AP Physics I Practice Problems PDF

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AP Physics 1: 1D Kinematics (Short Answer) Learning Objective:

3.A.1.1

1) The frame of a 10 story building is under construction. A worker on the 4th floor of the building throws an apple to a friend on the 6th floor. The worker throws the apple almost directly upwards and the friend is not ready so it passes him on the way up and he catches it on its’ way back down. In a clear, coherent, paragraph-length answer, explain why the speed of the apple half way between the release and the maximum height is not half the initial speed. Include a qualitative justification for the speed being greater or less than half the initial speed. You may use no equations to justify your conclusion.

KEY 7 Points Gravity decreases the speed of the apple uniformly with time as it rises. +2 Average speed for first half of the path is greater than the average speed over the second half. +1 Apple will travel the first half of the path in less time than the second half of the path. +1 Speed decreases less during first half of path than the second half of path. +1 Speed at mid-point is greater than half the initial speed. +2

AP Physics 1: Circular Motion (Quantitative/Qualitative Translation) Learning Objectives:

3.A.1.1, 3.A.2.1, 3.B.1.1, 3.B.1.2, 3.B.1.3, 3.B.2.1

1) A person on a Ferris wheel is shown at various points during the rotation. The rotation is counterclockwise so that the passengers have a constant speed, V0. The mass of the person is m, and the radius of the ride is R. Assume the radius, R, of the Ferris wheel is much greater than the distance between the person and the connection to the ride so that the radius of motion of the person is R. a) On the diagram below, draw and label vectors for the direction of the velocity and acceleration of the passenger when at Point P.

P

R

A

b) On the diagram to the right, draw and label all forces acting on the person at Point A.

c) Derive an expression for the maximum normal force on the passenger. Express the force in terms of V0, m, R and fundamental constants.

d) Derive an expression for the minimum period, Tmin, for the person to maintain contact with the ride. Express the period in terms of R and fundamental constants. The person moves through Positions A, B, C and D with a constant speed, V0 and radius, R.

C

e) Rank these four positions from greatest to least (1 – Greatest, 4 – Least) according to the magnitude of their centripetal acceleration. If more than one position has the same magnitude, give them the same ranking. D

B

Position A ______Position B ______ Position C______ Position D _______

R

A

Justify your answer using a multiple sentence paragraph. Include equations, fundamental laws, free body diagrams and graphs if needed to help justify your statement.

KEY 12 Points a) 2 Points For drawing and labeling a velocity vector tangent to the path and in the direction consistent with ccw. +1 For drawing and labeling an acceleration vector directed toward the center of the curved path. +1 V 0

a c

b) 2 Points For drawing and labeling the normal force vector up. +1 For drawing and labeling the gravitational force vector down. +1

F N

F g

c) 3 Points For summing the forces in the radial direction +1 Σ F r=ma r For summing forces correctly

+1

2

V F N −F g=m R0 For correct algebraic solution in terms of given variables and fundamental constants +1

(

F N =m g+

2

V0 R

)

d) 3 Points Σ F r=ma r V2 r FN = 0 at Tmin and Vmax For force of gravity being the only radial force V2 +1 F g=m max R Substitute Vmax and Fg +1 2 πR V max = T min F g=mg For correct algebraic solution in terms of given variables and fundamental constants +1 2 4π R T min= g F g− F N =m

√

e) 2 Points Position A ___1___Position B ___1___ Position C___1___ Position D ___1____ For all position having the same ranking +1 For complete justification +1 Example Centripetal acceleration is dependent on tangential speed and radius (ac = v2/r) All positions have the same speed and radius.

AP Physics 1: Circular Motion (Short Answer) Learning Objective: 3.A.3.1, 3.B.2.1 1) A person on a Ferris wheel is shown at various points (A, B, C & D) during the rotation. The rotation is counterclockwise so that the person has a constant speed, V0. The mass of the person is m, and the radius of the ride is R. Assume the radius, R, of the Ferris wheel is much greater than the distance between the person and the connection to the ride so that the radius of motion of the person is R.

C

D

Rank these four positions from greatest to least (1 – Greatest, 4 – Least) according to the magnitude of the normal force acting on the person. If more than one position has the same magnitude, give them the same ranking.

B

R

A

Position A ______Position B ______ Position C______ Position D _______ Justify your answer using a multiple sentence paragraph. Include fundamental laws, free body diagrams and graphs if needed to help justify your statement. You may use no equations or calculations.

