Energy Practice Problemscontent.njctl.org/courses/science/ap-physics-b/energy-2/... · 2014. 11....

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Energy Practice Problems PSI AP Physics B Name________________________________ 1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road. What is the average power in watts required to accelerate the sports car from 30 m/s to 60 m/s in 9 seconds? (A) 1,800 (B) 5,000 (C)10,000 (D)100,000 (E) 300,000 2. A force F is at an angle θ above the horizontal and is used to pull a heavy suitcase of weight mg a distance d along a level floor at constant velocity. The coefficient of friction between the floor and the suitcase is μ. The work done by the force F is: (A)Fdcos θ - μ mgd (B) Fdcos θ (C) -μ mgd (D) 2Fdsin θ - μ mgd (E) Fdcos θ 1 3. A force of 20 N compresses a spring with a spring constant 50 N/m. How much energy is stored in the spring? (A) 2 J (B) 5 J (C) 4 J (D) 6 J (E) 8 J 4. A stone is dropped from the edge of a cliff. Which of the following graphs best represents the stone's kinetic energy KE as a function of time t? (A) (B) (C) (D) (E) 5. A 4 kg ball is attached to a 1.5 m long string and whirled in a horizontal circle at a constant speed 5 m/s. How much work is done on the ball during one period? (A) 9 J (B) 4.5 J (C) zero (D) 2 J (E) 8 J

Transcript of Energy Practice Problemscontent.njctl.org/courses/science/ap-physics-b/energy-2/... · 2014. 11....

Page 1: Energy Practice Problemscontent.njctl.org/courses/science/ap-physics-b/energy-2/... · 2014. 11. 11. · Energy Practice Problems PSI AP Physics B Name_____ 1. A driver in a 2000

Energy Practice Problems

PSI AP Physics B Name________________________________

1. A driver in a 2000 kg Porsche wishes to pass a slow moving school bus on a 4 lane road.

What is the average power in watts required to accelerate the sports car from 30 m/s to 60 m/s

in 9 seconds?

(A) 1,800 (B) 5,000 (C)10,000 (D)100,000 (E) 300,000 2. A force F is at an angle θ above the horizontal and is used to pull a heavy suitcase of weight

mg a distance d along a level floor at constant velocity. The coefficient of friction between the

floor and the suitcase is μ. The work done by the force F is:

(A)Fdcos θ - μ mgd (B) Fdcos θ (C) -μ mgd (D) 2Fdsin θ - μ mgd (E) Fdcos θ – 1

3. A force of 20 N compresses a spring with a spring constant 50 N/m. How much energy is

stored in the spring?

(A) 2 J (B) 5 J (C) 4 J (D) 6 J (E) 8 J

4. A stone is dropped from the edge of a cliff. Which of the following graphs best represents

the stone's kinetic energy KE as a function of time t?

(A) (B) (C)

(D) (E)

5. A 4 kg ball is attached to a 1.5 m long string and whirled in a horizontal circle at a constant

speed 5 m/s. How much work is done on the ball during one period?

(A) 9 J (B) 4.5 J (C) zero (D) 2 J (E) 8 J

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6. A student pushes a box across a horizontal surface at a constant speed of 0.6 m/s. The box

has a mass of 40 kg, and the coefficient of kinetic friction is 0.5. The power supplied to the

box by the person is

(A) 40 W (B) 60 W (C) 150 W (D) 120 W (E) 200 W

7. A force F is applied in horizontal to a 10 kg block. The block moves at a constant speed 2

m/s across a horizontal surface. The coefficient of kinetic friction between the block and the

surface is 0.5. The work done by the force F in 1.5 minutes is:

(A) 9000 J (B) 5000 J (C) 3000 J (D) 2000 J (E) 1000 J

Questions 8-9 A ball swings from point 1 to point 3.

Assuming the ball is in SHM and point 3 is 2 m above the

lowest point 2. Answer the following questions.

8. What happens to the kinetic energy of the ball when it moves from point 1 to point 2?

(A) increases (B) decreases (C) remains the same (D) zero (E) more information is

required

9. What is the velocity of the ball at the lowest point 2?

(A) 2.2 m/s (B) 3.5 m/s (C) 4.7 m/s (D) 5.1 m/s (E) 6.3 m/s

10. A block with a mass of m slides at a constant velocity V0 on a horizontal frictionless surface.

The block collides with a spring and comes to rest when the spring is compressed to the

maximum value. If the spring constant is K, what is the maximum compression in the

spring?

(A) V0 (m/K)1/2 (B) KmV0 (C) V0K/m (C) m V0/K (D) V0 (K/m)1/2 (E) (V0m/K)1/2

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Questions 11-12

A 2 kg block released from rest from the top of an

incline plane. There is no friction between the block

and the surface.

