Energy conservation
Energiprincipen
PhysicsRare
Discovered 1847 · Mayer and Joule
SPARKON04 / 10
Energy conservation
The ideaEnergy never appears or disappears; it only changes form, so the total stays the same.
m·g·h = ½·m·v² (ideal drop)
Lets you predictSpeed at the bottom of a drop from rest, if friction is small.
Tests usually ask
  • Speed of a falling object
  • Where did the energy go?
Scan for the full explanation and a practice question.
SPARKON · 04 / 10
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Physics ◆ Rare: a famous discovery

Energy conservation

Swedish: Energiprincipen · Discovered: Mayer, Joule and Helmholtz, 1840s

Energy never appears or disappears; it only changes form, so the total stays the same.

m·g·h = ½·m·v² (ideal drop)

Why it works

Height energy turns into speed energy on the way down, and back again on the way up. Friction turns some of it into heat, but the total is still the same.

For an object that starts from rest, with air resistance and friction small enough to ignore, all the height energy becomes speed energy. The mass cancels out: v = √(2·g·h). A heavy ball and a light ball dropped from the same height reach the same speed.

What it lets you predict

Speed at the bottom of a drop from rest, if friction is small.

How tests ask about it

  • Speed of a falling object
  • Where did the energy go?

Try it

A ball is dropped from rest from 5 m. Ignoring air resistance, how fast is it going when it hits the ground? (g = 9.82 m/s²)

Show the answer

v = √(2 · 9.82 · 5) = √98.2 ≈ 9.9 m/s.

Connects to

Newton's second lawOhm's lawPhotosynthesis

Wins these Lab Duel challenges

  • Stop a car doing 20 m/s within 30 m on a level road. see challenge