KEY 7 Points Position A ___1___Position B ___2___ Position C___3___ Position D ___2____ For Position A ranking higher than Position C +1 For Position B and D having equal rankings +1 For recognizing the normal force is greater than the force of gravity at Position A +1 Relating forces at Position A to acceleration +1 Example FNA > Fg because FNA must overcome Fg and accelerate person up (toward center of Ferris wheel). For recognizing the vertical component acceleration is zero at Positions B and D +1 Example FNB = FND = Fg because there is no acceleration up or down.

For recognizing force of gravity is greater than the normal force at Position C +1 Relating forces at Position C to acceleration +1 Example FNC < Fg because Fg must overcome FNC and accelerate person down (toward center of Ferris wheel).

P1 - 22 Multiple Choice Questions 1) 100 Watt light bulbs are rated for 1600 lumens at 120 volts. 60 Watt light bulbs are rated for 800 lumens at 120 volts. 40 Watt light bulbs are rated for 450 lumens at 120 volts. Compare the total energy given off in one hour by 1-100 Watt bulb, TE100, 2-60 Watt bulbs, 2TE60, and 3-40 Watt bulbs, 3TE40. a) b) c) d)

TE100 < 2TE60 < 3TE40 TE100 > 2TE60 > 3TE40 TE100 = 2TE60 > 3TE40 TE100 = 2TE60 = 3TE40

Answer: d Difficulty: Easy Blooms: Application AP LO: 5.B.4.2

2) A satellite is held in a uniform circular orbit at a height of one earth-radius above the surface of the earth. An orbital period of 24 hours is maintained by the application of a force of constant magnitude. What is the direction of the applied force if the satellite is orbiting in a counter clockwise direction?

Answer: d Difficulty: Medium Blooms: Analysis AP LO: 2.B.2.2, 3.A.3.1

3) A solid sphere and a hoop roll down an incline without slipping, while a box slides down the same incline without friction. All three land on the floor after travelling the same horizontal distance from the end of the incline. Which of the following is the same for all three? a) Their velocity just before hitting the floor. b) Their starting position on the incline. c) Their kinetic energy just before hitting the floor. d) Their horizontal linear momentum just before hitting the floor. Answer: a Difficulty: Easy Blooms: Application AP LO: 3.A.1.3

2 Answer 4) A straight tunnel is found to resonate strongly at frequencies 93.4 Hz and 233.5 Hz. With what other frequencies will the tunnel also strongly resonate? Select two answers. a) 31.3 Hz

b) 70.1 Hz c) 186.7 Hz d) 280.2 Hz Answer: c, d Difficulty: Hard Blooms: Analysis AP LO: 6.D.3.2

SET OF 2 (5-6) 5) A uniform bar of mass, M, length, L, and moment of inertia, I, is hanging vertically at rest on a frictionless pivot when it is struck at the very end by a ball of mass, m, and velocity, v. The ball rebounds directly back at v/2, while the bar rotates at an initial angular velocity, ω, as the result of the collision. Derive an expression for the mass of the ball, m, in terms of L, I, ω, v, and fundamental constants.

a)

m=

2 Iω vL

b)

m=

Iω 2 vL

c)

m=

3 Iω 2 vL

d)

m=

Iω+ vL 2 vL

Answer: c Difficulty: Medium Blooms: Analysis AP LO: 4.D.2.1

6) Derive an expression for the maximum angle, θ , through which the bar rotates after collision in terms of M, L, I, ω, and fundamental constants.

2 a) θ=cos−1 (1− I ω ) MgL

b)

−1

θ=cos (1−

MgL ) I ω2 2

−1

c) θ=cos (1−

d)

−1

Iω ) 2 MgL

θ=cos (1−

2 MgL ) I ω2

Answer: a Difficulty: Medium Blooms: Analysis AP LO: 5.B.4.2

7) A car is towing a trailer down an incline when the driver applies the car's brakes. Which of the following best represents the Free Body Diagrams of the forces acting on the car and trailer separately?

Answer: b Difficulty: Easy Blooms: Application AP LO: 3.A.4.3, 3.B.2.1

8) A car driving up an incline at speed V o brakes hard and slides to a stop in a distance X. The same car driving down the same incline at Vo also brakes hard and slides to a stop in a distance 2X. Determine the angle of the incline, θ, if coefficient of kinetic friction of the car tires on road is 0.2. a) θ = 35° b) θ = 31° c) θ = 22° d) θ = 11° Answer: b

Difficulty: Hard Blooms: Application AP LO: 3.B.1.1

SET OF 2 (8 & 9) 9) A disk is rolled at constant velocity along a horizontal surface without slipping by the tension in a string attached to frictionless axel in the center of the disk. A uniform homogeneous bar is attached to a wall by a frictionless pin and rests horizontally on top of the disk. The coefficient of kinetic friction between the disk and bar is constant. Which of the following graphs best represents the tension in the string, T, as a function of X, the distance from the wall to the center of the disk?

