Slide 1 / 43 AP Physics C Work And Energy With Calculus Slide 2 / - - PDF document

AP Physics C Work And Energy With Calculus Slide 1 / 43

1 An object moves according to the function x = t5/2 where x is the distance traveled and t is the time. Its kinetic energy is proportional to

A t2 B

t5/2

C

t3

D

t3/2

E

t° (kinetic energy is constant)

Slide 2 / 43

2 Which of the following best describes the relationship between force and potential energy?

A Force is the anti-derivative of potential energy B

Force is the negative gradient of potential energy

C

Potential energy is the negative gradient of force

D

Potential energy is the derivative of force

E

Force is the anti-derivative of potential energy

Slide 3 / 43

3 A student throws a ball of mass m upward where the initial potential energy is 0. At a height H the ball has a potential energy of U and is moving upward with a kinetic energy of Ke. Ignoring air resistance, the maximum height achieved by the ball is most nearly

A (Ke-U)/mg B

(U-Ke)/mg

C

(U+Ke)/mg

D

mg/(U-Ke)

E

mg/(U+Ke)

Slide 4 / 43

4 A box of mass m is lifted a vertical distance h in time t with a constant velocity. The power supplied by the lifting force is approximately

A mght B

mgh/t

C

zero

D

mgt/h

E

mg/ht

Slide 5 / 43

5 A 5kilogram ball moves in the x direction where x represents the ball’s position. The potential energy U of the ball in joules is given as a function by: U(x) = 4x2 3x + 2. The force on the particle at x = 4 meters is

A 29 N in +x direction B

29N in -x direction

C

108 N in -x direction

D

45 N in x direction

E

108 N in +x direction

Slide 6 / 43

6 A student pushes a box across a rough, flat surface at a constant speed v. The box has a mass m, and the coefficient of sliding friction is represented by µ. The power supplied by the person to the box is

A 0 B

µmg/v

C

µv/mg

D

mg/µv

E

µmgv

Slide 7 / 43

7 The force exerted by a spring is given by: F=kx4/2. If k is 100 N/m find the work done from x=0 to x=2.

A 100 J B

320 J

C

800 J

D

1600 J

E

2400 J

Slide 8 / 43

8 A man lifts a mass m at constant speed to a height h in time t. How much work is done by the weight lifter?

A mgt B

zero

C

mgh

D

mgh/t

E

cannot be determined

Slide 9 / 43

9 It takes a force F given by F = 20x 12x2 to stretch an irregular spring by a distance x, where F is in newtons and x is in meters. What is the change in potential energy when the spring is stretched 3 meters from its equilibrium position?

A 18J B

28J

C

56J

D

64J

E

80J

Slide 10 / 43

10 On top of a skyscraper of height H, a ball of mass m is thrown directly downward with an initial speed vo. If the ball reaches the ground with a speed vf, the energy lost to friction is approximately

A

mgh- (1/2) m(vo

2-vf 2)

B

mgh+ (1/2) m(vo

2+vf 2)

C

mgh+ (1/2) m(vf

2 -vo 2)

D

mgh+(1/2) m(vf

2 +vo 2)

E

(1/2) m(vf

2 -vo 2)-mgh

Slide 11 / 43

11 A ball is attached to a string rotates in a complete

• circle. The work done during each revolution is

A 0 B

U

C

U+Ke

D

Ke

E

Ke-U

Slide 12 / 43

12 Potential energy of two molecules is given by: U= 2/r7-4/r5. If r is the distance between two molecules what is the force acting on the particles if r=1m

A 0.75 N B

0.67 N

C

2 N

D

6 N

E

10 N

Slide 13 / 43

13 A force of 40 N compresses a spring with a spring constant 80 N/m. How much energy is stored in the spring?

A 10 J B

15 J

C

20 J

D

25 J

E

30 J

Slide 14 / 43

14 When the object of mass m1 descends to a distance h, the potential energy of the system has decreases by

A

(m1 – m2)gh

B

m1gh

C

(m1 + m2)gh

D

½(m1 + m2)gh

E

M1 M2

Slide 15 / 43

15 What is the instantaneous power delivered by gravity to a 6kg block 4 seconds after it has fallen from rest?

A 2400 W B

1000 W

C

800 W

D

1200 W

E

2000 W

Slide 16 / 43

16 If F(x)=2x3-3x2 what is the work done from x=1 to x= 2?

A 0.5 J B

0.8 J

C

2 J

D

12 J

E

0 J

Slide 17 / 43

17 A 5 kilogram block is pushed horizontally across a rough surface with a coefficient of kinetic friction of 0.2 by a force F moving at 3 m/s. The work that is done by the force in 20 seconds is

A 200 J B

400 J

C

600 J

D

800 J

E

1000 J

Slide 18 / 43

18 The graph represents the force exerted on a

• particle. What is the work done on the object from

x=0 to x= 4 m?

A 8 J B

10 J

C

15 J

D

16 J

E

20 J

Slide 19 / 43

19 What is the work done on the object from x=0 to x=6 m?

A 4 J B

6 J

C

10 J

D

12.5 J

E

25 J

Slide 20 / 43

20 A constant force supplies an average power of 8 watts to a box during a certain time interval. If the box has an average speed of 4 meters per second and the force acts in the same direction as motion

• f the object, the magnitude of the force is

A 8 N B

6 N

C

4 N

D

2N

E

1N

Slide 21 / 43

21 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity vo. What is the kinetic energy of the ball at the top of the roof?

