Energy Conservation

A bead- or cart-style model on a track: gravitational potential energy converts to kinetic energy (plus any modeled dissipation). Bars or readouts show how KE, PE, and total mechanical energy evolve.

Who it's for: Intro mechanics; connecting energy bar charts to motion along a path.

Key terms

  • kinetic energy
  • potential energy
  • mechanical energy
  • conservation
  • work–energy

Live graphs

How it works

On a frictionless track, gravity does work that converts potential energy mgh into kinetic energy ½mv². With no non-conservative forces, the total E = KE + PE is constant in time. Small numerical drift can appear from discrete time steps.

Key equations

E = ½mv² + mgh(x)
Along the curve: aₜ = −g sin φ,   φ = slope angle

Frequently asked questions

When is total energy conserved?
In the frictionless idealization, only conservative gravity does work, so total mechanical energy stays constant while KE and PE trade off.