Under the action of a force of 60 N, the spring lengthened by 10 cm. What work must

Under the action of a force of 60 N, the spring lengthened by 10 cm. What work must be done to increase the length of the spring by another 5 cm?

Find the coefficient of spring stiffness:

F = kx, where F is the applied force, k is the stiffness coefficient, x is the displacement from the equilibrium position.

k = F / x = 60 N / 0.1 m = 600 N / m.

Potential spring energy when stretched by 10 cm:

W0 = kx02 / 2 = (600 N / m * 0.12 m2) / 2 = 3 J.

Potential spring energy when stretched by 15 cm:

W1 = kx12 / 2 = (600 N / m * 0.152 m2) / 2 = 6.75 J.

Work to increase the potential energy of the spring:

A = W1 – W2 = 6.93 J – 3 J = 3.75 J.

Answer: 3.75 J.