Elastic Potential Energy Formula

Elastic potential energy is the stored energy of a compressible or stretchable object like a spring or rubber band or molecule. Elastic potential energy is equal to the force times the distance of movement.

Elastic potential energy = force x distance of displacement.

W = Fs

W = elastic potential energy, in Joules

F = force, in Newtons

s = displacement, m

Because the force is = spring constant x displacement, then the Elastic potential energy = spring constant x displacement squared.

F = 1/2 ks

k = spring constant, Newtons/m

So W = (1/2 ks)s

W = 1/2ks² = PE

Elastic Potential Energy Formula Questions:

1) You have an elastic spring that has a spring constant of 1.5 x 10^-2 Newtons per meter, and the spring is compressed by 15.0 cm. What is the PE of the spring?

The spring constant k = 1.5 x 10^-2 Newtons/m and the Δs = 15.0 cm = 0.15 m.

PE = 1/2 ks²

PE = [1/2 x (1.5 x 10^-2) Newtons/m](0.15 m)²

PE = 1.69 x10^-4 Newtons-m = J

2) You attach a Hooke's law spring to a board, and use 3 J to stretch the spring 99 cm. What is the value of the spring constant?

We know that W = 3 J and s = 99 cm = 0.99 m. From this determine k, the spring constant.

W = [1/2 k] s²

1/2 k = W/s²

k = W/(1/2 s²)

k = (3J / [0.5 x 0.99 m²])

k = 3J/ 0.49 m²

k = 3 N/m / 0.49 m²

k = 6.122 N/m