Question 1

Which of the following correctly describes the work done by gravity when a body moves downward a vertical distance $$y_2$$ - $$y_1$$?

Accepted Answer

The work done by gravity is $$W_{grav} = m g (y_1$ - y_2$)$$ and is positive if $$y_2$$ \u003c $$y_1.$$

Question 2

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

Accepted Answer

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

Question 3

Which of the following is a property of conservative forces?

Accepted Answer

The work done can be expressed as the difference between initial and final values of a potential energy function.

Question 4

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

Accepted Answer

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

Question 5

An elevator of mass $$m$$ falls a distance $$d$$ and comes to rest after hitting a spring with constant $$k$$, with friction $$f$$ acting during the fall. Which equation correctly relates $$k to $$the system parameters?

Accepted Answer

$$k = \frac{2(mgd + \frac{1}{2}mv^2$ - fd)}{d^2$}$$

Question 6

A particle moves along the $$x-$$axis under a conservative force $$F_x. At a $$point where $$F_x = 0$$, what can be said about the potential energy $$U(x) at $$that point?

Accepted Answer

Not enough information to decide.

Question 7

Which of the following is true about the work-energy theorem in the presence of gravitational and elastic forces?

Accepted Answer

$$W_{other} = \Delta K + (\Delta U_{grav} + \Delta U_{el})$$

Question 8

A block is released from rest on a frictionless incline and compresses a spring. As the block moves down, which statement is correct?

Accepted Answer

$$U_{grav} is $$decreasing; $$U_{el} is $$increasing.

Question 9

A rock slides from point A to B along the inside of a frictionless hemispherical bowl. Why is mechanical energy conserved?

Accepted Answer

The normal force is perpendicular to the bowl's surface.

Question 10

Which of the following is true for the work done by friction?

Accepted Answer

It is more negative for longer paths.

Question 11

For a conservative force $$F$$, how is the force related to the potential energy function $$U(x) in $$one dimension?

Accepted Answer

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

Question 12

A particle is initially at $$x = a$$ and moves in the negative $$x$$ direction. At which of the labeled positions does the particle have the greatest speed?

Accepted Answer

At $$x = b$$

Question 13

A particle is initially at $$x = d$$ and moves in the negative $$x$$ direction. At which of the labeled positions is the particle slowing down?

Accepted Answer

At $$x = d$$

Question 14

At which $$x$$ values is there zero force on the particle, given the potential energy graph $$U(x)$$?

Accepted Answer

At $$x = a$$ and $$x = c$$

Question 15

The graph shows a conservative force $$F_x as a $$function of $$x in $$the vicinity of $$x = a. $$Which statement about the associated potential energy function $$U(x) at$$ $$x = a is $$correct?

Accepted Answer

$$U is a $$minimum at $$x = a$$

Question 16

The graph shows a conservative force $$F_x as a $$function of $$x in $$the vicinity of $$x = a. If$$ $$F_x = 0$$ and $$\frac{dF_x}{dx} \u003e 0 at$$ $$x = a$$, which statement about the associated potential energy function $$U(x) at$$ $$x = a is $$correct?

Accepted Answer

$$U(x) is a $$maximum at $$x = a$$

Question 17

A baseball of mass $$0.150\ \mathrm{kg} is $$thrown straight upward with initial speed $$20.0\ \mathrm{m/s}. $$What is its speed at a height of $$17.0\ \mathrm{m}$$, ignoring air resistance?

Accepted Answer

Greater than $$10.0\ \mathrm{m/s}$$

Question 18

Which statement is true about the gravitational potential energy $$U_{grav} of a $$body moving upward?

Accepted Answer

$$U_{grav}$$ increases as the body moves upward.

Question 19

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

Accepted Answer

It cannot be expressed as the difference between initial and final values of a potential energy function.

Potential Energy, Energy Conservation, and Conservative Forces: Study Notes

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