Final answer:
The thickness of a spring is related to the elastic potential energy possessed by the spring according to Hooke's law. The elastic potential energy of a spring is directly proportional to the square of its displacement from its undeformed position.
Step-by-step explanation:
The relationship between the thickness of a spring and the elastic potential energy possessed by the spring is described by Hooke's law. Hooke's law states that the force applied to a spring is directly proportional to the displacement of the spring. This means that the elastic potential energy of a spring is directly proportional to the square of its displacement from its undeformed position. Mathematically, the elastic potential energy (PEs) of a spring can be calculated using the formula: PEs = 1/2kx2, where k is the spring constant and x is the displacement from the spring's undeformed position.