What is the velocity at the bottom if released from 20m?

You can work it out this way: use v = √(2gh).

Can the cart reach a hill higher than its starting point?

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

How much energy is lost to friction over one full loop?

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

Pro 🔒~18 min

Energy Conservation Roller Coaster

Ride the energy transformation

How it works

The law of conservation of energy states that energy cannot be created or destroyed, only transformed. In a frictionless roller coaster, the total mechanical energy (KE + PE) remains constant. As the cart descends, PE converts to KE; as it climbs, KE converts back to PE.

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Step-by-step

Set the initial height and mass.
Press play to release the cart.
Watch the energy bar chart update in real time.
Enable friction to see energy dissipation.

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

What is the velocity at the bottom if released from 20m?: You can work it out this way: use v = √(2gh).
Can the cart reach a hill higher than its starting point?: You can work it out this way: think about total energy.
How much energy is lost to friction over one full loop?: You can work it out this way: compare total energy at start and end.