[Physics] How to work be done during collisions?


Consider a collision between two material points, with no external forces acting on the system.

Linear and angular momentum of the system are always conserved, while the kinetic energy of the system is conserved only if internal forces acting in the collision are conservative. This last point is not clear to me.

During the time interval $\tau$ of the collision we assume that the position of the two particles does not change, i.e. $\vec{r_1}=\vec{r_2}=\vec{r}$. But the velocity of each particle (precisely its momentum) does change during the collision, and, from WE theorem, that means that a work is done on each particle, equal to the change in kinetic energy of the particle itself.

Nevertheless work is force times a displacement, and we said that the position of particle is constant during the collision. So where is the displacement?

Supposing that I didn't made mistake in this reasoning, if there is no displacement there is no work, so how can the velocity of particles change actually?

And then if there is no work how can kinetic energy of each particle (and of the system) not be conserved?

Edit: with "material point" I mean point particle

Best Answer

The collision doesn't happen at a single point in space - rather the colliding objects exert a forces on each other over a distance as they approach and the recede. Consider a tennis ball hitting a racket - the ball and the strings of the racket deform and we get an increasing elastic restoring forces until the two objects at at their closest approach. Then, the forces get smaller again as they objects return to their original shape and drop to zero once they aren't touching.

You could consider a collision between electrons in the same way. There is an increasing electric force between them as they go into the collision and decreasing as the come out of the collision. In the case of the electrons though, there isn't a clear cut beginning and ending since the forces between them aren't zero at any distance.

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