A weight of mass m is suspended from a weightless spring with rigidity k. Determine the energy of an elastically deformed spring.

Given:

m is the mass of the load suspended from the weightless spring;

k is the stiffness of the spring;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the energy of an elastically deformed spring W.

Let us find the length of the deformation of the spring l:

F = k * l (where F is the force of gravity acting on the load suspended from the spring);

m * g = k * l;

l = m * g / k.

Then the energy of the spring will be equal to:

W = k * l ^ 2/2 = k * m ^ 2 * g ^ 2 / k ^ 2/2 = (m * g) ^ 2 / (2 * k).

Answer: the energy of an elastically deformed spring is W = (m * g) ^ 2 / (2 * k).