A spring of unextended length 0.50 m is stretched by a force of 2.0 N to a new length of 0.90 m.

Question 15

A spring of unextended length 0.50 m is stretched by a force of 2.0 N to a new length of 0.90 m.

The variation of its length with tension is as shown.

How much strain energy is stored in the spring?

A 0.40 J                       B 0.80 J                       C 0.90 J                      D 1.8 J

Reference: Past Exam Paper – June 2007 Paper 1 Q19

Solution:

Answer: A.

When the tension is 0 N (no force is applied), the length of the spring is 0.50 m. This is the original length of the spring.

A tension of 2.0 N causes the spring to extend, from its original length, by (0.9 – 0.5) m.

Strain energy = Area under tension-length graph

We need to consider the area of the triangle formed.

Strain energy = ½ × (2.0 – 0) × (0.9 – 0.5) = 0.40 J

Note that strain (= extension / original length) is NOT the same as strain energy.