01
What you will learn
- Elastic energy grows with the square of extension: ½kx².
- Energy moves between elastic, kinetic, gravitational, and thermal stores.
- More launch energy does not always produce a better result.
← EnergyFree game · no account needed
Energy · reward round
Energy Budget
Drag the pod back against the spring, let go, and stop dead on the beacon.
Score0stage best 0
- Motion 30 J
- Height 0 J
- Heat 0 J
Your launch · ½kx²29.8 J
Beacon needs · mgd(sin θ + μ cos θ)36.3 J
Nudge. Smooth ramp. Every joule you store turns into height.
How the physics works
The spring stores Us = ½kx². Sliding a distance d up the ramp spends mgd·sin θ raising the pod and μmgd·cos θ heating the surface, so the pod halts when ½kx² = mgd(sin θ + μ cos θ).
Solving for the stop distance gives d = kx² / (2mg(sin θ + μ cos θ)). The coloured bar is that equation drawn live: the total never changes during the climb, it just moves out of motion and into height and heat.
The dashed ghost on the ramp is that same equation solved before you let go — drag the pod and watch the predicted stop slide along the slope. It turns teal when your ½kx² sits inside the beacon window, and red when there is enough left over to fly off the end.
Game 04 · Energy learning guide
Turn the playthrough into a physics lesson.
Learning objectiveChoose a spring extension that converts elastic potential energy into motion and stops a pod inside the target zone.
02
How to play
- Drag the pod or use the pull slider to set the spring extension.
- Predict where the pod will stop, then launch it up the ramp.
- Adjust the pull until the pod comes to rest on the beacon.
03
Quick classroom check
If the spring extension doubles, by what factor does its stored elastic energy change?
Suitable forSecondary physics · conservation of energy and elastic stores
Continue this topic
Move from play to explanation and exam-style practice.
Teachers can share the page link with a class. The game is free and does not require an account.