Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

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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