# Conservation of linear momentum

1. Jul 13, 2008

### G.Chandra

Why do we apply law of conservation of linear momentum on a body that explodes in air when an external force, gravittional force- mg, is acting on it? The law says that the linear momentum is conserved in absence of the external forces.

Last edited: Jul 13, 2008
2. Jul 13, 2008

### pardesi

hmm that's because the force $$mg$$ into the time for which the explaosion happens $$dt=mgdt$$ is aver small qty so
$$P_{f}-P_{i}=mgdt \approx 0$$

3. Jul 13, 2008

### tiny-tim

Welcome to PF!

Hi G.Chandra! Welcome to PF!

Because an explosion, like a collision, is taken to be instantaneous.

So the force from gravity (which takes time!) is zero.

4. Jul 13, 2008

### pardesi

Re: Welcome to PF!

hmmmm i don't get this explaination of urs?

5. Jul 13, 2008

### G.Chandra

This means that the law will not be applicable if duration of explosion is longer?

6. Jul 13, 2008

### pardesi

no see it's an approximatiion!!!
so don't wry about the "law holding" or not
what's assumed is that the momentum change due to gravity is negligible as comapred to the initial momentum
say if teh intial momentum was some 500 untis and the change sone 1 or 2 units then it shud hardly matter u
it's an approximation and works real well

7. Jul 13, 2008

### Andy Resnick

That's the magic of representing extended objects as mass-points. The center of mass will follow the undisturbed trajectory (within reason- a mid-air collision is different than a 'simple explosion'), even though all the little pieces will tumble hither and yon.

8. Jul 14, 2008

### Redbelly98

Staff Emeritus
Re: Welcome to PF!

A better way to say it might be that the impulse due to gravity,

$$F \Delta t = m \ g \ \Delta t$$

is very small since delta-t is small. Equating impulse with change in momentum, we can also say this does not affect the momentum during a collision or explosion.

9. Jul 14, 2008

### pardesi

yeah perfect that's hwy i had questioned "tiny-tim"!!!