A load weighing 10 kg is suspended on a thin wire. In this case, the length of the wire increased

A load weighing 10 kg is suspended on a thin wire. In this case, the length of the wire increased by 0.5 mm. What is the stiffness of the thread?

Given:

m = 10 kilograms is the mass of the load suspended on a thin wire;

dx = 0.5 millimeters = 0.0005 meters – the amount of wire elongation;

g = 9.8 meters per second squared – the acceleration of gravity.

It is required to determine k (Newton / meter) – the stiffness coefficient of the wire.

A body suspended from a wire, acting on the wire with a force equal to the force of gravity:

F gravity = m * g = 10 * 9.8 = 98 Newtons.

Then the stiffness coefficient of the wire will be equal (according to Hooke’s law):

k = F gravity / dx = 98 / 0.0005 = 196000 N / m = 196 kN / m.

Answer: the stiffness factor of the wire is 196 kN / m.