Suppose that 2 Joules of work is needed to stretch a spring from its natural length of 35 cm to a length of 52 cm. How much work is needed to stretch it from 45 cm to 55 cm? Your answer must include the correct units.

2.08 J

Explanation:

From Hook's law,

The expression for the work required to stretch a spring is given as,

W = 1/2ke² Equation 1

Where W = Work require to stretch the spring, k = spring constant of the spring, e = extension.

make k the subject of the equation

k = 2W/e² Equation 2

Given: W = 2 Joules, e = 52-35 = 17 cm = 0.17 m

Substitute into equation 2

k = 2×2/(0.17²)

k = 138.41 N/m

First the work needed to stretch it to 45 cm

W = 1/2ke²

Where k = 138.41 N/m, e = 45-35 = 10 cm = 0.1 m

Substitute into equation above

W = 1/2(138.41)(0.1²)

W = 0.69205 J.

Also the work needed to stretch the spring to 55 cm

Given: e = 55-35 = 20 cm = 0.2 cm

W' = 1/2(138.41)(0.2²)

W' = 2.7682.

Hence the work needed to stretch the spring from 45 cm to 55 cm = 2.7682-0.69205 = 2.08 J

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