Q: What is the work done by kinetic friction as the box is pushed up the ramp?

$$W_{\mathrm{fr}} = -\mu m g d \cos \theta$$

Q: If you push the box up the ramp so that it starts and ends at rest, what is the total work you do on the box?

$$W_{\mathrm{you}} = \mu m g d \cos \theta + m g d \sin \theta$$

Q: After releasing the box from rest at the top of the ramp, what is its speed at the bottom, neglecting air resistance?

$$v = \sqrt{2 g d (\sin \theta - \mu \cos \theta)}$$

Q: For the skier, what is the work done by kinetic friction as she descends?

$$W_{\mathrm{fr}} = -\mu m g d \cos \theta$$

Q: A box is pushed up a ramp and then released from rest at the top. If the ramp is made frictionless, what is the speed of the box at the bottom?

$$v = \sqrt{2 g d \sin \theta}$$

Q: If the box is pushed up the ramp and ends at rest, but the ramp is made steeper (increasing $$\theta$$), what happens to the work you must do?

It increases, because both $$\sin \theta$$ and $$\cos \theta$$ increase the required work

Question 1

A box of mass $$m = 20\ \mathrm{kg} is $$pushed up a ramp of length $$d = 10\ \mathrm{m}$$ inclined at $$	heta = 30^\circ to $$the horizontal. The coefficient of kinetic friction is $$\mu = 0.3. If $$the box starts and ends at rest, what is the net work done on the box by all forces?

Accepted Answer

$$W_{\mathrm{net}} = 0$$

Question 2

For the same box and ramp scenario, what is the work done by gravity as the box is pushed up the ramp?

Accepted Answer

$$W_{g} = -m g d \sin 	heta$$

Question 3

What is the work done by kinetic friction as the box is pushed up the ramp?

Accepted Answer

$$W_{\mathrm{fr}} = -\mu m g d \cos 	heta$$

Question 4

If you push the box up the ramp so that it starts and ends at rest, what is the total work you do on the box?

Accepted Answer

$$W_{\mathrm{you}} = \mu m g d \cos 	heta + m g d \sin 	heta$$

Question 5

After releasing the box from rest at the top of the ramp, what is its speed at the bottom, neglecting air resistance?

Accepted Answer

$$v = \sqrt{2 g d (\sin 	heta - \mu \cos 	heta)}$$

Question 6

A skier of mass $$m = 50\ \mathrm{kg}$$ starts from rest at the top of a $$20\ \mathrm{m}$$ high slope inclined at $$	heta = 20^\circ. $$The coefficient of kinetic friction is $$\mu = 0.03. $$What is the total work done by all forces on the skier as she reaches the bottom?

Accepted Answer

$$W_{\mathrm{net}} = \frac{1}{2} m v^2$

Question 7

For the skier problem, what is the work done by gravity as she descends the slope?

Accepted Answer

$$W_{g} = m g d \sin 	heta$$

Question 8

For the skier, what is the work done by kinetic friction as she descends?

Accepted Answer

$$W_{\mathrm{fr}} = -\mu m g d \cos 	heta$$

Question 9

Which of the following forces can never do work on an object?

Accepted Answer

Static friction

Question 10

If the coefficient of kinetic friction is doubled in the box-on-ramp scenario, how does the work you must do to push the box up the ramp change?

Accepted Answer

It increases, because $$W_{\mathrm{you}}$$ depends linearly on $$\mu$$

Question 11

A box is pushed up a ramp and then released from rest at the top. If the ramp is made frictionless, what is the speed of the box at the bottom?

Accepted Answer

$$v = \sqrt{2 g d \sin 	heta}$$

Question 12

In the skier problem, if the skier starts with an initial speed $$v_0 at $$the top, how would you modify the work-energy equation to find her speed at the bottom?

Accepted Answer

$$W_{\mathrm{net}} = \frac{1}{2} m v^2$ - \frac{1}{2} m v_0$^2$$

Question 13

Why is the work done by gravity negative when pushing the box up the ramp?

Accepted Answer

Because the force of gravity acts opposite to the displacement up the ramp

Question 14

If the box is pushed up the ramp and ends at rest, but the ramp is made steeper (increasing $$	heta$$), what happens to the work you must do?

Accepted Answer

It increases, because both $$\sin 	heta$$ and $$\cos 	heta$$ increase the required work

Question 15

A skier descends a slope with both kinetic friction and air drag acting. If air drag is neglected, how does the final speed at the bottom change?

Accepted Answer

It increases, because less energy is lost to non-conservative forces

Question 16

Which of the following best describes the direction of the friction force relative to the displacement when the box slides down the ramp?

Accepted Answer

The friction force is opposite to the direction of displacement

Question 17

If the box is pushed up the ramp and the coefficient of kinetic friction is zero, what is the work you must do?

Accepted Answer

$$W_{\mathrm{you}} = m g d \sin 	heta$$

Question 18

A box is pushed up a ramp and then released from rest at the top. If the box slides back down and ends at rest at the bottom, what is the net work done by all forces during the entire up-and-down trip?

Accepted Answer

$$W_{\mathrm{net}} = 0$$

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