How do you identify the systems in which Newton's Third Law is obeyed?

[pkc111]

Homework Statement

Ive noticed that in doing a lot of physics questions, identifying the location of the reaction force can be very difficult.

Relevant Equations

F1,2 = -F2,1

eg. For a ball in free fall (ignoring air resistance) there is only one force acting if the system is just considered to be the ball. It seems necessary to go to the system which includes the Earth for identification of the reaction force to be made. Is there any rule for how big a system must be in order for Newtons Third Law to be obeyed within that system (ie both the action and reaction forces to be identified within it)?

 

[haruspex]

Generally when one speaks of a 'system' in mechanics it means a collection of bodies which will be treated as a unit for some purpose. I.e. we are concerned with forces between systems, not forces within them.
In that sense, Newtons Third Law concerns the force two systems exert on each other.

 

[PeroK]

Homework Statement:: I've noticed that in doing a lot of physics questions, identifying the location of the reaction force can be very difficult.
Relevant Equations:: F1,2 = -F2,1

eg. For a ball in free fall (ignoring air resistance) there is only one force acting if the system is just considered to be the ball. It seems necessary to go to the system which includes the Earth for identification of the reaction force to be made. Is there any rule for how big a system must be in order for Newtons Third Law to be obeyed within that system (ie both the action and reaction forces to be identified within it)?

Newton's third law is responsible for the law of conservation of momentum. It's only if you include the Earth in your system that momentum is conserved. Momentum of the falling ball is not conserved.

The question ultimately is whether your system has external forces.

 

[pkc111]

Sure, but how do you know how big to draw your system to capture all action/reaction forces?

 

[PeroK]

Sure, but how do you know how big to draw your system to capture all action/reaction forces?

You know from the problem statement. A ball is falling under gravity; a charged particle is placed in an electric field; a wagon is accelerating at $2m/s^2$ ... In all these cases, the object (ball, particle, wagon) is being influenced by some external force.

It shouldn't be hard to see when there are external things influencing the motion of the system.

 

[haruspex]

Sure, but how do you know how big to draw your system to capture all action/reaction forces?

You keep adding bodies until you have everything you care about.
E.g. bouncing a ball against a wall, there will be forces between the wall and the floor etc., reaching out to encompass the Earth. But you don't usually care about any of that, so you just treat the wall as having infinite inertial mass.

 

[pkc111]

That makes sense. Thank you both.