Hey, anyone like mechanics problems? I've got an interesting one here...
Two perfectly elastic rubber balls are released onto a perfectly elastic flat surface, exactly aligned along the vertical. There is a slight space such that the balls do not impact until the bottom ball M2 has finished it's collision. What is the optimal ratio of masses for the upper ball M1 to reach the greatest height?
If you do the math as the following:
* Solve for M1/M2 using energy.
* Solve for M1/M2 using momentum.
* Assume M2 and M1 collide at exact opposite velocites(pretty much a given.)
* Assume that for M1 to reach it's maximum height, the final speed of V2 would be essentially zero.
* Substitute the equations into each other using M1/M2 as the point of equality.
Then you get two possible results:
* M1/M2 = 1/3
* M1/M2 = infinite
Seems like the first one would be the right one, but experiments using an air track to simulate the problem show a linear relationship with no apparent peak. The experimental values tested ratios only from 1:1 to 4:1, in half steps, but the data shows the linearity very clearly. What gives?
Good luck.
I'm still trying to figure this one out myself.
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