given R = 110 Ω, l = 1.0 m, and A = 22× 10-6 m2, find ρ?

Section O: For problems 71 – 75 use the equations below.

BAcosθ

30 E = Bℓv

71. Find v if q = -4.8 × 10-19 C, B = 3.0 Teslas, θ = 90°, and F = -1.0 × 10-9 N? B

72. µ is a constant and so is always equal to 4π × 10-7 (Tm)/A. If I = 0.2 A, r = 0.003 m, θ = 270° and

ℓ = 0.15 m, then find F ? B

73. Find when B = 1.1 T, A = 2.0 m2, and θ = 53°?

31 74. Remember how “∆” means “final state minus initial state”? Using that, assume B does not change from 0.3 T and θ = 0°, but A changes from 0.1 m2 to 0.4 m2. If ∆t =

1.1seconds, use the above information to find E .

75. ε is 0.12 V, B is 2.0× 10-3 T, and v is 12,000 m/s. Find ℓ using the last equation in the list.

Section P: For problems 76 – 81, use the equations below.

76. Find E if h = 6.63 x 10-34 J·s, λ = 450 nanometers, and c = 3 x 108 m/s. To solve this problem correctly, convert λ into meters before plugging in the number?

77. h is a constant, so it is always equal to the value given in the prior problem. Assuming f is 4.2 x 1014 Hz and ϕ is 1.3 x 10-19 J, calculate the value of K?

32 78. Using the first equation from Section V for p, determine the value of λ given that m = 9.11 x

10-31 kg and v = 2.7 x 106 m/s?

79. c is also a constant, so it always equals 3 x 108 m/s. If the final state of m = 3.4824 x 10-27 kg and the initial state of m = 3.4829 x 10-27 kg, find ΔE?

80. K is not allowed to be negative. Find the minimum value of f that works for the third equation if ϕ is 4.3x10-19 J?

81. Find f using the first and last equation. Assume E = ΔE and that Δm = 8.3x10-31 kg?

33 V: Scalars and Vectors

Watch the following two videos:

Video 1 Link: http://www.khanacademy.org/science/physics/v/introduction-to-vectors-and-scalars

Video 2 Link: http://www.khanacademy.org/science/physics/v/visualizing-vectors-in-2-dimensions

Assignment: For each video, summarize the content Mr. Khan is presenting in two paragraphs for each video?

***You might have to watch them more than once. These concepts are some of the building blocks of Physics. A complete understanding of Scalars and vectors is essential to mastering Physics.

Conclusion:

Expect to be challenged! AP Physics 1is a college level course where you will be using your knowledge and understanding of everything you have learned in all your math and science classes to solve physics problems, analyze situations, arrange materials, compare data, design labs and build incredible things.

You cannot expect to acquire the understanding you need to do well on an AP Physics Exam by merely attending class and listening to the teacher. You must become INVOLVED. You must PARTICIPATE. If you get stuck, see ME, or other students! Ask for HELP. Your classmates will be your new best friends. You must study regularly. Students who study regularly have a good foundation to build on for new topics. This will pay off! If you are unorganized or inconsistent, things may start to fall apart – and nobody wants that to happen. Busy work is not assigned in this course so do what I ask you to do regularly! Especially the homework!!

Homework => Practice => Success

The Summer Assignment is due on September 6, 2017. The Assessment for the Summer Assignment is scheduled for September 7, 2017 and September 8, 2017.

Have a great summer! DR. Malik AP Physics Teacher [email protected]