A rebound and kinetic energy problem with a little specific heat

AI Thread Summary
The problem involves a ball thrown downward at 15 m/s that bounces back to a height of 5 meters. To find the speed after rebounding, conservation of energy principles are applied, equating initial kinetic energy to potential energy at maximum height. The energy lost during the bounce can be calculated by determining the difference in kinetic and potential energy, expressed as a function of mass. The specific heat of the ball is used to calculate the temperature increase from the absorbed energy, with the formula Q = mL(delta T). The discussion emphasizes the importance of energy conservation and the relationship between kinetic energy, potential energy, and temperature change.
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Homework Statement


A ball is thrown vertically downward strikes a surface with a speed of 15m/s. It then bounces, and reaches a maximum height of 5 meters. Neglect air resistance on the ball.

a) What is the speed of the ball immediately after it rebounds from the surface?
b)What fraction of the ball's initial kinetic energy is apparently lost during the bounce?
c)If the specific heat of the ball is 1,800 j/kg*C, and if all of the lost energy is absorbed by the molecules of the ball, by how much does the temperature of the ball increase?

Homework Equations


KE=1/2mv^2
Q=mL(delta "T")

The Attempt at a Solution


my answer for a was crazy so i am pretty much stuck with the rest
 
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Use law of conservation of energy - at any level (when there are no energy loss) potential energy+kinetic energy = constant. When ball is hitting a surface at 15 m/s, there is only a kinetic energy. When it reaches maximum height 5 m - there is only potential energy. Calculate what height would it be if all of kinetic energy at start where converted to potential. From difference you will find loss of energy during contact with surface ;] hope this will help. By the way - potential energy equation near Earth's surface: EP = mgh
 
but how do i find the mass ...i found the the joules lost to be 63(mass) joules
 
Well i don't know ;] so maybe express your answer as a function of mass, deltaT=(some number)/m.
 
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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