### Short Answer

### 9.1 Work, Power, and the Work–Energy Theorem

- Raising an object to a higher elevation does work as it increases its PE; increasing the speed of an object does work as it increases its KE.
- Raising an object to a higher elevation does work as it increases its KE; increasing the speed of an object does work as it increases its PE.
- Raising an object to a higher elevation does work as it increases its PE; decreasing the speed of an object does work as it increases its KE.
- Raising an object to a higher elevation does work as it increases its KE; decreasing the speed of an object does work as it increases its PE.

True or false—While riding a bicycle up a gentle hill, it is fairly easy to increase your potential energy, but to increase your kinetic energy would make you feel exhausted.

- True
- False

Which statement best explains why running on a track with constant speed at 3 m/s is not work, but climbing a mountain at 1 m/s is work?

- At constant speed, change in the kinetic energy is zero but climbing a mountain produces change in the potential energy.
- At constant speed, change in the potential energy is zero, but climbing a mountain produces change in the kinetic energy.
- At constant speed, change in the kinetic energy is finite, but climbing a mountain produces no change in the potential energy.
- At constant speed, change in the potential energy is finite, but climbing a mountain produces no change in the kinetic energy.

- ${v}_{1}$ is your speed at the top of the hill, and ${v}_{2}$ is your speed at the bottom.
- ${v}_{1}$ is your speed at the bottom of the hill, and ${v}_{2}$ is your speed at the top.
- ${v}_{1}$ is your displacement at the top of the hill, and ${v}_{2}$ is your displacement at the bottom.
- ${v}_{1}$ is your displacement at the bottom of the hill, and ${v}_{2}$ is your displacement at the top.

### 9.2 Mechanical Energy and Conservation of Energy

True or false—The formula for gravitational potential energy can be used to explain why joules, J, are equivalent to kg × mg^{2} / s^{2} . Show your work.

- True
- False

- Because kinetic energy is directly proportional to the square of the velocity.
- Because kinetic energy is inversely proportional to the square of the velocity.
- Because kinetic energy is directly proportional to the fourth power of the velocity.
- Because kinetic energy is inversely proportional to the fourth power of the velocity.

- When the coin hits the ground, the ground gains potential energy that quickly changes to thermal energy.
- When the coin hits the ground, the ground gains kinetic energy that quickly changes to thermal energy.
- When the coin hits the ground, the ground gains thermal energy that quickly changes to kinetic energy.
- When the coin hits the ground, the ground gains thermal energy that quickly changes to potential energy.

True or false—A marble rolls down a slope from height *h*_{1} and up another slope to height *h*_{2}, where (*h*_{2} < *h*_{1}). The difference *mg*(*h*_{1} – *h*_{2}) is equal to the heat lost due to the friction.

- True
- False

### 9.3 Simple Machines

Why would you expect the lever shown in the top image to have a greater efficiency than the inclined plane shown in the bottom image?

- The resistance arm is shorter in case of the inclined plane.
- The effort arm is shorter in case of the inclined plane.
- The area of contact is greater in case of the inclined plane.

Why is the wheel on a wheelbarrow **not** a simple machine in the same sense as the simple machine in the image?

- The wheel on the wheelbarrow has no fulcrum.
- The center of the axle is not the fulcrum for the wheels of a wheelbarrow.
- The wheelbarrow differs in the way in which load is attached to the axle.
- The wheelbarrow has less resistance force than a wheel and axle design.

A worker pulls down on one end of the rope of a pulley system with a force of 75 N to raise a hay bale tied to the other end of the rope. If she pulls the rope down 2.0 m and the bale raises 1.0 m, what else would you have to know to calculate the efficiency of the pulley system?

- the weight of the worker
- the weight of the hay bale
- the radius of the pulley
- the height of the pulley from ground

True or false—A boy pushed a box with a weight of 300 N up a ramp. He said that, because the ramp was 1.0 m high and 3.0 m long, he must have been pushing with force of exactly 100 N.

- True
- False