# 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 = 1/2ks^{2} = 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 ks^{2}

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] s^{2}

1/2 k = W/s^{2}

k = W/(1/2 s^{2})

k = (3J / [0.5 x 0.99 m^{2}])

k = 3J/ 0.49 m^{2}

k = 3 N/m / 0.49 m^{2}

k = 6.122 N/m

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