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Here is a paraphrase of a question from a physics text.
A ball falls, hits the ground, and rebounds at nearly the same speed.
a) Is the momentum of the ball conserved throughout this time?
b) Is the momentum of the (ball+earth system) conserved throughout this time?
My initial reaction was “no” and “yes” (and I just looked at the solution manual and that is what they say as well). But then I started thinking about what conservation means. Certainly the momentum of the ball is not *constant*, while the momentum of the (ball+earth) *is* constant.
Now my position is that this is a poorly worded, misleading question. Conservation of momentum still applies to the ball by itself. Conservation laws mean the quantity only changes to the extent that there is some flow into/out of the system. This is still true for the ball by itself – the change in momentum is equal to the impulse due to external forces.
So I now would to reword this this:
a) Is momentum conserved if we consider the system to be the ball by itself?
b) Is momentum conserved if we consider the system to be the (ball+earth)?
Then the answers would be “yes” and “yes” but require slightly different reasoning in each case. But it is too late because the students already turned in their answers. Comments?
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