Basically, two kids are on a skateboard and push against each other with a constant force. The question asks where the combined center of mass is and the answer is "is initially stationary and remains so." Why doesn't it move once the kids are in motion? The explanation says it has something to do with conservation of momentum. How does that come into play? :(
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The two skaters' momenta will be equal and opposite. That means that the total momentum of the system is zero. One skater has momentum equal to mass*velocity, but if you multiply that by time, you'd have mass*distance from the center. That would be his/her contribution to center of mass. Now consider doing that for both skaters. If
m1v1 = m2v2
as stated above, then as you multiply both sides by some amount of time you have:
m1d1 = m2d2
So this means they each contribute the same (and opposite) amount to center of mass as time goes on. Therefore the center of mass doesn't move with time.
m1v1 = m2v2
as stated above, then as you multiply both sides by some amount of time you have:
m1d1 = m2d2
So this means they each contribute the same (and opposite) amount to center of mass as time goes on. Therefore the center of mass doesn't move with time.
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The center of mass will obey conservation of momentum. In the absence of external force, the momentum cannot change, so the center of mass cannot move. If the skateboard is stationary, the center of mass will remain stationary. However, the distribution of mass can change--if a kid moves to the right, the skateboard will move to the left an amount required to keep the center of mass stationary.