The spring with a stiffness of 1000 N / m was compressed by 4 cm.

The spring with a stiffness of 1000 N / m was compressed by 4 cm. What work must be done to increase the compression of the spring to 18 cm?

The work required to compress a spring with a stiffness k by an amount x:

A = k x ^ 2/2.

Let us first determine the work required to compress the spring by x1 = 4 cm = 0.04 m:

A1 = k x1 ^ 2/2 = 1000 × 0.04 ^ 2/2 = 0.8 J.

On the other hand, we will find the work required to compress the spring from zero to x2 = 18 cm = 0.18 m:

A2 = k x2 ^ 2/2 = 1000 × 0.18 ^ 2/2 = 16.2 J.

The sought-for work of compression of the spring from x1 = 4 cm to x2 = 18 cm is equal to the difference:

A = A2 – A1 = 16.2 – 0.8 = 15.4 J.

Answer: 15.4 J.