Question
A wire that obeys Hooke’s Law of length x1 when it is in equilibrium under tension T1. It’s length becomes x2 when the tension is increased to T2. 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.