How Can Total Momentum Remain Zero Post-Explosion in a Moving System?

[suzsara7]

Homework Statement

how can the total momentum of an exploding cart still be zero after the collision if they are both moving? The momentum of cart one before the explosion was zero and so was the momentum of cart two before the explosion. The momentum of cart one after the explosion was 137.67 and the momentum of cart two after was 54.14.

Homework Equations

p=mv

The Attempt at a Solution

I thought that there might be something to do with them both being at rest before the explosion and maybe also that they are going in separate directions but I am not one hundred percent sure.

 

[tiny-tim]

Welcome to PF!

how can the total momentum of an exploding cart still be zero after the collision if they are both moving?

The momentum of cart one before the explosion was zero and so was the momentum of cart two before the explosion. The momentum of cart one after the explosion was 137.67 and the momentum of cart two after was 54.14.
…
I thought that there might be something to do with them both being at rest before the explosion and maybe also that they are going in separate directions but I am not one hundred percent sure.

Hi suzsara7! Welcome to PF!

Momentum is always conserved in both collisions and explosions (an explosion is basically a collision-in-reverse ) …

so, yes, if the momentum before is zero, then the momentum after must be also.

So the question you have been given doesn't seem to make sense …

can you copy it in full?

 

[suzsara7]

That is the exact question from my homework word for word. Glad I am not the only one totally confused by this question.

 

[tiny-tim]

That is the exact question from my homework word for word. Glad I am not the only one totally confused by this question.

Hi suzsara7!

Well, unless there's a third cart, or part of the bomb shot off at high speed, the only sensible answer seems to be "It can't!"

 

[chrisk]

Another way to think about this is since momentum is conserved and the initial momentum of the system was zero then the total final momentum of the system must be zero. In the case of an explosion, consider the final momentum of each individual piece with respect to a coordinate system with the origin at the center of mass of the exploding device prior to detination. The vector sum of all these peices will add up to zero, and the center of mass of the expanding system will not move.