A rubber band is stretched and then relaxed to its original length. The diagram

Q#7 (Past Exam Paper – November 2011 Paper 11 Q24 & P13 Q22 & June 2017 Paper 12 Q21)

A rubber band is stretched and then relaxed to its original length. The diagram shows the force-extension graph for this process.

As the force is increased, the curve follows the path OPQ to extension e. As the force is reduced, the curve follows the path QRO to return to zero extension.

The area labelled X is between the curves OPQ and QRO. The area labelled Y is bounded by the curve QRO and the horizontal axis.

Which statement about the process is correct?

A Area X is the energy which heats the band as it is stretched to extension e.

B (Area X + area Y) is the minimum energy required to stretch the band to extension e.

C Area X is the elastic potential energy stored in the band when it is stretched to extension e.

D (Area Y – area X) is the net work done on the band during the process.

Solution:

Answer: B.

The work done in stretching the rubber band along the path OPQ is the area under the curve OPQ for loading. This corresponds to (area X + area Y). [B is correct]

Area X between the stretching (OPQ) the contraction (QRO) curves represents the amount of thermal energy (heat) dissipated (lost) in the rubber.

Area Y represents the recoverable elastic potential energy stored at maximum extension.