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
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