The spring is compressed 2 cm with a force of 4 kN. How many times do you need to increase the force that compresses

The spring is compressed 2 cm with a force of 4 kN. How many times do you need to increase the force that compresses the spring so that the spring shrinks by another 3 cm?

Problem data: Δx1 (initial spring compression) = 2 cm; F1 (initial compression force) = 4 kN; Δx2 (additional spring compression) = 3 cm.

1) Calculate the force for additional compression of the spring by 3 cm: F1 / Δx1 = k = F2 / (Δx1 + Δx2), whence F2 = F1 * (Δx1 + Δx2) / Δx1 = 4 * (2 + 3) / 2 = 10 kN.

2) Determine the increase in the compression force of the spring: n = F2 / F1 = 10/4 = 2.5 times.

Answer: The compression force of the spring must be increased 2.5 times.