Analyzing Ball Bounces: How Surface Affects Height

AI Thread Summary
The height a ball reaches after bouncing is influenced by the surface it impacts, primarily due to the surface's hardness. The coefficient of restitution (e) quantifies the energy lost during the collision, indicating how much kinetic energy is retained after the bounce. A harder surface results in a higher coefficient, leading to less energy loss and a greater bounce height. Conversely, softer surfaces absorb more energy, resulting in lower bounce heights. Understanding these dynamics is essential for analyzing ball bounce behavior.
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Homework Statement



How is the height if the ball affected by the surface of which it bounces? And does it have something to do with the formula below? What does the formula mean in a easy to understand manner? Thanks a lot!

Homework Equations



e = (V2 - V1) / (U1 - U2)

The Attempt at a Solution



i think it has something to do with the amount of harness the surface has.
 
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well, the coeficient of restitution means the amount of energy that is lost due to the colision.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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