11. How much work is done by the gravitational force on the block?

(A) 80 J (B) 60 J (C) 50 J (D) 40 J (E) 30 J

12. What is the speed of the block when it reaches the horizontal surface?

(A) 3.2 m/s (B) 4.3 m/s (C) 5.8 m/s (D) 7.7 m/s (E) 6.6 m/s

13. A crane lifts a 300 kg load at a constant speed to the top of a building 60 m high in 15 s. The average power expended by the crane to overcome gravity is:

(A) 10,000 W (B) 12,000 W (C) 15,000 W (D) 30,000 W (E) 60,000 W

14. A satellite with a mass m revolves around Earth in a circular orbit with a constant radius R.

What is the kinetic energy of the satellite if Earth’s mass is M?

(A) ½ mv2 (B) mgh (C) ½GMm/R2 (D) ½ GMm/R (E) 2Mm/R

Questions 15-16

An apple of mass m is thrown in horizontal from the edge of a

cliff with a height of H.

15. What is the total mechanical energy of the apple with respect to the ground when it is at the

edge of the cliff?

(A) 1/2mv02 (B) mgH (C) ½ mv0

2- mgH (D) mgH - ½ mv02 (E) mgH + ½ mv0

2

16. What is the kinetic energy of the apple just before it hits the ground?

(A) ½ mv02 + mgH (B) ½ mv0

2 - mgH (C) mgH (D) ½ mv02 (E) mgh -1/2 mv0

2

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Questions 17-18 A 500 kg roller coaster car starts

from rest at point A and moves down the curved track.

Ignore any energy loss due to friction.

17. Find the speed of the car at the lowest point B.

(A) 10 m/s (B) 20 m/s (C) 30 m/s (D) 40 m/s (E) 50 m/s

18. Find the speed of the car when it reaches point C.

(A) 10 m/s (B) 20 m/s (C) 30 m/s (D) 40 m/s (E) 50 m/s

19. Two projectiles A and B are launched from the ground with velocities of 50 m/s at 60 ̊and 50

m/s at 30 ̊with respect to the horizontal. Assuming there is no air resistance involved, which

projectile has greater kinetic energy when it reaches the highest point?

(A) projectile A (B) projectile B (C) they both have the same none zero kinetic energy

(D) they both have zero kinetic energy at the highest point (E) more information is required

Questions 20-21 An object with a mass of 2 kg is

initially at rest at a position x = 0. A non-constant force F

is applied to the object over 6 meters.

20. What is the total work done on the object at the end of 6 meters?

(A) 200 J (B) 150 J (C) 170 J (D) 190 J (E) 180 J

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21. What is the velocity of the object at 6 meters?

(A) 150 m/s (B)25 m/s (C)300 m/s (D)12.25 m/s (E) more information is required

22. A metal ball is held stationary at a height

h0 above the floor and then thrown

downward. Assuming the collision with the

floor is elastic, which graph best shows the

relationship between the net energy E of the

metal ball and its height h with respect to the

floor?

23. A toy car travels with speed V0 at point X. Point Y is a height H below point X. Assuming

there is no frictional losses and no work is done by a motor, what is the speed at point Y?

(A)(2gH+1/2 V02)1/2 (B) V0-2gH (C) (2gH + V0

2)1/2 (D) 2gH+ (1/2 V02)1/2 (E) V0+2gH

24. A rocket is launched from the surface of a planet with mass M and radius R. What is the

minimum velocity the rocket must be given to completely escape from the planet’s gravitational

field?

(A) (2GM/R)1/2 (B) (2GM/R)3 (C) (GM/R)1/2 (D) 2GM/R (E) 2GM/16R2

25. A block of mass m is placed on the frictionless

inclined plane with an incline angle θ. The block is

just in a contact with a free end on an unstretched

spring with a spring constant k. If the block is

released from rest, what is the maximum

compression in the spring?

(A) kmg sinθ (B) kmg cosθ

(C) 2mg sinθ /k (D) mg/k (E) kmg

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Questions 26-28 In a physics lab a student uses three light

frictionless PASCO lab carts. Each cart is loaded with some blocks

of equal mass.

26. The same force F is applied to each cart and they move equal

distances d. In which one of these three cases is more work done

by force F?

(A) cart I (B) cart II (C) cart III

(D) the same work is done on each cart (E) more

information is required

27. The same force F is applied to each cart and they move equal

distances d. Which cart will have more kinetic energy at the end of distance d?

(A) cart I (B) cart II (C) cart IIII

(D) all three will have the same kinetic energy (E) more information is required

28. The same force F is applied to each cart and they move equal distances d. Which cart will

move faster at the end of distance d?

(A) cart I (B) cart II (C) cart IIII

(D) all three will move with the same speed (E) more information is required

29. A box of mass M begins at rest with point 1 at a height of 6R, where 2R is the radius of the

circular part of the track. The box slides down the frictionless track and around the loop. What is

the ratio between the normal force on the box at point 2 to the box’s weight?

(A)1 (B)2 (C)3 (D)4 (E) 5

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30. A ball of mass m is fastened to a string. The ball swings in a vertical circle of radius r with

the other end of the string held fixed. Neglecting air resistance, the difference between the

string’s tension at the bottom of the circle and at the top of the circle is:

(A) mg (B)2mg (C)3mg (D)6mg (E) 9mg

Free Response Problems

1. A 50 kg block is pulled from rest by a force of 1000 N at 37° across a horizontal rough

surface over a distance of 5.6 m. The coefficient of kinetic friction between the block and

the surface is 0.5.

a. Draw a free-body diagram and show all the applied forces.

b. How much work is done by force F?

c. How much work is done by the normal force?

d. How much work is done by the gravitational force?

e. How much work is done by the friction force?

f. What is the net work done on the block?

g. What is the change in kinetic energy of the block?

