Stored vs Moving
Potential and kinetic — energy's two bank accounts
What this lesson covers
Why it matters
A drawn bow hasn't moved an inch, yet it's loaded with energy. An arrow mid-flight has no height, no stretch — just speed. Two accounts, one currency.
The idea in plain words
The two formulas that run the chapter. Tap the terms.
U = mgh · K = ½mv²
A 0.5 kg ball is thrown up at 10 m/s. How high does it rise? (g = 10)
h = 5 m
- joule: U — gravitational potential energy — stored by position
- joule: K — kinetic energy — carried by motion
- metre: h — height above the reference level (you choose the zero!)
- (m/s)²: v² — speed SQUARED — the term students forget to square
- K at launch = ½ × 0.5 × 100 = 25 J
- All of it becomes U: mgh = 25 → 0.5 × 10 × h = 25
Predict first
Double a cart's SPEED. Its kinetic energy becomes…
K = ½mv². The square is why a car at 100 km/h needs FOUR times the braking distance of one at 50.
- four times — K depends on v² — correct
- double
- unchanged — energy depends on mass only
What you do
Tune the lifted block and the rolling ball until stored energy exactly equals moving energy.
Check yourself
Which has kinetic energy?
Wind = moving air = kinetic. Dam water and stretched springs hold POTENTIAL energy, waiting.
K and momentum: a body's kinetic energy can also be written…
Substitute p = mv into ½mv²: K = p²/2m — a favourite one-mark twist.
A coconut on a tall palm has potential energy because of…
Every joule of mgh was paid for by growth-work against gravity — repaid in full on the way down.
- Wind — correct
- Water stored in a dam
- A stretched spring
- K = p²/2m — correct
- K = p·v²
- K = mgh
- work done against gravity to get it there — correct
- its temperature
- air pressure around it