Elastic Potential Energy

Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs etc. The amount of elastic potential energy stored is related to the amount of stretch of the device - the more stretch, the more stored energy.

A force is required to compress a spring; the more compression there is, the more force which is required to compress it further. For certain springs, the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k). Springs are said to follow Hooke's Law. The equilibrium position (x=0) is the position that the spring naturally assumes when there is no force applied to it.

Examples Example 1: If the force to stretch a spring is given as F = (100 N/m)x, then what is the potential energy of the spring if it is stretched 2 meters from rest? Example 2: It takes a force of 20 Newtons to hold a spring stretched to a distance of 40 cm. What is the elastic potential energy of the spring at this position?

Solutions 1. Solution: Here k = 100N/m and x = 2 m. Therefore: E e = (1/2)kx 2 = (1/2)(100N/m)(2 m) 2 = 200 Joules 2. Solution: We know that F = -20 N when x = 40 cm = 0.40 m. Since F = -kx, then k = -F/x = -(-20 N)/(0.40 m) = 50 N/m. E E = (1/2)kx 2 = (1/2)(50 N/m)(0.40 m) 2 = 4 Joules.

Homework: P258#35-37 P261#38-40