Q: A stone of mass 7.5 kg compresses a spring by 13.0 cm. What is the spring constant $$k$$?

$$k = \frac{7.5 \times 9.8}{0.13} N/m$$

Question 1

Which of the following statements about conservative forces is TRUE?

Accepted Answer

The total mechanical energy of a system is conserved when only conservative forces do work.

Question 2

A ball of mass $$m is $$dropped from a height $$h in a $$uniform gravitational field $$g. $$What is the change in its gravitational potential energy as it falls to the ground?

Accepted Answer

$$\Delta U_{grav} = -mgh$$

Question 3

A climber pulls a supply pack up a slope at constant speed. Which statement is FALSE?

Accepted Answer

The work done on the pack by gravity is zero joules.

Question 4

Which equation correctly relates the work done by gravity to the change in gravitational potential energy?

Accepted Answer

$$W_{grav} = -\Delta U_{grav}$$

Question 5

A 0.2 kg mass is attached to a spring with $$k = 5 N/m $$and stretched from equilibrium by 0.1 m, then released from rest. What is its speed as it passes through equilibrium?

Accepted Answer

$$v = 0.3 m/s$$

Question 6

Which of the following is a correct expression for the elastic potential energy stored in a spring stretched by a distance $$x$$ from equilibrium?

Accepted Answer

$$U_{spring} = \frac{1}{2}kx^2$

Question 7

A stone of mass 7.5 kg compresses a spring by 13.0 cm. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{7.5 	imes 9.8}{0.13} N/m$$

Question 8

A mass slides from rest at the top of a frictionless hemispherical bowl of radius $$R. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gR}$$

Question 9

Which statement about the work done by gravity is correct?

Accepted Answer

It depends only on the vertical displacement between the endpoints.

Question 10

A 2000 kg elevator is brought to rest from 4.0 m/s by a spring and friction over 2.0 m. If friction does $$-34000 J of $$work, what spring constant $$k is $$needed?

Accepted Answer

$$k = \frac{212000}{(2.0)^2$} N/m$$

Question 11

If only conservative forces act on a system, which of the following is always true?

Accepted Answer

Any increase in potential energy is matched by a decrease in kinetic energy.

Question 12

A block slides down a frictionless ramp. Which equation best describes the conservation of mechanical energy for this process?

Accepted Answer

$$K_1 + U$$_{g,1} = $$K_2 + U$$_{g,2}$$

Question 13

A mass attached to a spring oscillates on a frictionless surface. At maximum displacement $$x = A$$, what is its kinetic energy?

Accepted Answer

$$K = 0$$

Question 14

Which of the following is NOT a property of a conservative force?

Accepted Answer

It always increases the kinetic energy of a system.

Question 15

A particle moves under a potential energy function $$U(x) = \frac{1}{2}kx^2$. At x = 0$, what is the force acting on the particle?

Accepted Answer

$$F = 0$$

Question 16

A baseball is thrown horizontally from a building. After it leaves the thrower's hand, which statement is correct (neglecting air resistance)?

Accepted Answer

Mechanical energy is conserved.

Question 17

A block is compressed against a spring and released. If the block has speed $$v$$ when the spring is compressed by $$x$$, what is the total mechanical energy?

Accepted Answer

$$E = \frac{1}{2}mv^2$ + \frac{1}{2}kx^2$

Question 18

Which of the following best describes the work-energy theorem?

Accepted Answer

$$W_{tot} = \Delta K$$

Question 19

A stone is released from rest after compressing a spring. If the spring potential energy is 40.82 J and the stone reaches a maximum height $$h$$, what is $$h$$?

Accepted Answer

$$h = \frac{40.82}{7.5 	imes 9.8} m$$

CH7-EXAM-2-Potential Energy and Energy Conservation: Gravitational Potential Energy and the Work-Energy Theorem

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