What work A must be done to compress the spring by Δl = 5.0 cm, if a force F = 200 N is required

What work A must be done to compress the spring by Δl = 5.0 cm, if a force F = 200 N is required to compress it by Δl1 = 1.0 cm?

Given:

F = 200 Newton – the force required to compress the spring by an amount equal to dx1;

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

dx2 = 5 centimeters = 0.05 meters is the required amount of spring compression.

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

Find the coefficient of spring stiffness:

k = F / dx1 = 200 / 0.01 = 20,000 Newton / meter.

Then, the work of compressing the spring will be equal to its potential energy in the compressed state:

A = E = k * dx ^ 2/2 = 20,000 * 0.05 ^ 2/2 = 10,000 * 0.0025 = 25 Joules.

Answer: To compress the spring by 5 centimeters, you need to do work equal to 25 Joules.