Newton's Third Law and the Conservation of Momentum

[Rishavutkarsh]

Newton's third law confusion?

If A exerts some force on B then it experiences a force of same magnitude and in opposite direction. This didn't seem intuitive to me so I thought of it this way, Let A and B be a single system.

Now there is no net external force acting on the system so the momentum must be conserved and thus the forces exerted should be equal. Is this the correct way of thinking this or not? Is there a more intuitive way of perceiving this law? Thanks in advance.

 

[Simon Bridge]

That works yes.

Also - every time you push on something, don't you feel it push back on your hand or whatever?
Newton's third law is a systematic way of thinking about this.

 

[Rishavutkarsh]

Thanks, Yeah I thought that way too, But suppose a karate guy breaks 12 pieces of tiles he feels a force on his hands but when that guy breaks cardboard pieces applying the same force would he feel the same force?

 

[jbriggs444]

Thanks, Yeah I thought that way too, But suppose a karate guy breaks 12 pieces of tiles he feels a force on his hands but when that guy breaks cardboard pieces applying the same force would he feel the same force?

A karate guy would not "apply the same force". He would "apply the same motion". That is, he would swing his hand through the same arc and strike the target at the same speed.

A light-weight non-rigid target will be accelerated away before the impact force can become large. The force that accelerates the light-weight non-rigid object away will be small, so the equal-but-opposite force on the karate guy's hand will also be small.

 

[A.T.]

But suppose a karate guy breaks 12 pieces of tiles he feels a force on his hands but when that guy breaks cardboard pieces applying the same force would he feel the same force?

If he applies the same force to the cardboard pieces as to the tiles, then he experiences the same opposite reaction in both cases.

 

[bp_psy]

Now there is no net external force acting on the system so the momentum must be conserved and thus the forces exerted should be equal.

Even If there is a net external force on the system and the momentum of the system changes the sum of the internal forces in the system is 0. I think the argument is a bit flawed. Also for a system with more then two bodies the condition that the vector sum of the internal forces is 0 does not necessarily mean that the forces on each object pair are equal and opposite.

Could you explain why conservation of momentum is more intuitive to you? In my opinion it makes sense only because we have the third law in the Newtonian formalism.

 

[Andrew Mason]

If A exerts some force on B then it experiences a force of same magnitude and in opposite direction. This didn't seem intuitive to me so I thought of it this way, Let A and B be a single system.

Now there is no net external force acting on the system so the momentum must be conserved and thus the forces exerted should be equal. Is this the correct way of thinking this or not? Is there a more intuitive way of perceiving this law? Thanks in advance.

The third law deals with interactions between bodies. Newton assumed, implicitly, that measurements of time and distance are the same for all observers regardless of their motion. Therefore, when two bodies (A and B) collide, the force of A on B endures for exactly the same amount of time that the force of B on A endures. Since, as you correctly point out, by the first law the motion of A+B taken together cannot change (no external forces), this means necessarily that the force of A on B must be equal and opposite to the force of B on A, such that F_ABΔt + F_BAΔt = 0

If this was not the case, (i.e. F_ABΔt + F_BAΔt ≠ 0)
it can be easily shown that the motion of the centre of mass would undergo a change. From the first law, this would imply that there is a net external force on the system

Therefore, if the forces between two interacting bodies did not follow the third law you would either have to abandon the concept of absolute time for all observers or abandon the first law (for the reason you gave).

AM

 

[Rishavutkarsh]

Even If there is a net external force on the system and the momentum of the system changes the sum of the internal forces in the system is 0. I think the argument is a bit flawed. Also for a system with more then two bodies the condition that the vector sum of the internal forces is 0 does not necessarily mean that the forces on each object pair are equal and opposite.

I guess you're right, but
If there is a net external force then (Suppose there is a force exerted from C to A) Then we could consider them as a combined system and say that the forces exerted would be equal and opposite can't we?

I never said that if the vector sum of all the internal forces in a system would be zero then the forces would be equal and opposite, I am just talking about one point mass exerting some force on other. Considering them both a system we can say that forces are equal, If there is a net external force acting on them then however I think this way of thinking fails, any other ideas? I'm stumped.

 

[Rishavutkarsh]

The third law deals with interactions between bodies. Newton assumed, implicitly, that measurements of time and distance are the same for all observers regardless of their motion. Therefore, when two bodies (A and B) collide, the force of A on B endures for exactly the same amount of time that the force of B on A endures. Since, as you correctly point out, by the first law the motion of A+B taken together cannot change (no external forces), this means necessarily that the force of A on B must be equal and opposite to the force of B on A, such that F_ABΔt + F_BAΔt = 0

If this was not the case, (i.e. F_ABΔt + F_BAΔt ≠ 0)
it can be easily shown that the motion of the centre of mass would undergo a change. From the first law, this would imply that there is a net external force on the system

Therefore, if the forces between two interacting bodies did not follow the third law you would either have to abandon the concept of absolute time for all observers or abandon the first law (for the reason you gave).

AM

Thanks, you just wrote down my thoughts mathematically. But as someone pointed out I can't see how would this work for multiple objects or when there is an external force. Any ideas?