Spring Constant Formula
According to Hooke’s law, the force required to compress or extend a spring is directly proportional to the distance it is stretched. It can be represented in an equation as F = kx, where F is the force applied, k is the spring constant and x is the extension of the object usually in meters.
In other words, spring constant is the force applied if the displacement in the spring is unity.
If a force F is considered that stretches the spring so that it displaces the equilibrium position by x.
The Spring Constant Formula is given as,
F = Force applied,
x = displacement by the spring
It is expressed in Newton per meter (N/m).
A spring with load 5 Kg is stretched by 40 cm. Determine its spring constant.
Mass m = 5 Kg,
Displacement x = 40 cm,
We know that,
Force F = m a
= 5 × 0.4
= 2 N
The spring constant is given as
k = – F / x
= – 2 / 0.4
= – 5 N/m
A boy weighing 20 pounds stretches a spring by 50 cm. Determine the spring constant of the spring.
Mass m = 20 lbs = 20 / 2.2 = 9.09 Kg.
Displacement x = 50 cm
The force F = ma = 9.09 × 9.8 = 89.082 N
The spring constant formula is given by
k = – F / x
= – 89.082 / 0.5
= – 178.164 N/m.