← Mechanical
Conservation Laws

Conservation of Energy

A ball on a frictionless track trades height for speed — but its total energy never changes.
Potential energy (height) Kinetic energy (speed) Lost to heat (friction)
Potential PE
0J
Kinetic KE
0J
Total energy
0J
Speed
0m/s
E = KE + PE = ½·m·v² + m·g·h   =   constant (no friction)
i About this experiment — click to learn the physics

What you're looking at

A ball is released from rest on a curved track and slides under gravity. As it drops into a valley it speeds up; as it climbs a hill it slows down. Energy is constantly converting between two forms, but — with no friction — the total never changes. The bar at the top splits the energy into its parts so you can watch the trade happen.

Two forms of mechanical energy

  • Gravitational potential energy PE = m·g·h — stored by virtue of height. Highest at the tops of hills.
  • Kinetic energy KE = ½·m·v² — the energy of motion. Highest at the bottoms of valleys, where the ball moves fastest.

The conservation principle

Energy is never created or destroyed, only transformed. For a frictionless system the mechanical energy is conserved:

½·m·v² + m·g·h = E = constant conservation of mechanical energy

This is why the ball climbs to exactly its starting height on the other side and no higher — all the kinetic energy it gains falling is precisely enough to lift it back up. The dashed line marks the highest level the ball can reach.

Where friction fits in

Friction doesn't destroy energy either — it converts mechanical energy into heat. Turn up the friction and watch the red slice of the bar grow as the ball's swings get smaller and smaller, until it finally settles at the bottom of a valley. The total of motion, height, and heat is still conserved — it's just no longer all available as motion.

Things to try

With friction at zero, release from the top and confirm the ball returns to the dashed line every time. Then add a little friction and watch the reachable height ratchet downward, lap by lap, as energy turns to heat.