A ball dropped from 1.8 m onto a floor bounces back up to 1.15 m…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A ball dropped from onto a floor bounces back up to . Taking , find
- its speed just before it hits the floor;
- its speed just after it leaves the floor;
- the percentage of its mechanical energy lost in the bounce.
Need a reminder? The key ideaShow
When only conservative forces (gravity, springs) do work, mechanical energy is conserved: . Forces that do no work, like a smooth surface's push or a string at right angles to the motion, do not spoil it.
The coefficient of restitution is . A ball bouncing on a floor keeps the fraction of its speed and of its height each bounce, so .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Energy is conserved during the fall and the rise; only the bounce loses energy.
Step 1. (a) .
Step 2. (b) .
Step 3. (c) Lost fraction , that is .
Answer: (a) . (b) . (c) .
Check. The coefficient of restitution is , and of the energy is kept. Same.
Watch out. The speed falls to , but the energy falls to : energy goes as the speed squared.
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