Determine the work that needs to be done in order to compress the spring by 10 cm

Determine the work that needs to be done in order to compress the spring by 10 cm, if a force of 100 N is needed to compress it by 1 cm.

Given:

dx1 = 1 centimeter = 0.01 meter – the amount of compression of the spring;

F = 100 Newton – the force that needs to be applied to compress the spring by dx1;

dx2 = 10 centimeters = 0.1 meter.

It is required to determine A (Joule) – the work that must be done to compress the spring by the amount dx2.

Find the coefficient of spring stiffness:

k = F / dx1 = 100 / 0.01 = 10000 N / m.

Then the work will be equal to:

A = k * dx2 ^ 2/2 = 10000 * 0.1 ^ 2/2 = 5000 * 0.1 ^ 2 = 5000 * 0.01 = 50 Joules.

Answer: To compress the spring by 10 cm, you need to do work equal to 50 Joules.