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Nov25-12, 10:07 PM
P: 3
Hello to everyone! This is my first post.

I have some basic knowledge in physics back from high-school, but since I decided now to pursue a degree in physics, I am starting from the bottom to get a good base.

As I am reading through some of the textbooks on the basics of physics (classical mechanics, the basis of electricity, magnetism, waves, thermodynamics and alike), I come across some "questionable" arguments and examples. I would like to put them forward onto this forum to see if I'm right in posing these, to me at least, very interesting mid-spinners.

Here's one of them:

Newtons third law of action and reaction:

I will first pose some general principles (as I understood them, from how textbooks present them; so please correct me if I make a mistake here)

- If we take a point of view looking at the system such that action-reaction force pairs are within the system, they do cancel out to zero and there is no acceleration; while if one of the forces in the pair is outer to the system it can result in an acceleration of the system (unless there is another outer force equal in magnitude but opposite in direction).

The examples are such as:

• Pushing on the car’s dashboard while inside (within the system) doesn't move (accelerate) the car, while pushing from the outside (of the system), using the force of friction with feet against the road, does accelerate the car;

• Trillions of inter-atomic forces within the football do not, while kicking the ball (acting on it outside of the system) does accelerate the ball; etc.

The difficulty I have is putting some of the situations into these broad definitions, such as when a canon fires a cannonball and recoils (perspective: cannon and the cannonball are both a part of the observed system), and alike.

As there are other forces acting on this system, to simplify, we can imagine the following idealised situation:

We are observing a system of two objects A and B acting on each other with an action-reaction force pair. The system is totally isolated from the outer world, i.e. two astronauts in the outer-space, holding hands and then pushing on each other. This would accelerate each astronaut in the opposite direction. Even-though I understand that only if we look at the each astronaut as a separate system, we would say it is accelerating, still our “whole” system is expanding through space. If we take the central point in-between the astronauts as the centre of the system, it is not moving, still if the system itself was to hit an object C on its path of expanding it would act on it with a force. Furthermore if object A has more mass than object B, they would accelerate differently. Would this mean that the central point of the system is moving thus the system itself is moving as well?

Let us take an example of inter-atomic forces within the football not accelerating it and replace it with an atomic bomb which explodes. Is there a difference here? Perhaps a better understanding is needed of what is actually meant by saying that “the forces cancel out” or that there is no acceleration of “the system”. If you see a hole in my thinking process, could you please point it out and explain how the above mentioned general rule (that action/reaction force pair within the system cannot accelerate it) holds in this situation. Since it is the law, I presume it should hold, but it does lead me to:...

...another related interesting question that I'm thinking about: if two astronauts hold hands and don’t let go after pushing on each other; then pull and push again but directing the force on an angle such that they start rotating (as a system, one around the other, like two orbiting stars), would it be possible for them to adjust these pushes and pulls and their directions and magnitudes such that they start moving (as a system) through space in a certain direction, or would this be fundamentally impossible (according to the laws of physics) and they would always just be rotating in one central “spot” in space?

Happy physics!
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