Energy Conservation Roller Coaster

Step-by-step

1. Set the energy head h₀ (the total energy budget expressed as a height) and the cart mass.
2. Press play to release the cart — it enters the track at the leftmost point within budget, with the surplus speed that head implies.
3. Watch the energy bar chart update in real time.
4. Enable friction to see energy dissipation accumulate until the cart settles in a valley.

Key formulas

• $E_{total} = KE + PE = \frac{1}{2}mv^2 + mgh$Total mechanical energy
• $v = \sqrt{2g(h_0 - h)}$Velocity from energy conservation
• $KE = \frac{1}{2}mv^2$Kinetic energy
• $PE = mgh$Gravitational potential energy

Frequently asked questions

With the energy head h₀ set to 20 m, how fast is the cart moving where the track bottoms out at h = 0?

The budget converts entirely to KE at h = 0: v = √(2g(h₀−h)) = √(2×9.8×20) ≈ 19.8 m/s.

Can the cart reach a hill higher than its energy head h₀?

You can work it out this way: think about total energy.

How much energy is lost to friction over the whole ride?

You can work it out this way: compare total energy at start and end.