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Question

The force exerted by a stretched chord at given displacements is shown in the table given below. Experimentally, the force is found to vary proportionally to the square of the displacement, i.e. F(x)=hx2 where h is some constant.
If the potential energy at x=0 m is U0=0 J, determine the potential energy at x=1.5 m.


A
1.13 J
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B
2.25 J
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C
4.50 J
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D
6.75 J
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Solution

The correct option is B 2.25 J
The force exerted by chord F=hx2
Given: F=2 N at x=1 m
2=h×12h=2
Thus the force is F=2x2 N
Potential energy U=Fdx=2x2dx=23x3+C
Given U=0 at x=0 C=0
U=23x3
U|x=1.5=23×(1.5)3=2.25 J

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