Acceleration in conservation of momentum problem

[dimitri151]

If a moving point mass collides with a point mass at rest then you can find the resulting velocities by conservation of momentum and conservation of kinetic energy. Are the accelerations in this case said to be infinite in the sense that the changes to the velocities happen instantaneously?

 

[dextercioby]

Nothing happens instantaneously. I think the 'time of collision' is assumed small, but non=zero in any theoretical treatment.

 

[Matterwave]

The first object will impart a certain impulse to the second object. The time of collision will be very short, but will not be 0. The forces will be large, but short forces between the two objects.

See: http://en.wikipedia.org/wiki/Impulse_(physics)

 

[CWatters]

The time or distance over which the collision occurs typically depends on the physical properties of the objects. The shorter the time or distance over which the collision occurs the higher the forces and accelerations involved.

It's not always true that force * time = constant but that's a useful concept when solving some types of problem. You may not always know the duration of the impact.

 

[dimitri151]

Is it like this: The conservation of momentum/kinetic energy tells you what the masses are doing before and after the collision, but not during, except perhaps that if a velocity is greater or less after collision then velocity is rising or decreasing during the collision in a continuous way.

 

[Khashishi]

Sort of. Conservation of momentum always holds, even during the collision. The reason you can't use conservation of kinetic energy during the collision is because there is some potential energy between the two colliding bodies due to forces between them (and due to some deformation of the objects, if they are not point particles), and it is the total energy that is conserved, not the kinetic energy. Before and after the collision, the bodies are far apart, so the potential energy between them is small enough to neglect in the calculation.

Collisions between point particles always occur over some range.

 

[Orodruin]

For the sake of the OP, I would like to elaborate a bit on this last point.

Two point particles can never collide in the sense that two extended hard spheres can by coming into contact with each other, the classical cross section for this is zero. Instead, a collision of point particles must be mediated by a ranged interaction such as electromagnetism or gravity. In those cases, the EM/gravity forces are acting on the particles for non-zero duration and the involved forces are not infinite.