Can someone help me to prove the law of conservation of momentum using an example?
Hmm... right now I can't really think of any that actually PROVES it. But I can prove that it always works no matter what situation it is applied to. Just show a situation, e.g. car accidents, rockets, springs even.
The proof is one line:
[tex]F = dp/dt = 0[/tex]
That is the definition of force. If the force acting is 0, dp/dt = 0 so p is constant.
I don't actually thinks that actually proves it. That just defines force. Other than practical experiments, or actually showing it works in every situations, I can't really think WHY it must be so.
Perhaps it is derived from elastic collisions, and kinetic energy is conserved. Perhaps not.
Conservation of momentum follows from Newton's first law. Since:
[tex]F = dp/dt[/tex]
[tex]F = 0[/tex]
then: P = constant.
Why is Newton's first law true? It may not be. But to prove something, youi have to start with a premise. The premise is that F = dp/dt, Newton's first law. So far, no one has been able to show that it is not true.
Ohhh... the problem of asking to "prove" versus "verify/demonstrate". :uhh:
Thats proof by contradiction that is. Since you can't disprove it that means its right. I suppose you might accept it that way. But what I am going about is more that you can't proof by induction and you can't really explain WHY momentum is conserved.
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