Calculating Inelastic Collision Force: Ball A and B at 1 m/s in Exterior Space

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Discussion Overview

The discussion revolves around the theoretical analysis of an inelastic collision between two identical spherical balls in a vacuum, specifically focusing on the forces exerted during the collision. Participants explore the implications of assuming no deformation occurs during the collision and the resulting physical realism of such a scenario.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant describes a scenario where ball A is at rest and ball B is moving towards it at 1 m/s, questioning the force exerted during an inelastic collision without deformation.
  • Another participant argues that an inelastic collision without deformation is impossible, suggesting that such a collision would result in infinite force due to zero collision time.
  • Some participants challenge the definitions of elastic and inelastic collisions, emphasizing the importance of collision duration in determining forces.
  • A later reply introduces the concept of using a delta function to mathematically represent the forces involved in such a collision, noting that it allows for an infinite force over an infinitesimally short time.
  • There is a discussion about the theoretical implications of creating a material that does not deform, with one participant asserting that all solids have some degree of 'sponginess' due to molecular forces.
  • Another participant raises a question about high-energy collisions between protons, suggesting that they could be considered elastic, which leads to clarification that the discussion is focused on macroscopic objects rather than elementary particles.

Areas of Agreement / Disagreement

Participants generally disagree on the feasibility of an inelastic collision without deformation, with some asserting it is impossible while others explore the theoretical implications. The discussion remains unresolved regarding the physical realism of the proposed scenario.

Contextual Notes

Limitations include the assumption of no deformation during the collision and the dependence on the definitions of elastic and inelastic collisions. The discussion also highlights the unresolved nature of the mathematical representation of forces involved.

misster y
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You have an ideal esferic ball A of 1 Kg in rest and another equal ball B of 1 Kg going to A (by an imaginary axe between centers) at 1 m/s. (Considering them in exterior space/vacuum with no frictions nor gravity)
What is the force produced to B (by A)(and viceversa) when the balls hits inelastically? If it is not infinit, what is the valor in Newtons?
(remember, inelastically, with no ball deformation)
 
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I think what you are asking is: If two perfect spheres collide inelastically but with no deformation, what force will they exert on each other during the collision? Realize that an inelastic collsion with no deformation is an impossible condition. If there is no deformation of the spheres, the collision will take 0 time and the force will be infinite. That should tell you that this thought experiment is not physically realistic! :smile:
 
how could two spheres have an elastic collision without being deformed momentarily
 
You may have a wrong idea about what "elastic" and "inelastic" collisions are. In any case, the crucial piece of information, that you have left out, is the time the collision takes.
 
oldunion said:
how could two spheres have an elastic collision without being deformed momentarily
They can't.
 
Doc Al said:
They can't.

But they can in a thought experiemnt.

The solution is to use something called a "delta function" for the forces.

This is a function that is infinite in intensity but is infinitelay narrow like
a needle. As long as you use it under an integral, it is a valid mathematical
tool. When you integrate the forces in time, you will get instantaneous
changes in momentum that are of the correct magnitude.
 
so if you made a material that would not deflect at all, what would happen if you hit that material against another sphere made of that same material.
 
so if you made a material that would not deflect at all, what would happen if you hit that material against another sphere made of that same material.

Short answer: you can't; solids are held together by electrostatic forces between molecules (nothing 'rigid'), so there is always some sort of 'sponginess' to them - they can deform, or propagate waves.

If you try to simulate it mathematically, you would (as antiphon pointed out) use a discontinuous dirac delta function to represent the force - you'd get an effective 'infinite' force for an 'inifinitely short' period of time (mathematicians are cringing as I say this), resulting in instantaneous, finite change of momentum for both spheres: the "perfectally inelastic collision" from introductory physics. I stress that this does not happen in the real world, rigid bodies are only a convenient approximation.

[tex]\delta[/tex]-function links from MathWorld:
http://mathworld.wolfram.com/DeltaSequence.html
http://mathworld.wolfram.com/DeltaFunction.html
 
Doc Al said:
I think what you are asking is: If two perfect spheres collide inelastically but with no deformation, what force will they exert on each other during the collision? Realize that an inelastic collsion with no deformation is an impossible condition. If there is no deformation of the spheres, the collision will take 0 time and the force will be infinite. That should tell you that this thought experiment is not physically realistic! :smile:

What about protons. If they are accelerated to sufficiently high energies such that they collide and then rebound instead of fusing, wouldn't that be a totally elastic collision.

Or any of the fundamental particles for that matter?
 
  • #10
Good point. I was referring to macroscopic objects (balls and spheres), not elementary particles. Sorry for not being clear.
 

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