Momentum during explosion

[September24]

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So an object is thrown straight up and when it reaches its fact height, it explodes. What is the total momentum carried by fragments.

The explanation says that the momentum depends on mass and velocity. At max height, when it explodes, the velocity is 0 so momentum at that point is zero. This makes sense.

However, it also says that there is no net force acting on the object so the momentum of the particle should be the same as when it explodes which is 0.

However, isn't gravity constantly acting on an object during free fall? How should I think about this problem?

 

[gettheleadout]

There is always net force upon the object because it's acceleration is constant and non-zero. However, the forces acting upon the object are irrelevant to its momentum.

Ignore whatever the explanation said about net force and just focus on conservation of momentum. The object at time of explosion has 0 momentum, so immediately after explosion (assuming the time duration of explosion is zero) no force has yet acted upon the fragments, so the system is still isolated; the total momentum of the fragments must sum to zero by conservation of momentum. As time begins to pass, the force of gravity acts on the fragments to increase the downward component of their momentum, breaking the isolation of the system, since now the total momentum of the fragments has a collective downward momentum component that is greater than the upward component.

 

[September24]

Understood. I think it makes sense. Thanks.