Answer: d Difficulty: Medium Blooms: Analysis AP LO: 4.A.2.3

10) Which of the following shows the correct Free Body Diagram for the bar while the sphere is rolling at constant velocity and located at position X = L/4?

Answer: a Difficulty: Easy Blooms: Analysis AP LO: 3.B.2.1

MC - 2 answers 11) Four small rocket cars initially at rest are launched along a horizontal frictionless road. Graphs for rocket cars 1 and 4 show the net force vs time for launches using a rocket car of 2 units mass, while graphs for rocket cars 2 and 3 show launches for rocket cars of 8 units mass. Which of the rocket cars have the same final kinetic energy? Select two answers.

a) Rocket car 1

b) Rocket car 2 c) Rocket car 3 d) Rocket car 4 Answer: a, b Difficulty: Hard Blooms: Analysis AP LO: 3.D.3.2

SET OF 2 (12 & 13) 12) A wheel-shaped space station is rotating with a period T far away from any gravitational field. An astronaut inside the space station is standing on a bathroom scale which indicates her weight to be W. If the period of rotation of the space station is changed to 2T, what would the reading of the bathroom scale now be the same astronaut?

a) 4W b) 2W c) W/2 d) W/4 Answer: d Difficulty: Easy Blooms: Application AP LO: 3.A.3.1

13) While the space station is rotating with a constant period T, the astronaut rides an elevator which takes her directly toward the center of the space station at a constant speed. Which of the following shows how the reading of the bathroom scale will change as the astronaut moves from her current location to the center of the space station?

a) Graph 1 b) Graph 2 c) Graph 3 d) Graph 4 Answer: b Difficulty: Medium Blooms: Application AP LO: 3.B.1.1

SET of 2 (14&15) 14) Two identical ideal springs are hung vertically from the same beam. When a uniform bar is attached to both springs they stretch a distance ΔX. The bar is then pulled down an additional distance ΔX and released from rest. How do the gravitational potential energy of the bar (Ug), kinetic energy of the bar (KE) and the total 3∆X above its release point? Assume spring potential energy (Us) compare when the bar reaches a position 2 Ug = 0 at the position the bar is released.

a) Ug < KE = Us b) Ug > KE = Us c) Ug > KE < Us d) Ug > KE > Us Answer: d Difficulty: Hard Blooms: Analysis AP LO: 5.B.3.3

15) Given that the spring constant for each spring is K, what would the spring constant of the system be that would be used to calculate the period of oscillation of the bar?

a) 2K b) √ 2 K c) K/2 d) √ K /2 Answer: a Difficulty: Easy Blooms: Analysis AP LO: 3.B.3.3

SET of 2 (16&17) A block is initially moving in a circle on a horizontal frictionless tabletop held by the force of a string that passes through a small hole in the center of the table. The string, which hangs vertically under the table, is pulled slowly downward.

16) The initial radius of rotation of the block is Ro, and the initial tension in the string is To. When R is reduced to Ro/2, what is the new tension in the string expressed in terms of To? a) 2To b) 4To c) 8To d) 16To Answer: c Difficulty: Hard Blooms: Analysis AP LO: 5.E.1.2

17) What is the ratio of the final kinetic energy of the block to its initial kinetic energy? a) 1:2 b) 1:1 c) 2:1 d) 4:1 Answer d Difficulty: Medium

Blooms: Application AP LO: 5.B.1.1

MC 2 answer 18) A traditional wheelchair uses a circular drive rim slightly smaller than the actual wheel which the user rotates in order to move. A newly designed wheelchair includes a long rod on each side which is attached to the center hub of the wheel by a ratchet mechanism. The ratchet causes the wheel to rotate when the rod is pushed forward causing the wheelchair to move forward, and also allows the rod to return to the initial position without affecting the forward motion of the wheelchair. By alternately pushing and pulling the rod, the user can keep the wheelchair in motion. Noting that the rod can be pushed at any position along its length, the manufacturer makes several claims concerning the advantage of this system. Which of the following claims might the manufacturer correctly make? Select two answers.

