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In a ballistic pendulum, a bullet stops inside a hanging block, which then swings up…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a ballistic pendulum, a bullet stops inside a hanging block, which then swings up.
- Why is kinetic energy lost in the collision of the bullet with the block?
- Why can we not use conservation of energy for the whole process, from just before the hit to the highest point of the swing?
Need a reminder? The key ideaShow
In a collision with no outside force, momentum is conserved: . In an elastic collision kinetic energy is conserved too. Head-on and elastic, with the target at rest: , .
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 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. Split the motion into the hit and the swing.
Step 1. (a) The hit. The bullet tears and heats the wood, and the two end up moving together: a perfectly inelastic collision. Most of the bullet's kinetic energy becomes heat, sound and broken wood.
Step 2. (b) The whole process. Mechanical energy is not conserved during the hit, so an energy equation from the start to the top would be wrong. Only momentum is conserved in the hit.
Step 3. The swing. After the hit, only gravity does work (the strings are at right angles to the motion), so energy is conserved from just after the hit to the top.
Answer: Use momentum for the hit and energy for the swing.
Watch out. Using energy for the hit gives a bullet speed far too small: often only a few percent of the bullet's energy survives the hit.
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