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your mass (conversion factors are located inside the front
PE = mgh
cover). Record your findings in your report.
h Second, find your power output by climbing the stairs
as fast as you can while someone measures the time with a
Reference position:
PE = 0 stopwatch. Find your power output in watts. Convert this to
horsepower by consulting the conversion factors inside the
front cover. Did you develop at least 1 hp? Does a faster
person always have more horsepower?
2
( kg)(9.8 m∙ s )( m)
___

walking power =
( s)
2
( kg)(9.8 m∙ s )( m)
___

running power =
( s)
Ground level PE = –mgh
FIGURE 3.7 The zero reference level for potential energy is
chosen for convenience. Here the reference position chosen is the
third floor, so the book will have a negative potential energy at KINETIC ENERGY
ground level.
Moving objects have the ability to do work on other objects be-
cause of their motion. A rolling bowling ball exerts a force on
EXAMPLE 3.5 the bowling pins and moves them through a distance, but the
ball loses speed as a result of the interaction (Figure 3.8). A mov-
What is the potential energy of a 2.14 kg book that is on a bookshelf ing car has the ability to exert a force on a small tree and knock
1.0 m above the floor?
it down, again with a corresponding loss of speed. Objects in
motion have the ability to do work, so they have energy. The
SOLUTION energy of motion is known as kinetic energy. Kinetic energy
Equation 3.3, PE = mgh, shows the relationship between potential can be measured in terms of (1) the work done to put the object
energy (PE), weight (mg), and height (h). in motion or (2) the work the moving object will do in coming
to rest. Consider objects that you put into motion by throwing.
m = 2.14 kg PE = mgh
You exert a force on a football as you accelerate it through a dis-
h = 1.0 m m _
(
2)
= (2.14 kg) 9.8 (1.0 m) tance before it leaves your hand. The kinetic energy that the ball
PE = ? s now has is equal to the work (force times distance) that you did
kg · m on the ball. You exert a force on a baseball through a distance
_

= (2.14)(9.8)(1.0) × m
2
s as the ball increases its speed before it leaves your hand. The
kinetic energy that the ball now has is equal to the work that
= 21 N · m
you did on the ball. The ball exerts a force on the hand of the
= 21 J
EXAMPLE 3.6
How much work can a 5.00 kg mass do if it is 5.00 m above the ground?
(Answer: 250 J)
W = F d
B 1 2
KE = mv
2
W = F d
p
CONCEPTS Applied F p
F
B
Work and Power
Power is the rate of expending energy or of doing work. You Distance Distance
can find your power output by taking a few measurements. A B C
First, let's find how much work you do in walking up
a flight of stairs. Your work output will be approximately FIGURE 3.8 (A) Work is done on the bowling ball as a force
equal to the change in your potential energy (mgh), so (F B ) moves it through a distance. (B) This gives the ball a kinetic
you will need (1) to measure the vertical height of a flight energy equal in amount to the work done on it. (C) The ball does
of stairs in metric units and (2) to calculate or measure work on the pins and has enough remaining energy to crash into the
wall behind the pins.

68 CHAPTER 3 Energy 3-8