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Force = w = mg In the metric system, power is measured in joules per sec-
ond. The unit J/s, however, has a name. A J/s is called a watt
W = mgh (W).* The watt (Figure 3.5B) is used with metric prefixes for
= (120 lb) (10.0 ft) large numbers: 1,000 W = 1 kilowatt (kW) and 1,000,000 W =
Height 10 ft kilowatt is equal to about 1 1/3 horsepower.
= 1,200 ft • lb 120 lb 1 megawatt (MW). It takes 746 W to equal 1 horsepower. One

The electric utility company charges you for how much
electrical energy you have used. Electrical energy is measured
by power (kW) multiplied by the time of use (h). The kWh is a
A unit of work, not power. Since power is
Force = w = mg W _
P =

t
then it follows that
mgh 120 lb
P = t W = Pt
(120 lb) (10.0 ft)
=
4 s So power times time equals a unit of work, kWh. We will re-
ft • lb turn to kilowatts and kilowatt-hours later when we discuss
= 300
Height 10 ft
s electricity.
EXAMPLE 3.3
An electric lift can raise a 500.0 kg mass a distance of 10.0 m in 5.0 s.
What is the power of the lift?
B
FIGURE 3.4 (A) The work accomplished in climbing a stairway SOLUTION
is the person’s weight times the vertical distance. (B) The power
level is the work accomplished per unit of time. Power is work per unit time (P = W/t), and work is force times
distance (W = Fd). The vertical force required is the weight lifted,
and w = mg. Therefore, the work accomplished would be W = mgh,
and the power would be P = mgh/t. Note that h is for height, a vertical
distance (d).
mgh
_
m = 500.0 kg P =

t
Force = g = 9.8 m∙ s 2 2
(500.0 kg)(9.8 m∙ s )(10.0 m)
Time = 1.0 s 550 lb ___

h = 10.0 m =
5.0 s

t = 5.0 s
m _
P = ? (500.0)(9.8)(10.0) kg· ·m
2
s

= __ _
5.0 s
Distance = _
N·m
1.0 ft = 9,800
s
J
_
A = 9,800
s
= 9,800 W
= 9.8 kW
Force = The power in horsepower (hp) units would be
Time = 1.0 s
1 newton
hp
(about _

0.22 lb) 9,800 W × = 13 hp
746 W
Distance = EXAMPLE 3.4
1.0 m
A 150 lb person runs up a 15 ft stairway in 10.0 s. What is the horse-
power rating of the person? (Answer: 0.41 hp)
B
FIGURE 3.5 (A) One horsepower is defined as a power rating
of 550 ft·lb/s. (B) One watt is defined as one newton-meter per
*Note that symbols for units, such as the watt, are not in italic. Symbols for quantities,
second, or joule per second. such as work, are always in italic.
66 CHAPTER 3 Energy 3-6