Q: A 75.0 kg skier rides a lift to the top of a mountain, reaching a height $$h$$ above the ground. What is the skier's gravitational potential energy at the top?

$$U = 75.0 \times 9.8 \times h$$

Question 1

Which of the following statements correctly describes a conservative force?

Accepted Answer

The work it does on an object moving around a closed path is zero.

Question 2

A 7.25 kg bowling ball is held 1.45 m above the ground. What is its gravitational potential energy relative to the ground? Use $$g = 9.8 \mathrm{\ m/s^2$}.$$

Accepted Answer

$$U = 103.2 \mathrm{\ J}$$

Question 3

Which of the following is NOT a conservative force?

Accepted Answer

Friction

Question 4

A block of mass $$m = 0.40 \mathrm{\ kg}$$ slides across a frictionless floor with an initial speed $$v_i = 0.50 \mathrm{\ m/s}$$ and compresses a spring with $$k = 750 \mathrm{\ N/m}. $$What is the maximum compression $$d of $$the spring?

Accepted Answer

$$d = 0.0258 \mathrm{\ m}$$

Question 5

Which equation correctly expresses the conservation of mechanical energy for a system with only conservative forces?

Accepted Answer

$$E_f = E_i$$

Question 6

A cart starts from rest and rolls down a frictionless 1.0 m high hill, then travels 2.0 m along a rough surface until it comes to rest. What is the coefficient of kinetic friction $$\mu_k$$ along the bottom surface?

Accepted Answer

$$\mu_k = 0.25$$

Question 7

Which of the following best describes the work done by friction on a closed path?

Accepted Answer

It is not zero and depends on the path taken.

Question 8

A spring with force constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 9

A roller coaster with a 127 m vertical drop has a rider of mass 55 kg. The speed at the top is 6.0 m/s and at the bottom is 45.0 m/s. What is the work done by non-conservative forces during the descent?

Accepted Answer

$$W_{nc} = E_f - E_i$$

Question 10

Which of the following is true about the work done by a conservative force?

Accepted Answer

It is the negative of the change in potential energy.

Question 11

A leaf falls to the ground with constant speed. Comparing its initial and final total energies (potential + kinetic), which statement is correct?

Accepted Answer

$$PE_i + KE_i \u003e PE_f + KE_f ($$energy lost to air resistance)

Question 12

Which of the following is a correct expression for gravitational potential energy?

Accepted Answer

$$U = mgh$$

Question 13

A 75.0 kg skier rides a lift to the top of a mountain, reaching a height $$h$$ above the ground. What is the skier's gravitational potential energy at the top?

Accepted Answer

$$U = 75.0 	imes 9.8 	imes h$$

Question 14

Which of the following is true about mechanical energy in the presence of nonconservative forces?

Accepted Answer

Mechanical energy can increase or decrease depending on the work done by nonconservative forces.

Question 15

A cart starts from rest and rolls down a hill, reaching a speed of 4 m/s at the bottom. If it is given an initial push so its speed at the top is 3 m/s, what will its speed be at the bottom?

Accepted Answer

6 m/s

Question 16

Which of the following best describes a potential energy curve?

Accepted Answer

A plot of potential energy versus position.

Question 17

Which of the following is NOT a form of potential energy?

Accepted Answer

Kinetic

Question 18

A block is released from rest at the top of a frictionless ramp of height $$h. $$What is its speed at the bottom?

Accepted Answer

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

Question 19

Which of the following is true about the work done by a spring force?

Accepted Answer

It is independent of the path taken.

Question 20

Which equation correctly relates the work done by nonconservative forces to the change in mechanical energy?

Accepted Answer

$$W_{nc} = \Delta E$$

Potential Energy and Conservation of Energy (Chapter 8 Study Notes)

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