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Skills Worksheet
Math Skills
Power
After you study each sample problem and solution work out the practice problems
on a separate sheet of paper. Write your answers in the spaces provided.
Problem
The world’s most powerful tugboats, which are built in Finland, are capable of providing 8.17 106 W of power. How much work does one of these
tugboats do in 12.0 s?
Solution
Step 1: List the given and unknown values.
Given:
power, P 8.17 106 W
time, t 12.0 s
Unknown:
work, W ? J
Step 2: Rearrange the power equation to solve for work.
work
W
power P
time
t
W
tW
t
Step 3: Insert the known values into the equation, and solve.
Pt
W (8.17 106 W) (12.0 s) (8.17 106 J/s) (12.0 s)
W 9.80 107 J
Practice
1. One horsepower (1 hp) is the unit of power based on the work that a horse
can do in one second. This is defined, in English units, as a force of 550 lb
that can move an object 1 ft in 1 s. In SI, 1 hp equals 745.7 W. Suppose you
have a horse that has a power output of 750 W. How much work does this
horse do in 0.55 s?
2. A race car with a 255 hp (1.90 105 W) engine is able to accelerate from rest
to its top speed in 9.00 s. How much work does the car’s engine do in this
interval of time?
3. A ship’s diesel engine has a power output of 13.0 MW (13.0 106 W). How
much work is done by this engine in 15.0 min?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Math Skills continued
Problem
Suppose a weightlifter’s power output is 178 W during the time he does
3310 J of work on the weights. How long does it take the weightlifter to
raise the weights?
Solution
Step 1: List the given and unknown values.
Given:
power, P 178 W
work, W 3310 J
Unknown:
time, t ? s
Step 2: Rearrange the power equation to solve for time.
power work
time
P
W
t
t W t W
P P t P P
Step 3: Insert the known values into the equation, and solve.
t
3310 J 3310 J
178 W 178 J/s
t 18.6 s
Practice
4. In order to sail through the frozen Arctic Ocean, the most powerful icebreaker
ever built was constructed in the former Soviet Union. At the heart of the ship’s
power plant is a nuclear reactor with a power output of 5.60 107 W. How long
will it take for this power plant to do 5.35 1010 J of work?
5. The heaviest loads ever raised were part of the offshore Ekofisk complex in
the North Sea. The 4.0 107 kg complex was raised 6.5 m by over a hundred
hydraulic jacks. The work done on the complex during the raising was
approximately 2.6 1011 J. Suppose the power output of all the jacks was
5.7 108 W. How long did it take the jacks to raise the complex?
6. Borax was mined in Death Valley, California, during the nineteenth century. It
was transported from the valley by massive wagons, each pulled by a team of
21 mules. Suppose each mule’s power output was 746 W (about 1 hp). If in a
certain time interval the total work done by the team on the wagon was
2.35 107 J, how long was that interval of time?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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Math Skills continued
Problem
A certain crane is able to lift 2.20 106 kg. If the crane is able to raise
this mass a distance of 20.0 m by doing 4.32 108 J of work in 35.0 s, how
much power has the crane provided?
Solution
Step 1: List the given and unknown values.
Given:
work, W 4.32 108 J
time, t 35.0 s
The distance of 20.0 m and the mass of 2.2 106 kg are not needed to calculate
power.
Unknown:
power, P ? W
Step 2: Write out the equation for power.
power work
time
P
W
t
Step 3: Insert the known values into the equation, and solve.
P
4.32 108 J
1.2 107 J/s 1.2 107 W
35 s
P 12 MW
Practice
7. A certain steam turbine is designed to be used as both a power generator and
as a pump. When used as a generator, the turbine provides enough power to
do 3 1010 J of work in 1 min. What is the power output of the turbine?
8. The space shuttle, which was first launched on April 12, 1981, is the world’s
first reusable space vehicle. The shuttle is placed in orbit by three engines
that do 1.4 1013 J of work in 8.5 min. What is the power output of these
engines?
9. Lithuania’s major nuclear power plant has one of the world’s most powerful
generators, which has a power output of 1.45 109 W. How long must this
generator run if it is to provide the energy to do 4.35 1011 J of work?
Copyright © by Holt, Rinehart and Winston. All rights reserved.
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TEACHER RESOURCE PAGE
2. input distance mechanical advantage
W 1.8 106 J
9.0 105 N
d
2.0 m
7. W Fd (3150 N) 75.5 m
2.38 105 J
8. W Fd (1.6 106 N) (2.0 103 m)
3.2 109 J
9. W Fd
(0.25) (1.5 106 N) (15 m)
5.6 106 J
W 3650 J
1.48 m
10. d F 2470 N
W 4365 J
3.353 m
11. d F 1302 N
W 1.67 104 J
5.48 103 N
12. F d
3.05 m
13. W Fd (2.23 104 N) (436 m)
9.72 106 J
W 1.10 109 J
4.35 102 m
14. d F 2.53 106 N
15. W Fd mad (70.0 kg)
(4.90 102 m/s 2)(8.05 m)
2.76 105J
6. F 3.
4.
5.
6.
7.
POWER
1. W P t (750 W) (0.55 s)
4.1 102 J
2. W P t (1.90 105 W) (9.00 s)
1.71 106 J
3. W P t
(13.0 106 J) (15.0 min)
60 s
1.17 1010 J
1 min
W 5.35 1010 J
4. t 9.55 102 s
P 5.60 107 W
W 2.6 1011 J
460 s
5. t P 5.7 108 W
W 2.35 107 J
1.5 103 s
6. t P 21 746 W
W 3 1010 J
5 108 W
7. P t
60 s
W
1.4 1013 J
8. P t (8.5 min) (60 s/min)
2.7 1010 W total
or 9.0 109 W per engine
W 4.35 1011 J
3.00 102 s
9. t P 1.45 109 W
8.
9.
10.
11.
12.
13.
MECHANICAL ADVANTAGE
1. output force mechanical advantage
input force
output force 2.2 202 N 440 N
output distance
input distance 5.5 2.0 cm 11 cm
output distance
input distance
mechanical advantage
3.0 cm
3.5 cm
0.85
input distance
input force mechanical advantage
2.22 103 N
2.49 104 N
8.93 102
output distance
input distance
mechanical advantage
1.57 m
0.126 m
12.5
mechanical advantage
input distance 4.6 m
3.3
output distance 1.4 m
output force
mechanical advantage input force
7406 N
24.00
308.6 N
mechanical advantage
input distance
output distance
15 cm
0.18
85 cm
output force
mechanical advantage input force
6350 N 3.86 2.45 104 N
output force
input force mechanical advantage
7500 N
9.6 103 N
0.78
output distance
input distance
mechanical advantage
0.64 m
4.0 m
0.16
input distance
output distance
mechanical advantage
11 m 48 530 m
mechanical advantage
output force 5.87 1025 N
input force
175 N
3.35 1023
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Holt Science Spectrum
117
Work and Energy