Find the spring constant k if the spring is stretched a distance 67 m by a suspended weight of 76 N. The acceleration of gravity is 9.8 m/s ^2 . Answer in units of N/m.

Question

A common technique used to measure the force constant k of a spring is the following: Hang the spring vertically, then allow a mass m to stretch it a distance d from the equilibrium position under the action of the “load” m g. Find the spring constant k if the spring is stretched a distance 67 m by a suspended weight of 76 N. The acceleration of gravity is 9.8 m/s ^2 . Answer in units of N/m.

Answer 1

First, we draw a free-body diagram for the object to represent the forces acting on it. Pointing down is the force of gravity, which is given as 76 N. Pointing up is the spring force, which is represented as F = -kx = -67k.

Since we are in equilibrium, the net force is 0, so the force of gravity + the spring force is 0. So, 76 + (-67k) = 0, and 76 = 67k. Then, k = 76 / 67 = 1.13 N/m.