# Chapter Review

### Concept Items

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

- No, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in KE requires a change in velocity. It is assumed that mass is constant.
- No, because the work-energy theorem states that work done on an object is equal to the sum of kinetic energy, and the change in KE requires a change in displacement. It is assumed that mass is constant.
- Yes, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in KE requires a change in velocity. It is assumed that mass is constant.
- Yes, because the work-energy theorem states that work done on an object is equal to the sum of kinetic energy, and the change in KE requires a change in displacement. It is assumed that mass is constant.

- Work is defined as the ratio of the force over the distance.
- Work is defined as the sum of the force and the distance.
- Work is defined as the square of the force over the distance.
- Work is defined as the product of the force and the distance.

A book with a mass of 0.30 kg falls 2 m from a shelf to the floor. This event is described by the work–energy theorem: $$W=\text{}fd\text{=}\frac{1}{2}m{v}_{2}^{2}-\frac{1}{2}m{v}_{1}^{2}$$ Explain why this is enough information to calculate the speed with which the book hits the floor.

- The mass of the book,
*m*, and distance,*d*, are stated.*F*is the weight of the book*mg . v*_{1}is the initial velocity and*v*_{2}is the final velocity. The final velocity is the only unknown quantity. - The mass of the book,
*m*, and distance,*d*, are stated.*F*is the weight of the book*mg . v*_{1}is the final velocity and*v*_{2}is the initial velocity. The final velocity is the only unknown quantity. - The mass of the book,
*m*, and distance,*d*, are stated.*F*is the weight of the book*mg . v*_{1}is the initial velocity and*v*_{2}is the final velocity. The final velocity and the initial velocities are the only unknown quantities. - The mass of the book,
*m*, and distance,*d*, are stated.*F*is the weight of the book*mg . v*_{1}is the final velocity and*v*_{2}is the initial velocity. The final velocity and the initial velocities are the only unknown quantities.

#### 9.2 Mechanical Energy and Conservation of Energy

- While going up, the person’s KE would change to PE. While coming down, the person’s PE would change to KE.
- While going up, the person’s PE would change to KE. While coming down, the person’s KE would change to PE.
- While going up, the person’s KE would not change, but while coming down, the person’s PE would change to KE.
- While going up, the person’s PE would change to KE, but while coming down, the person’s KE would not change.

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

The starting line of a cross country foot race is at the bottom of a hill. Which form(s) of mechanical energy of the runners will change when the starting gun is fired?

- Kinetic energy only
- Potential energy only
- Both kinetic and potential energy
- Neither kinetic nor potential energy

#### 9.3 Simple Machines

- It reduces the input force and the output force.
- It reduces the input force and increases the output force.
- It increases the input force and reduces the output force.
- It increases the input force and the output force.

Which type of simple machine is a knife?

- A ramp
- A wedge
- A pulley
- A screw

### Critical Thinking Items

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

Which activity requires a person to exert force on an object that causes the object to move but does not change the kinetic or potential energy of the object?

- Moving an object to a greater height with acceleration
- Moving an object to a greater height without acceleration
- Carrying an object with acceleration at the same height
- Carrying an object without acceleration at the same height

Which statement explains how it is possible to carry books to school without changing the kinetic or potential energy of the books or doing any work?

- By moving the book without acceleration and keeping the height of the book constant
- By moving the book with acceleration and keeping the height of the book constant
- By moving the book without acceleration and changing the height of the book
- By moving the book with acceleration and changing the height of the book

#### 9.2 Mechanical Energy and Conservation of Energy

True or false—A cyclist coasts down one hill and up another hill until she comes to a stop. The point at which the bicycle stops is lower than the point at which it started coasting because part of the original potential energy has been converted to a quantity of heat and this makes the tires of the bicycle warm.

- True
- False

#### 9.3 Simple Machines

- Anything that is swung by a handle, such as a hammer or racket. Force is applied near the fulcrum over a short distance, which makes the other end move rapidly over a long distance.
- Anything that is swung by a handle, such as a hammer or racket. Force is applied far from the fulcrum over a large distance, which makes the other end move rapidly over a long distance.
- A lever used to lift a heavy stone. Force is applied near the fulcrum over a short distance, which makes the other end lift a heavy object easily.
- A lever used to lift a heavy stone. Force is applied far from the fulcrum over a large distance, which makes the other end lift a heavy object easily

- In a baseball bat, effort force is smaller and is applied over a large distance, while the resistance force is smaller and is applied over a long distance.
- In a baseball bat, effort force is smaller and is applied over a large distance, while the resistance force is smaller and is applied over a short distance.
- In a baseball bat, effort force is larger and is applied over a short distance, while the resistance force is smaller and is applied over a long distance.
- In a baseball bat, effort force is larger and is applied over a short distance, while the resistance force is smaller and is applied over a short distance.

