How is work done by a collision?

>>8506632
instantaneousness doesnt exist

>>8506638
I know. Planck units and all that. That's why I said *more or less* instantaneously. My question still stands: the distance covered during the moment of contact does not intuitively seem sufficient to account for the work done

>>8506632
Well first of all, in elastic collisions there actually is no change in kinetic energy, and so there is no work done. Work is only done in inelastic collisions, for example when the two particles stick after colliding. Since the particles stick together after colliding, this give sufficient distance for force to be applied and for work to be done.

>>8506659
But A's kinetic energy changes and so does B's kinetic energy

I agree there's no change in the total kinetic energy OF THE SYSTEM (unless it's inelastic, then some is lost)

but i'm talking about, WITHIN the system, how is so much energy transferred between A and B without the two covering much distance while in contact?

>>8506641
It's got nothing to do with plank length.

>>8506632
At the instant of collision, the velocity of the balls change discontinuously, so an infinite force acts on it for an infinitesimal distance to change its kinetic energy. A formal proof can be given based on the dirac delta "function" (this is left as an exercise to the reader)

>>8506641
The distance is a lot fucking larger than Planck units. When two objects collide, they get compressed a little bit, then spring back. The distance is small, but the force is large.

>>8506659
>Well first of all, in elastic collisions there actually is no change in kinetic energy, and so there is no work done.
Wrong. There is a transfer of kinetic energy due to work done by one body on the other.

>>8506679
>infinite
>infinitesimal
Just no.

>>8506671
>how is so much energy transferred between A and B without the two covering much distance while in contact?
They may not cover much distance while in contact from your perspective, but if you zoom in, the distance the individual atoms move is sufficient enough to transfer that much energy.

Intermolecular forces in a rigid body can be modeled by springs connecting each atom. The small distance that the atoms move when in contact is actually huge compared to the intermolecular distance, therefore the potential energy in the "spring" is also quite large. I know this is not very mathematical but I hope you have a better picture of what's going on in your head.

>>8506686
There's literally nothing wrong with using infinitesimals.

>>8506695
The numbers in question are not infinitesimal.

>>8506699
Not in real life, but the case is different for perfectly rigid bodies.

>>8506686
>>8506688
Thanks. This makes sense. I never even thought of seemingly rigid objects getting compressed. That's crazy.

Also, I know the distance of contact would be longer than a Planck length anyway, I just meant that's the real reason why there's no such thing as instantaneous. Obviously that reason doesn't apply in this case, the reason in this case is more macroscopic, but that's the *general* reason.

>>8506679
Jesus what a fucking retard.

>>8506632
https://en.wikipedia.org/wiki/Contact_mechanics

Read up, buddy. It gets transformed to elastic potential energy for a bit before completely transferring. "Instantaneous" accelerations such as dropping something can be up to 5000 g's IIRC.

>>8506847
i mean he's not wrong if we're talking about infinitely rigid objects in an infinitesimally quantized space

these conditions don't actually exist of course but they're a useful mathematical model for reality

>>8506859
Even an infinitely rigid object would experience a period of acceleration as the electrons in the faster moving ball move closer, no?

>>8506868
yeah that's true

although an infinitely rigid object wouldn't have electrons

it would have to be a very large elementary particle that somehow had a negative charge near the surface, a positive charge near the center, and a neutral charge overall

>>8506632

Look up the dirac delta """""function"""""