374 Chapter 13 Energy and Power

Kinetic Energy

An object having a massmand moving with a speedVhas a kinetic energy, which is equal to

(13.2)

The SI unit for kinetic energy is the joule, which is a derived unit. The unit of joule is obtained

by substituting kg for the units of mass, and m/s for the units of speed, as shown here.

Note that the factor in the kinetic energy equation is unitless. In the British Gravitational

system of units, the unit for kinetic energy is lbf ft. This unit is obtained by substituting slug

for the unit of mass, and ft /s for the unit of speed and recognizing that lbf= (slug) (ft /s

2

). More-

over, when dealing with problems in which mass is given in pound mass (U.S. Customary unit),

convert the lbmto slug first. Then you can express your kinetic energy results in lbf ft. As we

discussed in the previous section, it is the change in kinetic energy (¢KE), that is used in engi-

neering analysis as given by Equation (13.1). The change in the kinetic energy is given by

(13.3)

Example 13.1 Determine the net force needed to bring a car that is traveling at 90 km/h to a full stop in a

distance of 100 m. The mass of the car is 1400 kg.

We begin the analysis by first changing the units of speed to m/s and then use Equation (13.1)

to analyze the problem.

Note that in Example 13.1, change in the kinetic energy was used in the analysis. Also note, the

negative value of force indicates that the force must be applied in opposite direction of motion,

as expected.

Potential Energy

The work required to lift an object with a massmby a vertical distance ¢his called gravita-

tional potential energy. It is the mechanical work that must be performed to overcome

force4375 N

1 force 21 100 m 2  0 

1

2

1 1400 kg2a 25

m

s

b

2

work 1  2  1 force 21 distance 2 

1

2

mV

2

2 

1

2

mV

2

1

V 2 Vfinal 0

V 1 Vinitial 90 a

km

h

ba

1 h

3600 s

ba

1000 m

1 km

b 25

m

s

¢KE

1

2

mV

2

2 

1

2

mV

2

1

1

2

kinetic energy

1

2

mV

2

 1 kg2a

m

s

b

2

 1 kg2a

m

s

2 b1m^2 N

#mjouleJ

d

kinetic energy

1

2

mV

2

N

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