Conservation of Momentum in an Isolated System: A Derivation

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Homework Statement

Derive a law of conservation of momentum for an isolated system consisting of two interacting particles.

Homework Equations

It says that "The law is derived by applying Newton's second law to each particle and Newton's third law to the system."

The Attempt at a Solution

I don't understand this at all... if you could explain me with an example, that would be so great...

 

[VinnyCee]

Newtons second law:

\overrightarrow{F}\,=\,\overrightarrow{m}\,a

Newtons third law:

"Whenever A exerts a force on B, B simultaneously exerts a force on A with the same magnitude in the opposite direction." - "[URL

What would you do to combine the forces of two particles?

 

[dotcom]

well, does that mean

-ma=ma for representing the situation where two particles collide?

but i still don't understand how to proceed tp get

initial total momentum =final total momentum

 

[daniel_i_l]

I think that for this problem it's easier to use the other version of Newtons second law:
F = dp/dt (change in momentum)*
Because of Newtons second law the total force inside a system will stay 0, so what does that say about the total change in momentum?
*From this you can derive F = ma:
F = dp/dt = d(mv)/dt = mdv/dt = ma

 

[dotcom]

all right, I think I got it. Thanx!