Momentum in Inelastic Collisions

[Cyrus]

no I understand that part, but its not what I am talking about. I am talking about the interal forces that are exhanged during a collision.

 

[Cyrus]

Hmm, I have another question. How come we know that the area of the internal forces that take place during a collsion always sum up to be the same. I know that the two bodys experience the same force for the same amount of time, but what I am talking about is from one experiment to the next. Example, If i have a cetrain projectile inelastically collide with another, they will stick and move off together, and their momentum beore will be equal to that after. Now, let's say I have a heavier projectile but moving slower, so that the momentum is the same as in the first experiment, then they two will inelastically collide and move off together in the same direction with the same amount of momentum as when we started. Now according to the conservation of momentum, the area that is underneath both curves of forces for time in both experiments will be equal. My question is how do we know that they will be equal from one experiment to the next. My problem is that, if I were Newton and I said ok these have equal forces for equal amounts of time that would be acceptable for one case of an experiment. But this formula alone is not enough to let me conclude that for any other inelastic experiment of equal initial momentum will encouter the same area in the force curve. Is this something that was determined through experimentation, or was Newton able to say that friction plays no role in momentum exchange without ever having to do a single experiment?