Energy on a track: kinetic, potential and heat, and the loop

Guide · Updated 2026-11-10

How kinetic and potential energy swap on a rolling ball, why friction makes heat, and how high a ball must start to get round a loop, with worked numbers.

Open the Energy skate track Free, in your browser, nothing uploaded.

When a ball rolls down a slope and up the other side, its energy changes form, but the total does not change. The energy skate track tool lets you shape a track with your finger, let a ball roll and watch that exchange. It then adds friction, so you can see energy turn into heat, and a loop, so you can find the lowest start that gets the ball round. For the forces behind the motion, see newton's laws sandbox; for friction on a slope, friction ramp; and for a swinging version of the same exchange, pendulum lab analyser.

What it is

• Kinetic energy (KE) is the energy of motion: KE = ½ × m × v², where m is mass in kg and v is speed in m/s.
• Potential energy (PE) is the energy of height: PE = m × g × h, where h is height in m and g = 9.8 m/s².
• Heat is energy that friction turns the motion into.

With no friction, KE + PE stays constant. A ball released from rest at height h₀ has only PE, and it returns to the same height on the other side. Its speed at any lower height h is set by the drop alone:

v = √(2g(h₀ − h))

So the shape of the track in between does not matter, and the mass cancels: a heavy ball and a light ball roll in exactly the same way. The mass only changes the energy in joules.

For a vertical loop of radius r, the ball must stay on the track at the top. Gravity alone has to be enough to keep it on its circle, which means v² ≥ g × r at the top. Using the energy at the top, v² = 2g(h − 2r), so the start height must satisfy h ≥ 2.5 × r.

How to use it

1. Pick a Level. Class 9 shows the energy bars and the sum KE + PE + heat. Class 11 adds the work done by friction and, in Loop the loop, where and why a ball leaves the track.
2. Shape a track by dragging the five round handles up and down. Tap the track to put the ball there. It starts at rest.
3. Press Play. Press it again to pause, and Reset to put the ball back.
4. Set friction (0 is perfectly smooth) and the mass. Friction makes the heat bar grow.
5. For Loop the loop, set the starting height h and the loop radius r, then press Play. The ball either gets round, falls off part-way, or rolls back.

A worked example

Start with a 2 kg ball at rest 8 m up on the left of the track.

• At the start: PE = 2 × 9.8 × 8 = 156.8 J, KE = 0, total 156.8 J.
• At 1 m high: the drop is 7 m, so v = √(2 × 9.8 × 7) = √137.2 ≈ 11.71 m/s. KE = ½ × 2 × 137.2 = 137.2 J and PE = 2 × 9.8 × 1 = 19.6 J. The two add to 156.8 J.
• At the bottom: v = √(2 × 9.8 × 8) ≈ 12.52 m/s, with all 156.8 J as KE. The speeds are the same for a 1 kg or a 10 kg ball.

Now the loop with r = 1.5 m. The ball needs h ≥ 2.5 × 1.5 = 3.75 m, so a start at 8 m is enough. The top of the loop is 2r = 3 m high. There, v² = 2 × 9.8 × (8 − 3) = 98, so v ≈ 9.90 m/s, well above the minimum of √(9.8 × 1.5) ≈ 3.83 m/s. At the top, With the same 2 kg ball, KE = ½ × 2 × 98 = 98 J and PE = 2 × 9.8 × 3 = 58.8 J, which again add to 156.8 J. If you lower the start to 3 m, it is below 3.75 m and the ball does not get round.

Where it is used

• Roller coasters and skate parks. Designers choose the height of each hill to give enough speed for the next loop or rise.
• Brakes. A car’s brakes turn its kinetic energy into heat through friction.
• Pendulums, springs and hydro power. Each swaps one form of energy for another, with some losses.
• Any circular path. The same idea tells you the least speed a vehicle or object needs at the top of a loop, before friction and spin are added.

Common mistakes

1. Saying energy disappears when the ball stops. The ball’s motion energy has become heat in the track and ball, so the total, counting heat, is the same as at the start.
2. Using different reference heights. Measure every height from the same level, usually the bottom of the track, so the PE values can be compared.
3. Expecting a heavier ball to go faster. Without friction, speed does not depend on mass. Mass changes the joules, not the motion.
4. Starting the ball at the height of the top of the loop (2r). The ball would arrive at the top with no speed at all (v² = 2g(h − 2r) = 0), so it cannot follow the circle. Start at 2.5r or higher.
5. Mixing up units. Heights in metres, g in m/s² and energy in joules (kg·m²/s²). Keep them consistent in every line of your working.

Questions people ask

Why does the ball not return to its start height with friction on? Friction takes some of its energy as heat, so the ball has less energy to climb back with and stops short.

Does a heavier ball need a lower start for the loop? No. In h ≥ 2.5r the mass has cancelled, so a 1 kg and a 10 kg ball need the same height. The heavier one just carries more joules.