# Why the net force is only from external forces?

1. Oct 30, 2007

### Feldoh

We're learning about a systems center of mass and have:

$$F_{net} = Ma_{com}$$

But I having a problem understanding why the net force is only from external forces? Is it because internal forces follow newtons third law so the net force from internal forces is 0? If that's the case then take for example a bottle-rocket firework. Once it explodes is we ignore air resistance (so the only force is gravity) would the fragments of the firework still fall with the same trajectory since the internal forces are 0?

2. Oct 31, 2007

### Staff: Mentor

Exactly.
Absolutely. The center of mass of all the pieces will follow the same trajectory that the bottle-rocket would have followed if it didn't explode.

3. Oct 31, 2007

### pmb_phy

The internal forces cancel each other out if they obey Newton's third law. If they don't the a modification is neccesary. E.g. Newton's Third Law is well known to fail in the case of the forces of two charged particles exerting forces on each other. Normally this would violate the principle of conservation of momentum. But in this case one has to then add in the momentum of the field and it is the total momentum of field+particles that has a conserved momentum.

For the classical (non-relativistic) situation in which Newton's Third Law holds I have derived it and placed it online at http://www.geocities.com/physics_world/mech/center_of_mass.htm

Best wishes

Pete

4. Oct 31, 2007

### Feldoh

So mechanically this concept works but is a little different when dealing with E&M concepts?

I haven't learned anything about E&M but in the case of the field+particles is that considered something similar to the COM in a very very generalized way?

5. Oct 31, 2007

### pmb_phy

Yes
The center of mass is still well defined but one has to take into account the mass of the electromagnetic field. See a general derivation here. Its pretty mathy and done from the stand point of SR and uses tensors. But perhaps you'll get a flavor of it

http://www.geocities.com/physics_world/sr/conservation_laws.htm

Good Luck

Pete

6. Oct 31, 2007

### Feldoh

Why would an electromagnetic field have a mass? Just because it has energy?

7. Oct 31, 2007

### pmb_phy

Yes. This was determined by Einstein in 1906 as I recall.

Pete