I've been arguing with some people about a situation in which two completely rigid bodies surrounded in a vacuum collide... they keep saying they will bounce off each other but that doesn't seem right. It's written up here http://midnightwiki.com/index.php?title=Inelastic_Collision.

 

What do you guys think? Also, would there have to be some sort of new energy released if they were to collide?

They will bounce off each other. The force that ultimately responsible for bodies to bounce off each other is the electrostatic force. It exists regardless whether the bodies are perfectly rigid or not.

"completely rigid" has not been defined well enough. One possibility is that in the collision, the objects will shatter into many pieces, conserving energy and momentum, unless "completely rigid" means they are indestructible.

Afaik, "rigid body" means that the distances between parts (atoms) of the body remain fixed which rules out shattering of the bodies. The "completely" is just a superfluous adjective.

the situation cannot occur.

If you use that definition then you are describing an unphysical condition. Such a body could not e.g. have molecular vibration, which means it cannot have a temperature. The description of the system is overconstrained (i.e. mutually exclusive conditions), so reading too much into the details is meaningless.

 

edit to add: for a more distilled version with less technobabble, see YT's response above

I´m afraid I didn´t understand you last post Swansont.

If you use that definition then you are describing an unphysical condition. Such a body could not e.g. have molecular vibration, which means it cannot have a temperature.

Who cares? You could deny the whole classical mechanics with the same argument (it´s unphysical - particles with definite position and momentum cannot exist). And the nonexistance of internal degrees of freedom is in fact the reason for the collision to be perfectly elastic.

 

The description of the system is overconstrained (i.e. mutually exclusive conditions)

Which conditions exactly do you mean which are "mutually exclusive"? You are aware that "fixed distances" only applies to particles within the same rigid body, I hope.

 

so reading too much into the details is meaningless.

Didn´t understand that, either. But that´s probably related to my non-understandings above.

In order for momentum to be conserved, they would have to bounce off of each other, and since they are perfectly rigid, this change in velocity takes place in zero time, requiring infinite acceleration, requiring infinite force. Or, rather, such is the limit that the situation approaches as one makes the bodies more and more rigid.

to bounce off, that would require elesticicty, and compliance, again, if these were perfectly rigid, this could not occur.

 

if the COG were at an offset then they would rotate and continue past each other (deflect/ricochet). perfectly alligned COGs cannot occur either.

Electrons bounce off each other and are not particulary well known for their internal elasticity. Why do you think bodies bounce off each other at all?

And what´s a COG ?

COG =Center Of Gravity.

An idealized, perfectly rigid collision would result in an infinite force for an infinitesimal amount of time.There are no rules at this point. They "bounce off", destruct, pass right through each other, or do pretty much anything imaginary in this imaginary situation.

 

Just my opinion and it's not even wrong.

i suppose the problem is akin to asking about a collision between an object of infinite mass and an object of finite mass.

I´m afraid I didn´t understand you last post Swansont.

 

Who cares? You could deny the whole classical mechanics with the same argument (it´s unphysical - particles with definite position and momentum cannot exist). And the nonexistance of internal degrees of freedom is in fact the reason for the collision to be perfectly elastic.

 

 

Which conditions exactly do you mean which are "mutually exclusive"? You are aware that "fixed distances" only applies to particles within the same rigid body' date=' I hope.

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You demand rigidity, which would violate physical laws and yet want to use other laws to predict behavior of the system. Relativity forbids perfectly rigid bodies. In order to transmit momentum the separation distance has to change.

Electrons bounce off each other and are not particulary well known for their internal elasticity. Why do you think bodies bounce off each other at all?

And what´s a COG ?

 

Electrons have no internal structure. "Rigidity" doesn't apply.

You demand rigidity, which would violate physical laws and yet want to use other laws to predict behavior of the system. Relativity forbids perfectly rigid bodies. In order to transmit momentum the separation distance has to change.

I wrote a pretty long response on that reply which was a bit disappointing to be honest. But then, I decided that I actually don´t really want to contribute to this thread any more so I´ll strip it down to: Thx for the answer, I think I see your point.

 

Electrons have no internal structure. "Rigidity" doesn't apply.

I you reread my post in the context of the preceding post (well, actually rereading my post again should suffice) you´ll see that I didn´t say that electrons are rigid bodies.

to bounce off, that would require elesticicty, and compliance, again, if these were perfectly rigid, this could not occur.

 

That's one way to take "perfectly rigid." You could also take it as infinite elasticity, as I did, just based on the fact that as the rigidity of the objects increase, the time needed to rebound approaches zero and the force exerted approaches infinity, so instantaneous rebound is the "limit" at this impossible situation. But actually trying to figure out what happens at infinity is rather pointless, I think... you're going to have some kind of paradox no matter what.

That's one way to take "perfectly rigid." You could also take it as infinite elasticity, as I did, just based on the fact that as the rigidity of the objects increase, the time needed to rebound approaches zero and the force exerted approaches infinity, so instantaneous rebound is the "limit" at this impossible situation. But actually trying to figure out what happens at[/i'] infinity is rather pointless, I think... you're going to have some kind of paradox no matter what.

 

I think this is the best "approach" if you will forgive the pun.