Question 1

Which of the following is a correct statement about conservative and non-conservative forces?

Accepted Answer

Conservative forces keep the total mechanical energy constant, while non-conservative forces change it.

Question 2

A block of mass $$m$$ slides down a frictionless incline and compresses a spring with spring constant $$k. If $$the block starts from height $$h$$ and comes to rest after compressing the spring by distance $$x$$, which equation correctly relates $$h$$ and $$x$$?

Accepted Answer

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

Question 3

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Question 4

The elastic potential energy stored in a spring stretched by a distance $$x is $$given by:

Accepted Answer

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

Question 5

A 0.200 kg block is compressed against a spring with $$k = 500 \ \mathrm{N/m}$$ from $$x_i = 0.100 \ \mathrm{m} to$$ $$x_f = 0.0800 \ \mathrm{m}. $$What is the velocity of the block at $$x_f$$ assuming no energy loss?

Accepted Answer

$$v_f = \sqrt{\frac{k}{m}(x_i^2$ - x_f^2$)}$$

Question 6

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

Accepted Answer

Total mechanical energy remains constant.

Question 7

A box slides down a frictionless ramp and then onto a rough surface with coefficient of kinetic friction $$\mu_k = 0.5. If $$the box starts at height $$H = 10 \ \mathrm{m}$$, how far $$d$$ does it slide on the rough surface before stopping?

Accepted Answer

Question 8

Which equation correctly expresses the work done by non-conservative forces in terms of changes in mechanical energy?

Accepted Answer

$$W_{other} = (K_f + U_{grav,f} + U_{el,f}) - (K_i + U_{grav,i} + U_{el,i})$$

Question 9

A roller coaster car of mass $$50.0 \ \mathrm{kg} is $$released from rest at height $$h = 60.0 \ \mathrm{m}$$ and travels along a frictionless track. What is its speed at ground level?

Accepted Answer

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

Question 10

What is the minimum speed $$v_{min} a $$roller coaster car must have at the top of a vertical loop of radius $$R to $$stay in contact with the track?

Accepted Answer

$$v_{min} = \sqrt{gR}$$

Question 11

A slingshot obeying Hooke's law launches a pebble vertically. If pulling back $$x_1 = 21.5$$ \ \mathrm{cm}$$ sends the pebble to height h_1$ = 4.00 \ \mathrm{m}$$, what height $$h_2$$ will it reach if pulled back $$x_2 = 43.0$$ \ \mathrm{cm}$$ (neglect air resistance)?

Accepted Answer

$$h_2 = 4h_1$

Question 12

Which of the following correctly defines power in terms of work and time?

Accepted Answer

$$P = \frac{W}{\Delta t}$$

Question 13

The SI unit of power is named after which historical figure?

Accepted Answer

James Watt

Question 14

A runner of mass $$m$$ climbs a vertical height $$h in $$time $$t. $$What is the average power output by the runner?

Accepted Answer

$$P = \frac{mgh}{t}$$

Question 15

If a spring is compressed by $$x$$ and the spring constant is $$k$$, what is the force exerted by the spring?

Accepted Answer

$$F = -kx$$

Question 16

Which of the following statements about mechanical energy is correct when non-conservative forces are present?

Accepted Answer

Mechanical energy can increase, decrease, or stay the same depending on the work done by non-conservative forces.

Question 17

A box of mass $$m$$ slides a distance $$d on a $$rough surface with coefficient of kinetic friction $$\mu_k. $$What is the work done by friction?

Accepted Answer

$$W_{friction} = -\mu_k mg d$$

Question 18

Which of the following is true about the path dependence of work done by conservative and non-conservative forces?

Accepted Answer

Work done by conservative forces depends only on the initial and final positions.

Conservative and Non-Conservative Forces, Energy Conservation, and Power

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