13.1 Work, Mechanical Energy, Thermal Energy 377
(13.6)
Example 13.3 Determine the change in the elastic energy of the spring shown in Figure 13.6 when it is
stretched from: (a) position 1 to position 2 , (b) position 2 to position 3 , and position 1 to posi-
tion 3. The spring constant isk100 N/cm. Additional information is shown in Figure 13.6.
change in elastic energy¢EE
1
2
kx
2
2
1
2
kx
2
1
elastic energy
1
2
kx
2
2
elastic energy
1
2
kx
2
1
Force
Unstretched
position x 2 = 5 cm
x 3 = 7 cm
1
2
3
■Figure 13.6 The spring in Example 13.3.
We begin by converting the units of the spring constant from N/cm to N/m in the fol-
lowing manner:
Using Equation (13.6), we can now answer the questions:
(a)
(b)
(c) ¢EE
1
2
kx
2
3
1
2
kx
2
1
1
2
1 10,000 N/m 21 0.07 2
2
0 24.5 J
¢EE
1
2
kx
2
3
1
2
kx
2
2
1
2
1 10,000 N/m 21 0.07 2
2
1
2
1 10,000 N/m 21 0.05 2
2
12 J
¢EE
1
2
kx
2
2
1
2
kx
2
1
1
2
1 10,000 N/m 21 0.05 2
2
0 12.5 J
change in elastic energy¢EE
1
2
kx
2
2 kx
2
1
1 100 N/cm 21 100 cm/m 2 10,000 N/m
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