How to Calculate Energy and Forces on a Spring Using Hooke's Law

spring potential energy force hooke's law

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By Andrew Bennett

How Do We Use Springs in Physics?

One of the common objects we examine in physics is a spring. One of the interesting properties of a spring is the resting length, also called the equilibrium length. When you stretch or compress the spring from the resting length, it stores energy and exerts a force.

What Is Hooke's Law?

The amount of force that a spring pushes or pulls with depends on how far you stretch or compress the spring. The more you stretch or compress the spring, the more force it exerts. In fact, there is a linear relationship between the stretch or compression length and the force exerted by the spring. This relationship is described by Hooke's Law. The law is commonly rewritten as:

spring potential energy force hooke's law equation

The coefficient that relates the stretch or compression length (x) to the force (F) on the spring is called the spring constant (or sometimes the force constant). It is written as k.

How Do We Calculate Spring Potential Energy?

Springs always try to return to their relaxed length by pushing or pulling. Spring potential energy is the energy stored in a compressed or stretched spring.

On the atomic scale, this energy is associated with pushing the spring's atoms closer together or pulling them farther apart. This is a special case of "electric potential energy," which deals with the positions of charged particles. Rather than calculating the energy of each individual proton and electron in the spring, we have a much faster formula to find the spring potential energy:

Hooke's Law Problems and Solutions

Now that you understand a bit about the physics of springs, check out this video for some spring force and potential energy problems and solutions.

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