A spring with a stiffness of k = 500 N / m is compressed by a force of F = 100 N.

A spring with a stiffness of k = 500 N / m is compressed by a force of F = 100 N. What work must be done to additionally compress this spring by 2 cm?

Data: k (spring rate) = 500 N / m; F (compression force) = 100 N; Δх1 (additional compression) = 2 cm (in SI system Δх1 = 0.02 m).

1) Determine the initial compression of the spring: Δх = F / k = 100/500 = 0.2 m.

2) We will find work for additional compression of the spring: ΔA = A2 – A1 = k * (Δx + Δx1) ^ 2/2 – k * Δx ^ 2/2 = 500 * (0.2 + 0.02) ^ 2/2 – 500 * 0.2 ^ 2/2 = 12.1 – 10 = 2.1 J.

Answer: The work for additional spring compression is 2.1 J.