How is potential energy stored in a spring?

Potential energy is stored in a spring through the work done in stretching or compressing it from its equilibrium position.

When a spring is stretched or compressed, it stores potential energy. This is a direct application of Hooke's Law, which states that the force needed to extend or compress a spring by some distance is proportional to that distance. In other words, the more you stretch or compress a spring, the more force you need to apply. This force you apply does work on the spring, and this work is stored as potential energy.

The potential energy (PE) stored in a spring is given by the equation PE = 1/2 kx^2, where k is the spring constant (a measure of the spring's stiffness) and x is the displacement from the spring's equilibrium position. This equation tells us that the potential energy stored in a spring is directly proportional to the square of the displacement. This means that if you double the displacement, the potential energy increases by a factor of four.

When the spring is released, this stored potential energy is converted into kinetic energy as the spring returns to its equilibrium position. This is an example of the conservation of energy, a fundamental principle in physics which states that energy cannot be created or destroyed, only transferred or converted from one form to another.

In summary, potential energy is stored in a spring through the work done in stretching or compressing it. The amount of energy stored is proportional to the square of the displacement from the equilibrium position, as given by the equation PE = 1/2 kx^2. This stored energy can then be converted into other forms of energy, such as kinetic energy, when the spring is released.