Collision of two particles, momentum and velocity

[Xilor]

Hello, I was wondering what a collision between two (elementary) particles looks like exactly. Most classical mechanics formulas seem to describe larger systems and their rules may not necessarily be the same. So I had several questions:

Can the same formulas of larger bodies about force, acceleration, velocity, momentum and such be translated down to single particles perfectly?

If two particles have different momenta, will their eventual momenta always lie closer together? Will it always completely average out, or is there room for partial momentum changes?

If two particles have identical momentum, will they always leave the collision at identical momentum? Or can properties such as spin or even the spinaxis affect the momenta in such a way that they might go apart a bit?

 

[mathman]

The only thing that is conserved is total momentum. Transfer of momentum will depend on how the collision takes place.

 

[Xilor]

Right, how exactly is that transfer decided then? Are there any formulas on that? Can a particle A with lower momentum than particle B cause B to speed up if the two collide and the circumstances are right?

 

[mathman]

Assume A has small mass and high velocity while B has high mass and low velocity, both going in the same direction, with A behind B. Let A hit B, B will speed up.

Example: your car is not moving (brake off and in neutral) - you could give it a push, transferring your momentum to the car, and it will move.

 

[Xilor]

Well both the car and the human consist of many particles. The momentum of the individual particles of the car might never exceed the momentum of the individual particles of the human. But anyway, does the energy transfer depend more on velocity than on kinetic energy then?
In that case, if two particles have the same mass, velocity, momentum and kinetic energy, could they ever affect each other in such a way that their momentum/velocity/kinetic energy changes?

 

[mathman]

Well both the car and the human consist of many particles. The momentum of the individual particles of the car might never exceed the momentum of the individual particles of the human. But anyway, does the energy transfer depend more on velocity than on kinetic energy then?
In that case, if two particles have the same mass, velocity, momentum and kinetic energy, could they ever affect each other in such a way that their momentum/velocity/kinetic energy changes?

If all the items described are the same and the positions are different, the particles will never collide.

 

[Xilor]

Right, sorry, I meant speed instead of velocity.

 

[rktpro]

If two particles have identical momentum, will they always leave the collision at identical momentum? Or can properties such as spin or even the spinaxis affect the momenta in such a way that they might go apart a bit?

They will both stop. Since one value is positive and other negative (sign convention), addition will result a zero.

 

[Xilor]

I see, thank you. Is that regardless of the angle they collide at? Or would a small difference in angle between them cause a different result?

 

[mathman]

You need to describe your scenario better. Equal and opposite direction, they bounce into each other and continue in the opposite direction, net momentum remains 0.

 

[Xilor]

Alright, take two particles with the same speed, kinetic energy, momentum and mass. Now put the two of them on a collision course in the following ways:

- They move almost parallel but have just enough of a difference in angles (1 degree or less) to be able to hit each other.

- They move perpendicular to each other and collide at 90 degrees

- They move in completely the opposite direction, causing a collision head-on at 180 degrees

For each of these situations, what can be said about the following? And how do the situations compare to each other?

- The speed/kinetic energy/momentum of the individual particles after the collision
- The direction of the particles after collision
- The total kinetic energy/speed/momentum of the particles combined after the collision

Also, does any of this change when the spins of the particles involved are defined or change?

 

[cryora]

I'm wondering: what force causes the momentum change of elementary particles?

From what I understand, there are four fundamental forces: Strong Atomic Force, Weak Atomic Force, Electromagnetic Force, and Gravity; and in everyday situations, it is the Electromagnetic Force from the electrons surrounding the atoms that repel objects from each other. In the subatomic world, you might not have particles of the same charge that repel each other, so for all I know, they could simply go through each other and not collide.

 

[mathman]

For each of these situations, what can be said about the following? And how do the situations compare to each other?

- The speed/kinetic energy/momentum of the individual particles after the collision
- The direction of the particles after collision
- The total kinetic energy/speed/momentum of the particles combined after the collision

In general the answer will depend on whether or not the collision is elastic. If it is elastic the total K.E. will be preserved. Inelastic, some of the energy gets lost to some internal process. In all cases momentum is conserved. The direction after collision has a degree of freedom, depending on exactly where the points of impact are on the particles.

On spin question - I have no comment.