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

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SUMMARY

The discussion clarifies the relationship between the conservation of momentum and Newton's third law of motion. It emphasizes that in a static system, where acceleration is zero, the net force is also zero, leading to the conclusion that the forces acting on the system are equal and opposite. Specifically, it illustrates this with an example of a rope pulling a box, where the forces from the rope and static friction balance each other, resulting in constant momentum. The key takeaway is that if the time-derivative of momentum is zero, momentum remains conserved.

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  • Understanding of Newton's laws of motion
  • Basic knowledge of static friction and forces
  • Familiarity with the concept of momentum
  • Algebraic manipulation skills
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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
 
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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
 


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


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


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
 

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