9702/May Jun/13/2015/Q23

The graph shows the non-linear force-extension curve for a wire made from a new composite
material.

What could be the value of the strain energy stored in the wire when it is stretched elastically to
point P?

A 0.09 J
B 0.10 J
C 0.11 J
D 0.20 J

Solution:

Answer: C.

The strain energy is given by the area under the force-extension curve.

Consider a straight line joining point (0, 0) and point P (2.0, 100). This line would be below the curve shown in the question.

For the linear force-extension curve (drawn joining point (0, 0) to point P),

Strain energy = ½ Fx = ½ (100)(2x10^-3) = 0.1J.

But the shape of graph implies that the area of under the curve shown in the question should be greater than the area calculated. [A and B are incorrect]

However, the answer should be about 10% greater than this straight line graph value to account for the difference. Choice D (0.20 J) is twice the value calculated. This is too big. [D is incorrect]

Reference: PYQ - May/Jun 2015 Paper 13 Q23