What is the energy stored in a spring when it is stretched?

The energy stored in a spring when it is stretched is fundamentally a result of the work done on the spring to deform it from its equilibrium position. When a spring is stretched or compressed, it stores potential energy, which allows it to do work when it returns to its natural length.

The concept of potential energy in springs is governed by Hooke's Law, which states that the force required to stretch or compress a spring is proportional to the displacement from its rest position. The potential energy stored in a spring can be expressed mathematically as ( PE = \frac{1}{2} k x^2 ), where ( k ) is the spring constant and ( x ) is the amount of deformation.

While "the work done on the spring" captures part of the idea—since work is indeed done to stretch the spring—it's more accurate to refer to the energy stored as the potential energy of the spring. This potential energy quantifies the amount of energy stored within the spring due to its deformation. The term "the energy stored in a spring" is a direct description of this potential energy as a result of the action of stretching or compressing it.