Hw can we relate conervation of momentum with Newton's third law?

[ehabmozart]

Hw can we relate conervation of momentum with Newton's third law??

Hw can we relate conervation of momentum with Newton's third law??.. Quantitavely and qualitatevely i want a clarification for the realation between these.. Assume an apple falling towards earth.. Thanks in advance

 

[ozone]

Ok well it might help to imagine a situation that is "static". This means that the objects involved are not undergoing acceleration. A good example would be a rope pulling on a box that has yet to exceed its static friction.

In that case you know that Newtons first law holds so you have

$\sum F = 0$

now if you consider it a closed system then the only two forces acting are would be the force from the rope (f1), and the force opposing it from the static friction (f2).

hence you have

$F1 + F2 = 0$

simple algera yields

$F1 = - F2$

 

[ehabmozart]

I get this point but i need in terms of momentum!

 

[mfb]

Forces are the time-derivative of momentum. If the time-derivative of momentum is always 0, momentum is constant (conserved).

 

[ozone]

Also going back to my example. If $F = ma$ and we know that a = 0 then F must equal 0, and hence you can reach the conclusion using algebra above