IB Physics SLTopic A.3 — Work, Energy & PowerPaper 1 & 2Elastic PE~6 min read
Elastic PE
Stretch a spring or a rubber band and you’re storing energy in it — elastic potential energy. Let go, and that stored energy is released, usually converting rapidly into kinetic energy.
📘 What you need to know
Elastic PE is the energy stored in a material when it’s stretched or compressed
For a material obeying Hooke’s law, it’s calculated using EH = ½k(Δx)²
It can also be written as EH = ½FΔx, using the restoring force F = kΔx
A material’s elastic PE is stored whether it’s stretched or compressed — the sign of Δx doesn’t matter, since it’s squared
When a strained material suddenly releases, its elastic PE converts into kinetic energy — sometimes dangerously fast
What Is Elastic PE?
Elastic potential energy is the energy stored within a material — like a spring, a rubber band, or a strained wire — when it’s stretched or compressed away from its natural length. As long as the material obeys Hooke’s law, this stored energy can be calculated directly from how far it’s been deformed.
Elastic potential energy equationEH = ½k(Δx)²
Where EH is elastic potential energy in joules, k is the spring constant in N m⁻¹, and Δx is the extension or compression in metres.
A spring stores elastic potential energy whether it is stretched or compressed away from its natural length
Using the Restoring Force Instead
Alternative formEH = ½FΔx
Here F is the restoring force — the same force described by Hooke’s law, F = kΔx. This version is handy when you’re given the force directly rather than the spring constant.
Why Elastic PE Can Be Dangerous
When a strained material — a stretched wire, a loaded cable, a drawn bowstring — suddenly releases, its elastic potential energy is converted almost entirely into kinetic energy. Equating the two shows a useful relationship:
EH = EK → ½k(Δx)² = ½mv² → v ∝ Δx
The greater the extension before release, the faster the resulting speed — which is exactly why a wire under a large strain snapping suddenly is genuinely hazardous.
Quick recap: EH = ½k(Δx)² — squaring Δx means it doesn’t matter whether the material is stretched or compressed, and doubling the extension quadruples the stored energy.
WE 1
A trampoline spring, modelled as obeying Hooke’s law, has a spring constant of 250 N m⁻¹. Calculate the elastic potential energy stored when it is stretched by 0.15 m.
A bungee cord, assumed to obey Hooke’s law, is stretched by 3.4 m and exerts a restoring force of 221 N at that extension. Calculate the elastic potential energy stored in the cord at maximum stretch.
Step 1 — Write the alternative form of the equation
E_H = ½FΔx
Step 2 — SubstituteE_H = ½ × 221 × 3.4≈ 380 J (2 s.f.)
💡 Top tips
Because Δx is squared, it makes no difference whether the material is stretched or compressed — use its size, not its direction
Use ½k(Δx)² when you know the spring constant, and ½FΔx when you’re given the restoring force directly
Doubling the extension of a spring quadruples the elastic PE stored, just like with kinetic energy and speed
Remember that EH = EK only holds if all the elastic PE converts to kinetic energy, with nothing dissipated
⚠ Common mistakes
Forgetting to square Δx in the ½k(Δx)² equation
Assuming the equation applies beyond the point where a material stops obeying Hooke’s law — it only holds within the elastic limit
Mixing up the spring constant k with the restoring force F — they’re related, but not interchangeable
Treating elastic PE as automatically converting entirely into kinetic energy, when in reality some is often dissipated
Up next: Conservation of Mechanical Energy — where kinetic, gravitational and elastic PE all come together in one system.
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