What it does
A ball rolls along a track that you shape yourself. Four bars show its energy as it goes: kinetic energy (KE, from its speed), potential energy (PE, from its height), heat made by friction, and the total. Watch KE and PE swap places: high up the ball is slow and has lots of PE; at the bottom it is fast and has lots of KE. With no friction the total never changes and the ball always climbs back to the dashed line at its starting height. Turn friction up and the heat bar grows until the ball stops.
The Loop the loop mode sends a ball down a smooth ramp into a vertical loop. Change the starting height and the loop size to find out whether it gets round, falls off part-way (and where), or just rolls back.
It follows the school topics on energy: kinetic and potential energy and the conservation of energy (Class 9 Science, work and energy), and the work-energy theorem, conservative forces and motion in a vertical circle (Class 11 Physics, work, energy and power). Friction itself is explored on a slope in friction ramp and forces on a trolley in newton's laws sandbox; a real pendulum swaps the same energies in pendulum lab analyser.
How to use it
- Pick a Level. Class 9 shows the energy bars and the KE + PE + heat sum with your numbers. Class 11 adds the work done by friction (the work-energy theorem) and, in Loop the loop, where and why the ball leaves the track.
- Shape a track: drag the five round handles up and down. Tap anywhere on the track to put the ball there (it starts at rest).
- Press Play. Press it again to pause, and Reset to put the ball back.
- Set friction (0 is perfectly smooth) and the mass. The mass changes every energy in joules but not the way the ball moves.
- Loop the loop: set the starting height h and the loop radius r and press Play.
Worked example
Open the page: a 2 kg ball starts at rest 6 m up on the left. Its energy is all potential: 2 × 9.8 × 6 = 117.6 J. As it rolls down, the PE bar shrinks and the KE bar grows, and the total stays 117.6 J. Near the lowest point (0.5 m high) its speed is √(2 × 9.8 × 5.5) ≈ 10.4 m/s. It bounces off the right wall and comes back up to 6 m again.
In Loop the loop with r = 2 m: from h = 6 m the ball reaches the bottom at 10.84 m/s and gets round with 6.26 m/s at the top (it needs at least √(9.8 × 2) = 4.43 m/s). The lowest start that works is 5 m (2.5 × r). From 4 m it falls off the loop 3.33 m up, 131.8° of the way round.
Tips
- Energy is never lost, only changed into other forms. Friction turns it into heat (and a little sound).
- The speed at a given height does not depend on the shape of the track in between, only on how far below the start it is (without friction).
- The mass cancels from every speed: a heavy and a light ball roll in exactly the same way.
FAQ
Is the ball rolling or sliding? The model treats it as a small sliding bead, so all its kinetic energy is in moving along. A real rolling ball also stores some energy in its spin and so goes a little slower.
Why does it need 2.5 times the radius, not 2? At the top it must still be moving fast enough for gravity alone to keep it on its circle, so it needs some kinetic energy left over: half a radius’ worth of height.
Is anything stored? No. Everything runs in your browser and nothing is saved or sent.
Where the numbers come from
- Kinetic energy ½mv², potential energy mgh, conservation of mechanical energy, the work-energy theorem and the loop-the-loop condition (v² ≥ gr at the top, h ≥ 2.5r): standard school physics found in any textbook. g = 9.8 m/s² (rounded).
- The energy-based motion was checked against an independent force-based (velocity Verlet) integration along the same track, against v = √(2gΔh), and the loop results against hand-worked values. The track shape and friction values are made up.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Read more on the Blog
- Energy on a track: kinetic, potential and heat, and the loop(the full guide)
Last updated 2026-11-09.