a) The work required to be done by the user to move the wheelchair is reduced. b) The user is able to climb an inclined ramp with a reduced effort force. c) Less arm movement is required to maintain a high speed by pushing on the rod close to the hub. d) The system is more efficient due to the longer lever arm of the rod. Answers: b, c Difficulty: Medium Blooms: Evaluation AP LO: 3.F.2.1

SET of 3 (19 - 21)

A popular amusement park ride consists of 3 rotating arms, each of which has a smaller 3 rotating-arm system attached at the end. The 3 main arms sweep out a 5.4-meter diameter circle while rotating clockwise at 1.6 rad/s. Riders, located in seats attached to the ends of the smaller arms, sweep out a 3.6-meter diameter circle while rotating counterclockwise at 2.0 rad/s. Riders are currently located in seats at positions A, B and C. 19) Which rider is experiencing the greatest angular velocity around the center of the ride? a) A b) B c) C d) All riders are experiencing the same angular velocity Answer: a Difficulty: Medium Blooms: Analysis AP LO: 3.A.1.1

20) Determine the ratio of the centripetal acceleration of rider A to the centripetal acceleration of rider B. a) 1.8 b) 5.0 c) 9.0 d) 16 Answer: d Difficulty: Hard Blooms: Analysis AP LO: 3.A.1.3

21) Which vector best represents the current acceleration of rider C?

Answer: b Difficulty: Medium Blooms: Analysis AP LO: 3.A.1.3

MC 2 Answer 22) A spring is hanging in equilibrium when a mass is attached to the end of the spring and released. The spring-mass system oscillates vertically in simple harmonic motion. A second identical spring is hanging in equilibrium when an identical mass is attached to the spring and released. However, when the second mass reaches the lowest point of its motion, half of the mass breaks off and the spring with the remaining mass oscillates in simple harmonic motion. When compared to the values of the first spring-mass system, which of the following values are different for the second spring-mass system? Select two answers. a) Period b) Amplitude c) Velocity at the equilibrium position d). Energy Answer: a, c Difficulty: Medium Blooms: Analysis AO LO: 3.B.3.1 1AP Physics 1 Multiple Choice Questions 1.

A student investigating the motion of an object measures the distance that it moved and the time that it took to move this distance. From these measurements only, which of the following does the student have enough information to calculate?

a. b. c. d.

Average speed only. Acceleration only. Average speed and acceleration. Instantaneous speed only.

Difficulty: Easy Blooms: Comprehension AP LO: 3.A.1.1

a. b. c. d.

Two objects are next to each other and begin moving from t = 0. They then each move in a straight line in the same direction according to the acceleration - time graph here. Which of the following statements is true for these objects? Both objects have the same speed at t = t1 The objects are again beside each other at t = t1 The objects have the same speed at t = t2 The objects are again beside each other at t = t2

Difficulty: Difficult Blooms: Application AP LO: 3.A.1.1

rest at

object 2 a c c e le ra tio n

2.

0

shown

object 1 t1

t2

time

A ball of clay is thrown upwards. It strikes the ceiling where it remains stuck for a short time before falling down to the same position it was thrown from. Which of the following velocity-time graphs most accurately shows the motion of the clay ball?

a. b. c. d.

time

Graph 3

time

Graph 4

time

v e lo c ity

Graph 2

v e lo c ity

v e lo c ity

Graph 1

v e lo c ity

3.

time

Graph 1 Graph 2 Graph 3 Graph 4

Difficulty: Medium Blooms: Analysis AP LO: 3.A.1.1 4.

Two objects are dropped at the same time from the same height above the ground. Due to the presence of air resistance, they do not hit the ground at the same time. Which of the following is true for these objects?

a. b. c. d.

The heavier object must have hit the ground first. The smaller, more compact object must have hit the ground first. The object with the smaller average air resistance force must have hit the ground first. The object with the smaller average air resistance force to weight ratio must have hit the ground first.

Difficulty: Medium Blooms: Evaluation AP LO: 3.B.1.1 5.

A group of students are working on a physics problem involving a block accelerating down a frictionless inclined plane. Student A claims “There are only two forces acting on the block: the normal force and the force of gravity. These forces must be equal and opposite according to Newton’s 3rd Law.” Student B claims “There are only two forces acting. The normal force on the block is equal and opposite to the force of gravity on the block, but this could not be Newton’s 3rd Law since both of these forces act on the same object.” Student C claims “The normal force can...