The variation with applied force of the extension of a spring is shown in the graph.

Question 4

The variation with applied force of the extension of a spring is shown in the graph.

When there is no force applied to the spring, it has a length of 1.0 cm.

What is the increase in the strain energy stored in the spring when its length is increased from 2.0 cm to 3.0 cm?

A 0.020 J                     B 0.030 J                     C 0.040 J                    D 0.050 J

Reference: Past Exam Paper – June 2015 Paper 11 Q23

Solution:

Answer: B.

The spring has a length of 1.0 cm when no force is applied.

Original length = 1.0 cm

The strain energy stored in the spring can be obtained by the area under the force-extension graph.

It is important to note that the word ‘length’ is in bold.

One of the axes of the graph is ‘extension’, and not ‘length’. We need to find the corresponding extensions for the lengths given.

Original length = 1.0 cm

When length = 2.0 cm, extension = 2.0 – 1.0 = 1.0 cm

When length = 3.0 cm, extension = 3.0 – 1.0 = 2.0 cm

So, we need to find the area under the graph between 1.0 cm and 2.0 cm.

We also need to use the extension in SI units, i.e. metre.

Strain energy stored = area under graph (= area of trapezium)

{Area of trapezium = ½ × sum of parallel sides × height}

Strain energy stored = ½ × (2.0 + 4.0) × (0.01)

Strain energy stored = 0.030 J