Determine the energy that the spring receives when it is compressed by 5 cm, if it is known that to compress

Determine the energy that the spring receives when it is compressed by 5 cm, if it is known that to compress the spring by 1 cm, a force of 30 kN must be applied.

Given:

dx1 = 1 centimeter = 0.01 metro – the amount of compression of the spring when the force F;

F = 30 kN = 30,000 Newton – force acting on the spring;

dx2 = 5 centimeters = 0.05 meters.

It is required to determine W (Joule) – the energy of the spring when it is compressed by dx2.

Let’s find the coefficient of elasticity of the spring:

k = F / dx1 = 30,000 / 0.01 = 3,000,000 N / m.

Then the energy of the compressed spring will be equal to:

W = k * dx ^ 2/2 = 3,000,000 * 0.05 ^ 2/2 = 1,500,000 * 0.05 ^ 2 =

= 1500000 * 0.0025 = 3750 Joules.

Answer: the energy of the compressed spring will be equal to 3750 Joules.