What is Elastic Potential Energy?

Elastic Potential Energy

Any object than can be deformed (have its shaped changed) and then return to its original shape can store elastic potential energy.
• We’re still talking about potential energy, since it is stored energy until the object is allowed to
bounce back.
• “Elastic” does not refer to just things like elastic bands…other materials that would be referred
to as elastic would be
• pole vaulter’s pole
• springs

You learned in Physics that Hooke’s Law is…
F = kx
F = force (N)
k = spring constant for that object (N/m)
x = amount of expansion or compression (m)
We can use this formula to figure out a formula for the energy stored in the spring.
• Remember that W = F d

• We might be tempted to just shove the formula for Hooke’s Law into this formula to get
W = kxd = kx2
, but this is wrong!
• You have to take into account that the force is not constant as the object returns to its original
shape… it’s at a maximum when it is deformed the most, and is zero when the object is not
deformed.
• Let’s graph Force vs Distance of Expansion for a spring that was stretched and we are now
letting go of it…

But this is really just a Force vs Displacement Graph like the ones we just looked at a couple of
sections back! To figure out the energy of the spring we can just figure out the work it does by looking at the area under the graph.

Area = ½ bh
= ½ F x
= ½ (kx) x
Area = ½ kx2 = W
So the work done by the spring (and then energy it stored) can be calculated using…
Ee = ½ kx2
Ee = eleastic potential energy (J)
k = spring constant (N/m)
x = amount of expansion or compression [deformation] (m)

Example 1: Determine how much energy a spring with a spring constant of 15 N/m stores if it is
stretched by 1.6m.
Ee = ½ kx2
= ½ (15N/m) (1.6 m)
2
Ee = 19 J