# Infinit force at 1 m/s?

1. Mar 17, 2005

### misster y

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)

2. Mar 17, 2005

### Staff: Mentor

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!

3. Mar 17, 2005

### oldunion

how could two spheres have an elastic collision without being deformed momentarily

4. Mar 18, 2005

### HallsofIvy

Staff Emeritus
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.

5. Mar 18, 2005

### Staff: Mentor

They can't.

6. Mar 18, 2005

### Antiphon

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.

7. Mar 18, 2005

### oldunion

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.

8. Mar 19, 2005

### rachmaninoff

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.

$$\delta$$-function links from MathWorld:
http://mathworld.wolfram.com/DeltaSequence.html
http://mathworld.wolfram.com/DeltaFunction.html

9. Mar 27, 2005

### sid_galt

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. Mar 27, 2005

### Staff: Mentor

Good point. I was referring to macroscopic objects (balls and spheres), not elementary particles. Sorry for not being clear.