Question

Example 2: How much power is needed to lift a book to a height of
2.0 meters in a time of 1.0 second, if the book exerts a
force of 20 newtons?
Given: Distance � 2.0 m
Time � 1.0 s
Force � 20 N
Unknown: Power
Equations: Power � and Work � Force � Distance
Solution: Find the value for work by substituting the
given values for force and distance in the
work equation:
Work � 20 N � 2.0 m � 40 N·m � 40 J
Substitute the values for work and time in the
power equation to find the value for power:
Power � � 40J
1 s 40 J/s � 40 W
Work
Time
40 J>s
1 s
40 W
1 s
Work
Time
Physical Science Math Skills and Problem Solving Workbook 53



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Practice Exercises
Exercise 1: A light bulb does 100 joules of work in 2.5 seconds.
How much power does it have?
Exercise 2: A man exerts 700 newtons of force to move a piece of
furniture 4 meters. If it takes him 2 seconds to move the
furniture, how much power does it require?
Exercise 3: A hair curling iron uses 13 watts of power. How long
must it operate to do 1,040 joules of work?
Exercise 4: A 4-watt night light is left on for 8 hours each night.
How much work does it do per night?
Exercise 5: How much horsepower is needed to move a box that
has a force of 1,492 newtons a distance of 2 meters in
1 second?

Answer 1

Here are the solutions, with steps:

1) A light bulb does 100 J in 2.5 s.
Power = W/t = 100 J / 2.5 s = 40 W.

2) Force = 700 N, distance = 4 m → Work = F·d = 700 N·4 m = 2800 J. Time = 2 s.
Power = W/t = 2800 J / 2 s = 1400 W.

3) Power = 13 W, Work = 1040 J.
Time = W/P = 1040 J / 13 W = 80 s.

4) Night light: P = 4 W, time = 8 h = 8·3600 = 28,800 s.
Work = P·t = 4 W · 28,800 s = 115,200 J ( = 32 Wh = 0.032 kWh ≈ 115.2 kJ).

5) Force = 1492 N, distance = 2 m → Work = 1492·2 = 2984 J in 1 s → Power = 2984 W.
Convert to horsepower: 2984 W / 746 W per hp = 4.00 hp.