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person catching the ball and moves it through a distance. The
net work done on the hand is equal to the kinetic energy that the SOLUTION
ball had. Therefore, The relationship between kinetic energy (KE), mass (m), and velocity
2
(v) is found in equation 3.4, KE = 1/2 mv :
work done to increase in
increase in 1 _
put an object = = work the object m = 7.00 kg KE = mv 2

kinetic energy 2
in motion can do v = 5.00 m/s
1 _ m _ 2

KE = ? = (7.00 kg) (5.00 )

A baseball and a bowling ball moving with the same 2 s

velocity do not have the same kinetic energy. You cannot knock 1 _ _ 2
m
= (7.00 × 25.0) kg ×

down many bowling pins with a slowly rolling baseball. Obvi- 2 s
2
ously, the more massive bowling ball can do much more work 2
kg· m
1 _ _
than a less massive baseball with the same velocity. Is it possible = 175

2 s
2
for the bowling ball and the baseball to have the same kinetic
kg·m
energy? The answer is yes, if you can give the baseball suffi- _

= 87.5 ·m

2
cient velocity. This might require shooting the baseball from a s
cannon, however. Kinetic energy is proportional to the mass of = 87.5 N·m
a moving object, but velocity has a greater influence. Consider
= 87.5 J
two balls of the same mass, but one is moving twice as fast as the
other. The ball with twice the velocity will do four times as much
work as the slower ball. A ball with three times the velocity will EXAMPLE 3.8
do nine times as much work as the slower ball. Kinetic energy is
2
2
proportional to the square of the velocity (2 = 4; 3 = 9). The A 100.0 kg football player moving with a velocity of 6.0 m/s tackles a
stationary quarterback. How much work was done on the quarterback?
kinetic energy (KE) of an object is
(Answer: 1,800 J)
1 _ 2

kinetic energy = (mass) (velocity)

2
1 _ 2

KE = mv 3.3 ENERGY FLOW

2
equation 3.4 The key to understanding the individual concepts of work and
energy is to understand the close relationship between the two.
The unit of mass is the kg, and the unit of velocity is m/s. There-
When you do work on something, you give it energy of position
fore, the unit of kinetic energy is
(potential energy) or you give it energy of motion (kinetic energy).
m _ 2 In turn, objects that have kinetic or potential energy can now do
KE = (kg) ( )

s
work on something else as the transfer of energy continues. Where
2
( ) does all this energy come from and where does it go? The answer
_
m
= (kg)
2
s to these questions is the subject of this section on energy flow.
kg· m
_ 2

= 2
s WORK AND ENERGY
Energy is used to do work on an object, exerting a force through
which is the same thing as
a distance. This force is usually against something (Figure 3.9),
kg·m
( ) and here are five examples of resistance:
_

(m)

2
s 1. Work against inertia. A net force that changes the state of
or motion of an object is working against inertia. According
to the laws of motion, a net force acting through a distance
N·m is needed to change the velocity of an object.

or 2. Work against gravity. Consider the force from gravitational
attraction. A net force that changes the position of an
joule (J) object is a downward force from the acceleration due to
Kinetic energy is measured in joules. gravity acting on a mass, w = mg. To change the position
of an object, a force opposite to mg is needed to act
through the distance of the position change. Th us, lift ing
an object requires doing work against the force of gravity.

3. Work against friction. The force that is needed to maintain
EXAMPLE 3.7 the motion of an object is working against friction.
A 7.00 kg bowling ball is moving in a bowling lane with a velocity of Friction is always present when two surfaces in contact
5.00 m/s. What is the kinetic energy of the ball? move over each other. Friction resists motion.
3-9 CHAPTER 3 Energy 69