To stretch a spring by 5 cm, you need to do a work of 20 J. What work must be done to stretch

To stretch a spring by 5 cm, you need to do a work of 20 J. What work must be done to stretch the same spring by another 5 cm?

Given:

A1 = 20 Joules – the work that needs to be done to stretch the spring by dx1;

dx1 = 5 centimeters = 0.05 meters – the amount by which the spring was stretched;

dx2 = 5 centimeters.

It is required to determine what work A2 (Joule) needs to be done in order to stretch the same spring additionally by dx2.

We believe that it is necessary to find work to stretch an already stretched spring.

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

k = 2 * A1 / dx1 ^ 2 = 2 * 20 / 0.05 ^ 2 = 40 / 0.0025 = 16000 N / m.

The total tension of the spring will be equal to:

dx = dx1 + dx2 = 0.05 + 0.05 = 0.1 meter.

Then the total work expended will be equal to:

A = k * dx ^ 2/2 = 16000 * 0.1 ^ 2/2 = 8000 * 0.01 = 80 Joules.

It turns out that it is additionally necessary to complete the work:

A2 = A – A1 = 80 – 20 = 60 Joules.

Answer: you need to do work equal to 60 Joules.