Nothing is Lost

Why it matters

Museum pendulums swing for hours. Release one from your nose and it will swing back to a millimetre of your face — and never hit you. That millimetre is the whole law.

The idea in plain words

The law and its favourite exam example. Tap the terms.

K + U = constant

Verify for free fall: 1 kg dropped from 20 m (g = 10). Check K + U at 20 m, 10 m, 0 m.

K + U = 200 J at every point ✓

• joule: K + U — total mechanical energy — the sum never changes in free fall or a swing
• turning points: ends of swing — v = 0: all PE, no KE
• the mean position: bottom — h = 0: all KE, no PE — maximum speed
• the fine print: friction — in real life a little leaks to heat each swing — energy DEGRADES, never vanishes
• Top: U = 200 J, K = 0 → 200 J
• Halfway: U = 100 J, v² = 2×10×10 → K = 100 J → 200 J
• Ground: U = 0, K = 200 J

Predict first

A pendulum bob at the TOP of its swing has 12 J of PE (taking the bottom as zero). At the bottom, its KE is…

With air resistance ignored, PE trades for KE joule-for-joule: K + U stays constant at every point of the swing.

• 12 J — every joule of PE became KE — correct
• less than 12 J always, by a lot
• more than 12 J — it sped up

What you do

Drag the bob along its arc and watch the three bars: PE falls exactly as KE rises. Visit both ends and the bottom.

Check yourself

Where is the pendulum bob's speed greatest?

All the PE has become KE at the bottom — maximum speed exactly where height is zero.

A real pendulum eventually stops because its energy…

The universe's account still balances — the energy is just in a useless, spread-out form now (degradation).

A ball dropped from 5 m bounces back to 3.2 m. The missing energy went to…

The thud you hear and the warmth in the rubber are the missing joules, accounted for.

• At the lowest point of the swing — correct
• At the extreme ends
• Same everywhere
• leaks to heat via air resistance and friction — total energy is still conserved — correct
• is destroyed slowly
• returns to the hand that released it
• heat and sound in the bounce — correct
• nowhere — it's gone
• the air on the way up