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10 May 2021

The velocity of a system's center of mass doesn't change in a collision...

After I posted my 2021 AP Physics 1 solutions, I got an important question about problem 3, the qualitative-quantitative translation.  The problem asked students to estimate the speed of the center of mass in two separate collisions.  The "estimate based on a thought experiment" part is very similar to 2019 problem 2, which asked a very similar question about the acceleration of a modified Atwood machine.

The question, though, was about the center of mass speed:

The velocity V_cm is the velocity of the center of mass for the two-object system.  I agree that the velocity of object 1 would change or not change depending on its relative mass to object 2, but because there are no external forces on the system, I think there would not be a change in velocity of that system, thus V_cm will remain unchanged.  

So, this physics is 100% correct - *within each trial*, the center of mass speed does not change.  That's why we can say that whatever the combined objects' speed is after the collision, that's the speed of the center of mass throughout.

The actual question asks about different situations, though!  In the first situation, Edna the hippopotamus is moving, and she catches a peanut.  The center of mass of the Edna-peanut system doesn't change speeds during this trial - right.  So the center of mass is moving at whatever speed Edna moves with the peanut after collision.  That's pretty darned close to Edna's initial speed.

In the SECOND situation, Bertha the elephant is stationary and catches a peanut.  It's correct that the speed of the Bertha-peanut system doesn't change after collision.  The speed of the peanut does change, though - the peanut slows down when Bertha catches it.  After the catch, Bertha and the peanut are hardly moving at all.  So the center of mass speed is very small!

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