Exploring Conservation Laws in Closed Systems

[fisico30]

In classical mechanics (also in QM I guess), the fundamental laws of conservation (energy, momentum and angular momentum. tell me if I forget something) are valid only if the system is closed and the net external force is zero.
WE define what the system is. We can include or exclude things. These things could exert (or not) forces of different nature (gravitational, electric,magnetic, etc...) on the objects that are part of the system.
We call the system closed if no energy is coming in or out. The net external force being zero is the necessary condition for the conservation laws.

My dilemma: Can we really decide, arbitrarily, that all those external forces sum up to zero when they are much smaller (how much smaller?) than all the forces exerted by the internal objects of the system? Do we include to be part of the system ONLY those objects that we think could have a role in the situation under study? Any example?

My example is this: a collision between two cars. Total Momentum is conserved. This implies and assumes that the "net external force is zero (however there must be some other things in the world beside those 2 cars, that exert forces on those two cars too. I guess those forces are negligible and taken to be zero when compared to the mutual, action reaction forces between the two cars).

Can anyone validate?fix my thinking?
thanks for the help.

 

[Meir Achuz]

In a collision, the impact time is very short.
This means that the impulse (F*t) of the non-impact forces is usually negligible.
That is why momentum is conserved, but energy may not be.

 

[fisico30]

Thank you clem. That is clear. the impulse is defined as the change in momentum. The external forces could actually be large but they act over a short time so their net impulse is zero. that is your point, right?
But wouldn't this be the same for the internal forces (i.e. short time of action and small impulse)? what makes us choose certain forces to be internal and others to be external then? do the the forces that we take as external an impulse much much smaller than the impulse due to the external ones?
thanks again.

 

[fisico30]

Sorry for the typos. I meant" do the the forces that we take as external have an impulse much much smaller than the impulse due to the internal ones?"
thanks

 

[Meir Achuz]

Free body diagrams still apply. Internal forces do not affect the motion of an object.
When two balls collide, the force of ball A on ball B is external to B, and is very large for a short time.

 

[james77]

Free body diagrams still apply. Internal forces do not affect the motion of an object.
When two balls collide, the force of ball A on ball B is external to B, and is very large for a short time.

Hi

Does this mean that all of the force of ball A is absorded by ball B. However this I suspect is not the same as all of the Energy (E), right?

Thanks
(Good Forum)

 

[Meir Achuz]

absorbed is not what happens. The force F of A on B for a time t changes the momentum of B by Ft. More has to be known to determine what happens to the energy.

 

[james77]

So, If there wasn't much distance between A & B, then the momentum as a function of Ft would get smaller and smaller with increasing closeness (until it would disappear, in the classical sense when the balls come to rest) or with the number of balls or objects that interact with A within a defined space