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Whenever we consider an explosion of a projectile in air, we solve for the velocities of the exploded elements by using the Law of Conservation of Momentum (ignoring any sound or light effect here). But I just don't get it, how can we conserve momentum, when the external force gravity is acting on each and every particle considered.

The same problem came up to me while solving one more question. Let us say we have an Atwood machine in the vertical plane with a pan on one side and a block on the other side. Suddenly a particle comes up and hit the pan from the bottom and stick to it, here also we considered the impulse imparted due to the normal reaction between the pan and the particle and due to the tensions in the string. Why are we not considering any impulse due to the gravity here?

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  • $\begingroup$ I think the following link will really help you: physlink.com/education/askexperts/ae602.cfm $\endgroup$ – rb612 Jan 15 '17 at 8:33
  • $\begingroup$ I can't say I've had any trouble with it in classical mechanics with gravity; it's conserved at every particle considered. $\endgroup$ – Mozibur Ullah Jan 15 '17 at 8:34
  • $\begingroup$ "when the external force gravity is acting on each and every particle considered." - do you actually consider the force of gravity and conserve momentum? Or are the solutions you're talking about implicitly ignoring gravity? $\endgroup$ – ACuriousMind Jan 15 '17 at 13:31
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Well, you are right about force due to gravity being ignored. But that's a good approximation. In case of explosion the velocity of fragments after explosion changes significantly in very small time. This significant change in momentum means high impulsive force. So impulse due to internal forces on fragments is very large in comparison to force due to gravitation. Similar is the case of an object hitting on the pan. Force due to change in momentum is very high compared to gravitational force, hence force due to gravity can be ignored in calculation. Try solving the problem you have, including gravitational force. You conclude yourselves if it is significant.

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