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2. A boy pushes a 10 kg sled at a constant speed by applying a force of 75 N at 30° with

respect to the horizontal. The sled is pushed over a distance of 15 m.

a. Draw a free-body diagram and show all the applied forces.

b. How much work is done by force F?

c. How much work is done by the normal force?

d. How much work is done by the gravitational force?

e. How much work is done by the friction force?

f. What is the coefficient of kinetic friction between the sled and the surface?

g. How much work is done by the net force on the sled?

3. A 5 kg block is released from rest at the top of a quarter-circle type curved frictionless

surface. The radius of the curvature is 3.8 m. When the block reaches the bottom of the

curvature it then slides on a rough horizontal surface until it comes to rest. The

coefficient of kinetic friction on the horizontal surface is 0.02.

a. What is the kinetic energy of the block at the bottom of the curved surface?

b. What is the speed of the block at the bottom of the curved surface?

c. Find the stopping distance of the block?

d. Find the elapsed time of the block while it is moving on the horizontal part of the

track.

e. How much work is done by the friction force on the block on the horizontal part of the

track?

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4. Spring gun with a spring constant K is placed at the edge of a table which distance

above the floor is H and the apparatus is used to shoot marbles with a certain initial

speed in horizontal. The spring is initially compressed by a distance X and then

released. The mass of each marble is m.

a. How much work is done by the spring on the marble?

b. What is the speed of the marble at the edge of the table?

c. What is the total energy of the marble at the edge of the table with respect to floor

level?

d. How much time it will take the marble to reach the floor level from the table?

e. What is the horizontal range of the marble?

f. What is the kinetic energy of the marble just before it strikes the floor?

5. A 5 kg object is initially at rest at x0 = 0. A non-constant force is applied to the object.

The applied force as a function of position is shown on the graph.

a. How much work is done on the object during first 12.5 m?

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b. What is the change is kinetic energy at the end of 12.5 m?

c. What is the speed of the object at the end of 12.5 m?

d. What is the total work done by the force for the entire trip?

e. What is the change in kinetic energy for the entire trip?

f. What is the speed of the object at the end of 20 m?

6. A 900 kg roller coaster car starts from rest at point A rolls down the track and then goes

around a loop and when it leaves the loop flies off the inclined part of the track. All the

dimensions are: H = 80 m, r = 15 m, h = 10 m, ϴ = 30̊.

a. What is the speed of the car at point B?

b. What is the speed of the car at point C?

c. What is the speed of the car at point D?

d. What is the force applied by the surface on the car at point B?

e. What is the force applied by the surface on the car at point C?

f. How far from point D will the car land?

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PSI Physics AP B Work and Energy Answers Work and Energy Presentation

1. 30J 2. -67.5J 3. 0 4. 256J 5. 160J 6. 5N 7. 4m 8. 21600J 9. 0 10. C 11. 350J 12. -40J 13. 0.8m 14. 3.6m 15. -180J 16. 600J 17. 133J 18. 15m/s 19. 8.5m/s 20. 0.8J 21. 520N/m 22. 0.84m 23. 1200N/m 24. 0.375J 25. C 26. 3.5m 27. 0.2m 28. 5m/s 29. 2m 30. 9.8m/s 31. 31.3m 32. 250000N/m 33. 0.5m/s 34. -250J 35. 0.09J 36. C 37. E 38. D 39. A

40. B 41. C 42. C 43. 4.2W 44. 2057s 45. 1500N

Work and Energy Practice Problems

1. E 2. B 3. C 4. B 5. C 6. D 7. A 8. A 9. E 10. A 11. B 12. D 13. B 14. D 15. E 16. A 17. C 18. B 19. B 20. B 21. D 22. B 23. C 24. A 25. C 26. D 27. D 28. A 29. A 30. B

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Work and Energy Free Response

1. a.

b. 447.2 J

c. 0

d. 0

e. -123.1 J

f. 324.1 J

g. 324.3 J

2. a.

b. 974.3 J

c. 0

d. 0

e. -974.3 J

f. 0.47

g. 0

3. a. 190 J

b. 8.7 m/s

c. 190 m

d. 43.5 s

e. 190 J

F

mg

f

FN

F

f

mg

FN

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4. a. W = 1

2KX2

b. v = x√𝐾

𝑚

c. ET = 1

2KX2 + mgH

d. t = √2𝐻

𝑔

e. r = x√2𝐾𝐻

𝑚𝑔

f. ET = 1

2KX2 + mgH

5. a. 200 J

b. 250 J

c. 10 m/s

d. 340 J

e. 340 J

f. 11.7 m/s

6. a. 40 m/s

b. 31.6 m/s

c. 37.4 m/s

d. 105, 000 N

e. 52, 440 N

f. 136 m