A 0 B

mgh

C

½ mvo

2

D

mgh-½ mvo

2

E

mgh+½ mvo

2

Slide 22 / 43

22 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity vo. What is the potential energy of the ball when it hits the ground?

A 0 B

mgh/2

C

½ mvi

2

D

mgh/2+½ mvi

2

E

mgh+½ mvi

2

Slide 23 / 43

23 Questions 21-23 A ball of mass m is tossed from roof of height h with an initial velocity vo. What is the kinetic energy of the ball right before it strikes the ground? A 0

B

mgh

C

½ mvi

2

D

mgh-½ mvi

2

E

mgh+½ mvi

2

Slide 24 / 43

24 The following graphs represent the net force F as a function of displacement x for an ball that moves in a straight line. Which graph best represents the force that will cause the least change in the kinetic energy

• f the object from x = 0 to x = x1?

A B C D E

Slide 25 / 43

25 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. At which point is the kinetic energy of the ball at maximum?

A Point A B

Point B

C

Point C

D

Points A&B

E

Kinetic energy is the same at all points A B C

Slide 26 / 43

26 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. What happens to the potential energy as the ball passes from point A to point B?

A increases B

decreases

C

stays the same

D

zero

E

not enough information A B C

Slide 27 / 43

27 Questions 25-27 A block is attached to a spring that oscillates in simple harmonic motion. Which of the following is true about the system?

A

Potential energy is never equal to Kinetic energy

B

Potential energy is equal to Kinetic energy at all points

C

The system will eventually stop moving

D

There is a restoring force

E

Both B&D

A B C

Slide 28 / 43

28 A 4 kg mass is moving with a velocity given by v (t) = ¼t4. At t= 1 s, the instantaneous power delivered by the net force is

A 1 W B

3 W

C

12 W

D

14 W

E

20 W

Slide 29 / 43

29 What is the instantaneous power delivered by the net force at the t = 2 s to a 2 kg mass moving according to x(t) = t3/3?

A 2 W B

10 W

C

16 W

D

24 W

E

32 W

Slide 30 / 43

30 A particle of mass m follows the potential energy graph as shown below. The mass is initially at rest at RO. Determine the particle’s speed at position 4ro.

A B C D E

U(R) 4U U R 4R R

Slide 31 / 43

31 A particle of mass m follows the potential energy graph as shown below. The mass is initially at rest at RO. The function U(r) = ar-3/2 + b represents the potential energy of a particle, where b and c are constants, which of the following is an expression for the force

• n the particle?

A B C D E

U(R) 4U U R 4R R

Slide 32 / 43

32 The force exerted by a non-uniform spring is F = -kx3. The maximum displacement of the spring is x = 2 m. The spring constant of the spring is 36 N/m and the mass of the block is .5 kg. Find the total energy of the system.

A 12 J B

144 J

C

36 J

D

120 J

E

432 J

Slide 33 / 43

33 The force exerted by a non-uniform spring is F =

• kx3. The maximum displacement of the spring is

x = 2 m. The spring constant of the spring is 36 N/m and the mass of the block is .5 kg. Find the maximum speed of the system.

A 9.8 m/s B

24 m/s

C

15 m/s

D

20 m/s

E

27 m/s

Slide 34 / 43

34 A block of mass m slides down an incline and experience a friction force with a coefficient of kinetic friction µ on the ramp and the track it follows. The block comes to rest at point 4. At which point is the kinetic energy the greatest?

A Point 1 B

Point 2

C

Point 3

D

Points 4

E

Between Point 1&2

H 1 2 3 4

Slide 35 / 43

35 A block of mass m slides down an incline and experience a friction force with a coefficient of kinetic friction µ on the ramp and the track it follows. The block comes to rest at point 4. Which of the following best represents the energy lost to friction from point 1 to point 4?

A µmgH B

MgH

C

√(2gH)

D

2mg/H

E

2gH

H 1 2 3 4

Slide 36 / 43

36 A mass moves under the influence of a potential energy given by: U(x) = x3 – 2x2 At x=2, the force on the mass will be

A 4 N, + direction B

4 N, - direction

C

1.3 N, + direction

D

1.3 N, - direction

E

7 N, + direction

Slide 37 / 43

37 A mass is attached to a spring on a frictionless horizontal surface. It is displaced by an amount of x meters and then released. Which of the following statements are true?

• I. PE and KE will never be equal
• II. KE is largest when the mass is passing through the

equilibrium point.

• III. PE is largest when the mass has a displacement of

±x.

A I only B II only C III only D I and II E II and III

Slide 38 / 43

38 A 6 kg onject's potential energy is represented by U = 9r2 + 4. Find the acceleration of the object at r = 2.

A 1 m/s2 B

4 m/s2

C

6 m/s2

D

9 m/s2

E

12 m/s2

Slide 39 / 43

39 A restoring force F = -2x3 acts on an object, where x is the displacement of the object from its equilibrium

• position. How much work must be done to move the
• bject from x= 0 to x= 2 m?

A 2 J B

24 J

C

8 J

D

10 J

E

15 J

Slide 40 / 43

40 Find the work done from x = 0 to x = π/2.

A 0 J B

1 J

C

π/2 J

D

5 J

E

10 J

Slide 41 / 43

41 Find the work done from x = 0 to x = π.

A 0 J B

1 J

C

1.5 J

D

• 1 J

E

4 J

Slide 42 / 43

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