The spring is compressed by a force of 100N per 1 cm. What work must be done to compress the spring by 1 cm more?

Spring rate: k = F / x1,

where F is the force, F = 100 N; x1 – initial compression of the spring, x1 = 1 cm = 0.01 m;

k = 100 / 0.01 = 10000 N / m.

The work required to compress this spring from zero to x1 = 1 cm:

A1 = k x1 ^ 2/2 = 10000 × 0.01 ^ 2/2 = 0.5 J.

The work required to compress the spring from zero to x2 = 2 cm = 0.02 m:

A2 = k x2 ^ 2/2 = 10000 × 0.02 ^ 2/2 = 2 J.

The sought-for work of compression of the spring from x1 = 1 cm to x2 = 2 cm is equal to the difference:

A = A2 – A1 = 2.0 – 0.5 = 1.5 J.

Answer: 1.5 J.