The coefficient of restitution, e, of a ball hitting the floor is defined as the ratio of the speed of the ball after it rebounds from the impact to the speed of the ball right before it hits the floor.
Derive a formula for the coefficient of restitution when a ball is released from an initial height H and rebounds to a final height h.
The textbook solution is set up this way:
Before: mgH=1/2mv2before
vbefore=√2gH
After: 1/2mv2after=mgh
vafter=√2gh
With the final answer being e= √(h/H).
I'm confused on the set up, where do the before and after equations come from, particularly mgH and mgh? I know mgy is the gravitational potential energy at a given height, but why is it set equal to 1/2mv2 in the before and after equation?
Derive a formula for the coefficient of restitution when a ball is released from an initial height H and rebounds to a final height h.
The textbook solution is set up this way:
Before: mgH=1/2mv2before
vbefore=√2gH
After: 1/2mv2after=mgh
vafter=√2gh
With the final answer being e= √(h/H).
I'm confused on the set up, where do the before and after equations come from, particularly mgH and mgh? I know mgy is the gravitational potential energy at a given height, but why is it set equal to 1/2mv2 in the before and after equation?
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