Energy Conservation
Height turns into speed and speed into height. How fast does something hit the ground, how high does a throw go, and how fast is a roller coaster at the next hill — with or without energy lost to friction.
What is Energy Conservation?
Energy cannot appear or disappear: it only changes form. A falling ball swaps potential energy (height) for kinetic energy (speed); a ball thrown upward does the reverse. Without friction, the total of the two stays exactly the same.
In real life some energy turns into heat through friction and air resistance. That is why a roller coaster can never climb back to its starting height, and why every hill after the first one is lower.
Energy Before and After
totalHeight and Speed
Earth, no friction| Fall height | Landing speed | in km/h |
|---|---|---|
| 1 m (a table) | 4.43 m/s | 16 |
| 3 m (one floor) | 7.67 m/s | 28 |
| 10 m (a diving board) | 14.0 m/s | 50 |
| 39 m | 27.7 m/s | 100 |
Worked Techniques
From rest and without friction, the speed after a drop depends only on the height — not on the mass, and not on the shape of the slope.
At the top all the kinetic energy has become potential energy. Twice the throwing speed gives four times the height.
The energy lost to friction is no longer available as speed. Now the mass matters: the same loss slows a light object more.
Sources & Verification
- D. Halliday, R. Resnick & J. Walker, Fundamentals of Physics, 10th ed., Wiley, 2014 — Ch. 8 (Potential Energy and Conservation of Energy).