A roller coaster climbs slowly to the top of the first hill, then races down. Where does its speed come from? From the height. Potential energy turns into kinetic energy on the way down, and back again on the way up.
Key idea
Energy is never created or destroyed; it only changes form. Without friction, $\text{KE} + \text{PE}$ stays the same. With friction, some energy becomes thermal energy (and sound), but the total, including the thermal part, is still the same.
Why it works
Falling, an object loses height and gains speed, and the two changes match joule for joule: every joule of PE that disappears shows up as a joule of KE. A real swing slows down because the air and the chains turn a little energy into heat and sound on every swing. That energy is not lost; it is spread into the air as warmth.
Worked example: Dropped from a height
A 2 kg ball is dropped from 5 m. Ignoring air resistance, find its kinetic energy just before it lands.
- At the top: $\text{PE} = 2 \times 9.8 \times 5 = 98$ J and $\text{KE} = 0$.
- At the bottom: $\text{PE} = 0$, so all 98 J is kinetic.
Answer: 98 J
Worked example: Partway down
The same ball is 2 m above the ground. Find its PE and KE there.
- PE: $2 \times 9.8 \times 2 = 39.2$ J.
- Total is still 98 J, so $\text{KE} = 98 - 39.2 = 58.8$ J.
Answer: PE 39.2 J, KE 58.8 J
Common mistake
Thinking energy is lost when a swing slows down. It is turned into thermal energy and sound by air resistance and rubbing at the pivot. Check: total energy at the start = KE + PE + thermal energy later.
Watch fifteen pendulums trade energy in the Science Lab: Pendulums and Resonance.