A different bouncy ball question....

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Discussion Overview

The discussion revolves around the energy dynamics of a bouncy ball, specifically focusing on how much additional energy is required for the ball to return to its original drop height after bouncing. The context includes practical observations and calculations related to the ball's mass, density, and bounce heights.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant describes the initial conditions of the bouncy ball, including its mass, density, drop height, and observed bounce height, and seeks guidance on calculating the energy needed to achieve the original height after the first bounce.
  • Another participant proposes that the height of the bounce is proportional to the potential energy and calculates the fraction of energy retained after the first bounce, suggesting that to achieve the original height, the ball must be dropped from a greater height.
  • A subsequent reply asks for clarification on how to achieve the original height from a specific drop height, indicating a desire for further exploration of the energy calculations involved.
  • Another participant suggests calculating the difference in potential energy and applying that energy to the initial kinetic energy of the ball, offering a method to approach the problem.

Areas of Agreement / Disagreement

Participants appear to be exploring different methods to address the energy requirements for the bouncy ball, with no consensus reached on a definitive approach or solution. The discussion remains open to further clarification and exploration.

Contextual Notes

The discussion includes various assumptions about energy retention and the relationship between height and potential energy, which may depend on additional factors not fully addressed in the posts.

SHO-NUFF
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So I've seen all over the internet about the efficiency of a bouncy ball and how high will it bounce on the 2nd, 3rd, 4th, etc. bounces? That's easy to figure out. Now I was thinking about it for a while and the question that hit me was how much energy do I need to add to the initial drop in order for the ball to return to the exact original height? I have a table that's 1.03 m high, the ball has a mass of 7.362 g and a density of 0.90 g/cm^3. The ball is bouncing off a concrete floor that, from what I can find, has a density of 2,400 kg/cm^3. The ball also take approximately 0.5 seconds to fall and impact the floor and approximately another 0.25 seconds to reach the height of the first bounce of about 0.835 m.

I'm not sure if all this information is all relevant but it's what I've observed by simply bouncing the ball a couple dozen times. Please someone help point me in the right direction here. Again, what I'm looking for is the amount of energy required to be added in order for the ball to return to the exact original drop height on the first bounce. I'm missing something, overthinking it, or both.
 
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Using an Earth constant gravity approximation, the height is proportional to the potential energy of the ball. If the ball height is 1.03m before the first bounce and 0.835m after the first bounce, the fraction of energy retained after a bounce is
0.835/1.03 = 0.811
So, to bounce up to a height of 1.03m, you need to drop it from a higher height
1.03m / 0.811 = 1.27m
The potential energy is mgh, so the extra energy to lift to 1.27m is
W = mg(1.27m-1.03m)
(You shouldn't round the quantities until the end.)
 
Khashishi,

Thanks for the tip on rounding. What if I wanted to bounce it from a given height (in this case 1.03 m) and have it return to the exact height it was released from though?
 
Calculate the difference in potential energy as I have shown above, and apply that energy to the initial kinetic energy of the ball.
 
Thanks for the help! My apologies for not getting the first time around. I'm new to physics.
 

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