Question

A spring has a natural length of 15 cm. A force of 30 N is required to keep the spring stretched to a length of 25 cm. Calculate the work that will be required to stretch the spring from 25 cm to 30 cm.

Answer 1

C. 1.875 J

Explanation:

You want the work done stretching a spring from 25 cm to 30 cm, given that the force required to stretch it to 25 cm from its natural length of 15 cm is 30 N.

Spring constant

In newtons per meter, the spring constant is ...

k = (30 N)/(0.25 m -0.15 m) = 300 N/m

Work

Work is the product of force and distance. When the force is a function of distance, the work can be found by integrating:

dW = k(x -0.15)dx

`\displaystyle W=\int_(0.25)^(0.30)300(x-0.15)dx = (300)/(2)((0.30-0.15)^2-(0.25-0.15)^2)\\\\=150(0.0125)=1.875\quad\text{joules}`

The work required to stretch the spring to 30 cm is 1.875 J.

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Additional comment

The units of work (energy) used here are newton-meters (joules), so the distance dimensions need to be in meters. 15 cm = 0.15 m, for example.

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