A rubber cord hangs from a rigid support. A weight attached to its lower end is gradually

Q#1 (Past Exam Paper – June 2013 Paper 12 Q22)

A rubber cord hangs from a rigid support. A weight attached to its lower end is gradually

increased from zero, and then gradually reduced to zero.

The force-extension curve for contraction is below the force-extension curve for stretching.

What does the shaded area between the curves represent?

A the amount of elastic energy stored in the rubber

B the amount of thermal energy dissipated in the rubber

C the work done on the rubber cord during stretching

D the work done by the rubber cord during contraction

Solution:

Answer: B. 

The area under a force-extension graph gives us the energy (work).

Work is done on the rubber cord to stretch it. This is given by the area under the ‘stretching’ curve. In other words, this area can be considered to be the total energy input.

However, it is observed that, for rubber, as the weight attached is reduced, the ‘contraction’ curve is a bit below the ‘stretching curve’. 

The area under this curve represents the energy stored in the rubber. That is, it is the useful energy recovered.

It can be seen that this area is lower than the area under the ‘stretching’ curve. This indicates that some energy is lost (it is the amount of thermal energy dissipated in the rubber). 

This is represented by the shaded area between the 2 curves.