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Colliding bullets

Question: Here's a hypothetical question: If you have two rifles 10 metres apart that are firing exactly the same type of bullets at the exactly the same muzzle velocity, what happens when they meet? Assume that they both are going directly towards each other at exactly the same speed.

Answer:

I am afraid that there is no exact answer to this. It all depends on what happens to the bullets when they collide.
The two important laws that govern such (in fact any) collision are:
Conservation of energy the energy before impact must be the same as the energy after impact.
Conservation of momentum the momentum after impact must be the same as the momentum before impact. In this case since you have two bullets of the same mass moving at the same speed but in opposite directions the total momentum of the system is zero. Momentum is a vector quantity and since the directions of motion are opposite one of the bullets has negative momentum compared with other.

Here is a set of possibilities.
1. A completely elastic collision
All the kinetic energy is retained. The total must remain zero and so they simply bounce off each other and return back along their original paths at the same speed!

2. A completely inelastic collision.
All the kinetic energy is destroyed and is converted into sound, heat, light and the deformation of the bullets as they collide and stick together. In this case the bullets have no speed after collision and simply come to rest.

3. Something in between.
Some of the kinetic energy is lost. There is some deformation and sound etc. and the bullets bounce back along their original paths with reduced speed.

4. The bullets break up on impact.
Some kinetic energy will be lost. The total momentum of the fragments must be zero after collision. In other words some move one way and some move the other. There is no way of knowing exactly how they may break up and so we cannot really predict the speed of any fragment.

Colliding bullets

1. Completely elastic no kinetic energy lost



Momentum is conserved.

2. Completely inelastic all kinetic energy converted to other forms


Momentum is conserved.

3. Some kinetic energy lost



Some of the kinetic energy is lost. Final velocities are equal and opposite but reduced. Momentum is conserved.

4. Bullets disintegrate



Bullets disintegrate. The sum of the momenta of the fragments is equal to the sum of the momenta of the two bullets before collision.
 

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© Keith Gibbs 2020