Chapter 4: Machines, Work, and Energy
Homework Solutions
Section 4.1
Understanding Vocabulary
1. A unit of power equal to 746 watts is called one horsepower.
2. Power is the rate of doing work.
3. Force multiplied by distance is equal to work.
4. The measurement unit of power equal to one joule of work performed in 1 second is called the
Watt.
Reviewing Concepts
2. If you lift a box of books one meter off the ground, you are doing work. How much more work do
you do by lifting the box 2 meters off the ground? Twice as much as the distance is twice as much.
3. Decide whether work is being done (using your physics definition of work) in the following
situations:
a. Picking up a bowling ball off the floor. YES
b. Two people pulling with the same amount of force on each end of a rope. NO – nothing is moving
c. Hitting a tennis ball with a tennis racket. YES
d. Pushing hard against a wall for an hour. NO – nothing is moving
e. Pushing against a book so it slides across the floor. YES
f. Standing very still with a book balanced on your head. NO – nothing is moving
5. What is the difference between work and power? Power is the rate at which work is done.
6. What is the meaning of the unit of power called a watt? It is how many Joules of work are done
on an object each second, or how many Joules of energy is being used each second.
Solving Problems
1. Calculate the amount of work you do in each situation.
a. You push a refrigerator with a force of 50 N and it moves 3 meters across the floor. 150 J
b. You lift a box weighing 25 N to a height of 2 meters. 50 J
c. You apply a 500 N force downward on a chair as you sit on it while eating dinner. Nothing!
d. You lift a baby with a mass of 4 kg up 1 meter out of her crib. Force = 40 N, W= 40 J
e. You climb a mountain that is 1000 meters tall. Your mass is 60 kg. Force = 600 N, W= 600,000 J
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5. One machine can perform 500 joules of work in 20 seconds. Another machine can produce 200
joules of work in 5 seconds. Which machine is more powerful?
P (machine 1) = 500/20 = 25 W
P (machine 2) = 200/5 = 40 W
Machine 2 is more powerful – it can do more work each second, even though it did less total work.
7. An elevator lifts a 500 kg load up a distance of 10 meters in 8 seconds.
a. Calculate the work done by the elevator. F = mg = (500)(10) = 5000 N, W = (5000)(10) = 50,000 J
b. Calculate the elevator’s power. P = W/t =50,000/8 = 6,250 W
Section 4.2
Understanding Vocabulary
5. The ramp, the lever, and the wheel and axle are examples of simple machines.
6. Pushing on the pedals of a bicycle is an example of the input to a machine.
7. Moving a heavy load is an example of the output from a lever.
8. To calculate a machine’s mechanical advantage, you divide the output force by the input force.
9. A machine is a device with moving parts that work together to accomplish a task.
10. The pivot point of a lever is known as its fulcrum.
11. The side of a lever where the input force is applied is the input arm.
12. The pulling force in a rope is known as tension.
Reviewing Concepts
7. List five types of simple machines. wheel and axle, rope and pulleys, ramp, lever, gears, screw
9. A certain lever has a mechanical advantage of 2. How does the lever’s
output force compare to the input force? If the MA is 2, then you only
have to push or pull with ½ of force or weight of the object to get it to
move.
11. Draw a diagram of each of the three types of levers. Label the input
force, output force, and fulcrum on each. See diagram to the right.
13. A pulley system has four strands of rope supporting the load. What is
its mechanical advantage? 4 – each strand of rope holds 1/4th of the total
weight.
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Solving Problems
8. A lever has an input force of 5 newtons and an output force of 15 newtons. What is the mechanical
advantage of the lever? M.A. = output force ÷ input force = (15 N) ÷ (5 N) = 3
9. A simple machine has a mechanical advantage of 5. If the output force is 10 N, what is the input
force? You need only push or pull with 1/5th of the output force, this would be 2 N.
10. You use a rope and pulley system with a mechanical advantage of 5. How big an output load can
you lift with an input force of 200 N? 5 times as much or 1,000 N.
11. A lever has an input arm 50 cm long and an output arm 20 cm long.
a. What is the mechanical advantage of the lever? M.A. = Li ÷ Lo => M.A. = 50 cm × 20 cm = 2.5
b. If the input force is 100 N, what is the output force? You could move a weight equal to 2.5 times
the input force, or 250 N.
13. A rope and pulley system is used so that a 20 N force can lift a 60 N weight. What is the minimum
number of ropes in the system that must support the weight? M.A. = Fo ÷ Fi = 60 N ÷ 20 N = 3
Three strands of ropes
15. You push a heavy car weighing 500 newtons up a ramp. At the top of the ramp, it is 2 meters
higher than it was initially.
a. How much work did you do on the car? W = Fd = (500 N)(2 m) = 1000 N
b. If your input force on the car was 200 newtons, how long is the ramp?
work input = work output
(200 N)(Din) = (500 N)(2 m)
Din = 5 meters
Section 4.3
Understanding Vocabulary
13. Efficiency is the ratio of work output to work input and is usually expressed as a percent.
14. A process with less than 100% efficiency is irreversible.
Reviewing Concepts
15. Why can’t the output work for a machine be greater than the input work? Explain.
The output work for a machine cannot be greater than the input work because some of the energy
is converted to other forms because of friction.
16. Can a simple machine’s efficiency ever be greater than 100%? Explain your answer.
No, because some of the energy s converted to other forms because of friction, the output work is
always less than the input work, so efficiency is always less than 100%.
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17. List two examples of ways to increase efficiency in a machine.
A machine’s efficiency can be increased by reducing friction. Methods of reducing friction include
using ball bearings, oil, slippery substances like teflon®, and designing with more streamlined
shapes.
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