When a metal rod was lengthened with a stiffness of 500 N / m, an elastic force of 100 N appeared in it.

When a metal rod was lengthened with a stiffness of 500 N / m, an elastic force of 100 N appeared in it. What was the initial length of the rod if, after lengthening, its length became 30 cm.

An elastic force acts on a metal rod, it is equal to the product of the stiffness coefficient by the change in length (deformation value): F = k * Δl. This force arises due to the electromagnetic interaction between the atoms and molecules of the substance.
We know the stiffness of the metal rod, the length of the body subsequently and the value of the elastic force. Therefore, we can find the initial length of the bar. We should express the value of deformation Δl from the force formula and subtract this value from the length of the rod (since the body has lengthened): Δl = F / k = 0.2 m = 20 cm; l1 = l2 – Δl = 30 – 20 = 10 cm.