Q: A 5-kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Assume $$g = 9.8 \mathrm{\ m/s^2$})$$

$$v = \sqrt{2 \times 9.8 \times 10} = 14 \mathrm{\ m/s}$$

Q: A block slides down a frictionless incline from height $$H$$ and then up a second incline with kinetic friction coefficient $$\mu_k. If $$the block reaches height $$h_f on $$the second incline, which equation relates the initial and final energies?

$$m g H = m g h_f + \mu_k m g \frac{h_f}{\sin \theta}$$

Q: A 0.5-kg mass attached to a spring ($$k = 200 \mathrm{\ N/m}) is $$compressed by $$0.1 \mathrm{\ m}$$ from equilibrium. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} \times 200 \times (0.1)^2$ = 1 \mathrm{\ J}$$

Question 1

Which of the following statements correctly describes a conservative force?

Accepted Answer

The work done by the force around any closed path is zero.

Question 2

A 2-kg ball is lifted vertically from the ground to a height of 3 m. What is the change in its gravitational potential energy? (Assume $$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$\Delta U = 58.8 \mathrm{\ J}$$

Question 3

Which equation correctly expresses the relationship between force and potential energy in one dimension?

Accepted Answer

$$F_x = -\frac{dU}{dx}$$

Question 4

A block of mass $$m is $$attached to an ideal spring with spring constant $$k. If $$the block is displaced by $$x$$ from equilibrium, what is the elastic potential energy stored in the spring?

Accepted Answer

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

Question 5

A 5-kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Assume $$g = 9.8 \mathrm{\ m/s^2$})$$

Accepted Answer

$$v = \sqrt{2 	imes 9.8 	imes 10} = 14 \mathrm{\ m/s}$$

Question 6

Which of the following is true about the zero of potential energy?

Accepted Answer

It is arbitrary and can be chosen for convenience.

Question 7

A block slides down a frictionless incline from height $$H$$ and then up a second incline with kinetic friction coefficient $$\mu_k. If $$the block reaches height $$h_f on $$the second incline, which equation relates the initial and final energies?

Accepted Answer

$$m g H = m g h_f + \mu_k m g \frac{h_f}{\sin 	heta}$$

Question 8

Which of the following best describes the effect of nonconservative forces on the mechanical energy of a system?

Accepted Answer

They change the amount of mechanical energy, often dissipating it as heat.

Question 9

A 0.5-kg mass attached to a spring ($$k = 200 \mathrm{\ N/m}) is $$compressed by $$0.1 \mathrm{\ m}$$ from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1 \mathrm{\ J}$$

Question 10

Which mathematical condition must be satisfied for a force to be conservative in three dimensions?

Accepted Answer

$$\vec{F} = -
abla U$$

Question 11

A pendulum of length $$L is $$released from an angle $$\$$theta_0$$. What is the change in gravitational potential energy from its lowest point to the release point?

Accepted Answer

$$\Delta U = m g L (1 - \cos \$$theta_0$$)$$

Question 12

Which of the following is a property of energy diagrams for conservative forces?

Accepted Answer

The total energy is represented by a horizontal line, and the particle can move where $$U(x) \u003c E.$$

Question 13

A block of mass $$m$$ slides on a horizontal surface with friction. If it starts with velocity $$v_0$$, what is the stopping distance $$x_f$$ for a frictional force $$f = \mu_k m g$$?

Accepted Answer

$$x_f = \frac{v_0$^2}{2 \mu_k g}$$

Question 14

Which of the following is true about the mechanical energy of a system with only conservative forces acting?

Accepted Answer

Mechanical energy is conserved.

Question 15

A block attached to a spring oscillates with amplitude $$A. $$What is its total mechanical energy?

Accepted Answer

$$E = \frac{1}{2} k A^2$

Question 16

If a system involves both gravitational and elastic forces, what is the total potential energy?

Accepted Answer

$$U = U_{grav} + U_{el}$$

Question 17

Which of the following is a correct statement of the law of conservation of energy including internal energy changes?

Accepted Answer

$$\Delta K + \Delta U + \Delta U_{int} = 0$$

Question 18

A block of mass $$m is $$released from rest at height $$h$$ and falls freely. What is its speed just before hitting the ground?

Accepted Answer

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

Question 19

Which of the following is true about the work done by gravity when moving an object along a curved path from height $$y_1 to$$ $$y_2$$?

Accepted Answer

It depends only on the vertical displacement $$\Delta y.$$

Potential Energy and Energy Conservation (Chapter 7) Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards