## Question

A wire that obeys Hooke’s Law of length x_{1} when it is in equilibrium under tension T_{1}. It’s length becomes x_{2} when the tension is increased to T_{2}. What is the extra energy stored in the wire as a result of this process?

A) 1/4 ( T2 + T1 ) ( x2 - x1 )

B) 1/4 ( T2 + T1 ) ( x2 + x1 )

C) 1/2 ( T2 + T1 ) ( x2 - x1 )

D) 1/2 ( T2 + T1 ) ( x2 + x1 )

E) ( T2 - T1 ) ( x2 - x1 )

## Answer

The extra energy is stored as elastic potential energy.

The graph of tension against total length is shown below. The extra elastic potential energy is given by the shaded area.

Answer is C.