376 Chapter 13 Energy and Power

Note that the amount of energy required to lift the elevator from the first to the second floor and

from the third to the fourth floor is the same. Also realize that we have neglected any frictional effect

in our analysis. The actual energy requirement would be greater in the presence of frictional effect.

Elastic Energy

As we explained in Chapter 10, springs are used in a variety of products such as cars, weight-

ing scales, clothespins, and printers. When a spring is stretched or compressed from its

unstretched position, elastic energyis stored in the spring, energy that will be released when

the spring is allowed to return to its unstretched position (see Figure 13.4). The elastic energy

stored in a spring when stretched by a distancexor compressed is given by

(13.5)

where

kspring constant (N/m)

xdeflection of spring from its unstretched position ( m)

The SI unit for elastic energy is also the joule. It is obtained by substituting N/m for the

units of spring constant and m for the units of deflection, as shown:

Note once again that the factor in the elastic energy equation is unitless. In the U.S. Customary

and British Gravitational systems of units, the unit of elastic energy is expressed in lbf ft. Let us

now consider the spring shown in Figure 13.5; the spring is stretched byx 1 to position 1 and then

stretched byx 2 to position 2. The elastic energy stored in the spring in position 1 is given by

1

2

elastic energy

1

2

kx

2

a

N

m

b1m 2

2

N#mJ

elastic energy

1

2

kx

2

Force

Unstretched

position

Stretched

position

x

Force

Unstretched

position x

1

Position (^1) x 2
Position 2
■Figure 13.4
The elastic energy of a spring.
■Figure 13.5
The change in the elastic energy of a spring.
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