### Problems

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

- $-36.5\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $-25.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $25.8\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$
- $36.5\phantom{\rule{thinmathspace}{0ex}}\text{m/s}$

A boy pushes his little sister on a sled. The sled accelerates from 0 to 3.2 m/s . If the combined mass of his sister and the sled is 40.0 kg and 18 W of power were generated, how long did the boy push the sled?

- 205 s
- 128 s
- 23 s
- 11 s

#### 9.2 Mechanical Energy and Conservation of Energy

- $3.5\phantom{\rule{thinmathspace}{0ex}}\text{J}$
- $7\phantom{\rule{thinmathspace}{0ex}}\text{J}$
- $2.45\times {10}^{3}\phantom{\rule{thinmathspace}{0ex}}\text{J}$
- $2.45\times {10}^{5}\phantom{\rule{thinmathspace}{0ex}}\text{J}$

- $0.1\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $0.2\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $0.4\phantom{\rule{thinmathspace}{0ex}}\text{m}$
- $2\phantom{\rule{thinmathspace}{0ex}}\text{m}$

The potential energy stored in a compressed spring is $$U=\frac{1}{2}k{x}^{2}$$, where *k* is the force constant and *x* is the distance the spring is compressed from the equilibrium position. Four experimental setups described below can be used to determine the force constant of a spring. Which one(s) require measurement of the fewest number of variables to determine *k*? Assume the acceleration due to gravity is known.

- An object is propelled vertically by a compressed spring.
- An object is propelled horizontally on a frictionless surface by a compressed spring.
- An object is statically suspended from a spring.
- An object suspended from a spring is set into oscillatory motion.

- I only
- III only
- I and II only
- III and IV only

#### 9.3 Simple Machines

A man is using a wedge to split a block of wood by hitting the wedge with a hammer. This drives the wedge into the wood creating a crack in the wood. When he hits the wedge with a force of 400 N it travels 4 cm into the wood. This caused the wedge to exert a force of 1,400 N sideways increasing the width of the crack by 1 cm . What is the efficiency of the wedge?

- 0.875 percent
- 0.14
- 0.751
- 87.5 percent

If the cutter blades are 2 cm wide and 0.3 cm thick, what is the overall IMA of this complex machine?

- 1.34
- 1.53
- 33.3
- 33.5

### Performance Task

#### 9.3 Simple Machines

Conservation of Energy and Energy Transfer; Cause and Effect; and S&EP, Planning and Carrying Out Investigations

Plan an investigation to measure the mechanical advantage of simple machines and compare to the *IMA* of the machine. Also measure the efficiency of each machine studied. Design an investigation to make these measurements for these simple machines: lever, inclined plane, wheel and axle and a pulley system. In addition to these machines, include a spring scale, a tape measure, and a weight with a loop on top that can be attached to the hook on the spring scale. A spring scale is shown in Figure 9.15.

LEVER: Beginning with the lever, explain how you would measure input force, output force, effort arm, and resistance arm. Also explain how you would find the distance the load travels and the distance over which the effort force is applied. Explain how you would use this data to determine *IMA* and efficiency.

INCLINED PLANE: Make measurements to determine *IMA* and efficiency of an inclined plane. Explain how you would use the data to calculate these values. Which property do you already know? Note that there are no effort and resistance arm measurements, but there are height and length measurements.

WHEEL AND AXLE: Again, you will need two force measurements and four distance measurements. Explain how you would use these to calculate *IMA* and efficiency.

SCREW: You will need two force measurements, two distance traveled measurements, and two length measurements. You may describe a screw like the one shown in Figure 9.11 or you could use a screw and screw driver. (Measurements would be easier for the former). Explain how you would use these to calculate *IMA* and efficiency.

PULLEY SYSTEM: Explain how you would determine the *IMA* and efficiency of the four-pulley system shown in Figure 9.12. Why do you only need two distance measurements for this machine?

Design a table that compares the efficiency of the five simple machines. Make predictions as to the most and least efficient machines.