Worked Example: Hooke's Law (Spring Force)
This worked example applies Hooke's Law to determine the restoring force produced by a spring when it is displaced from its equilibrium position.
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This worked example applies Hooke's Law to determine the restoring force produced by a spring when it is displaced from its equilibrium position.
An industrial return spring in a valve assembly has a spring constant of 250 N/m. During operation, the spring is compressed by 0.08 m (80 mm) from its natural length. Calculate the magnitude of the restoring force exerted by the spring.
Hooke's Law: The restoring force () exerted by a spring is proportional to the displacement () from equilibrium, with the spring constant () as the proportionality factor:
For the magnitude of the force:
Calculate the spring force using the magnitude form:
The spring exerts a restoring force of N directed opposite to the compression. In this valve assembly, this force is what pushes the valve back to its seated position when the actuating pressure is released. Engineers select the spring constant to ensure that this restoring force exceeds the minimum seating force required for a proper seal, while remaining within the elastic limit of the spring material.