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A 10g bullet traveling at 1000 m/s collides with a 100g wood block initially at rest. The system is co-linear, and the impact is completely plastic. Find the final velocity of the bullet and wood. Please solve using BOTH conservation of energy AND conservation of momentum. See if you get the same velocities. I can’t.
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You can’t solve this using conservation of energy, because MECHANICAL energy (kinetic and potential) are not conserved. Some energy is converted into heat, sound, etc, during the collision.
The only way you could use conservation of energy would be
1. Find the kinetic energy before the collision.
2. Fine the velocities after collision by conservation of MOMENTUM.
3. Find the kinetic energy after the collision.
4. Find the amount of energy converted into heat (i.e. Answer 1 – Answer 3).
5. If you knew the thermal capacity of the wood, etc, you could then estimate the temperature rise during the collision (energy gain = M. Cp. delta T).
If the collision was perfectly elastic, then no mechanical energy is lost (that’s what “perfectly elastic” means). There are two unknown quantities after the collision, the velocity of the block and the velocity of the bullet. Conservation of energy and conservation of momentum give you two simultaneous equations that you can solve for the two velocities.