I need a formula for bouncing balls

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SUMMARY

The discussion focuses on deriving a formula for calculating the bounce height of a ball based on empirical data collected from various drop heights. The average bounce height is approximately 83% of the initial height, influenced by energy loss due to inelastic collisions and air resistance. Participants suggest using a graphical approach to plot the data and apply curve fitting techniques to determine the bounce ratio accurately. This method allows for a visual representation of the relationship between drop height and bounce height, facilitating a better understanding of the energy loss involved.

PREREQUISITES
  • Understanding of basic physics principles, specifically energy conservation and inelastic collisions.
  • Familiarity with data collection and analysis techniques.
  • Knowledge of graphing tools and curve fitting methods.
  • Basic mathematical skills for calculating percentages and interpreting slopes.
NEXT STEPS
  • Research "energy loss in inelastic collisions" to understand the physics behind bounce height.
  • Learn how to use "Excel" or "Python" for data visualization and curve fitting.
  • Explore "linear regression" techniques to analyze the relationship between drop height and bounce height.
  • Investigate materials science to comprehend how different ball materials affect bounce performance.
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Students in physics, educators teaching mechanics, and anyone interested in experimental data analysis and the principles of energy loss in bouncing objects.

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Homework Statement


I dropped a ball from different heights, and got height they bounced up to, but I need a formula for it.

Data
Gravity = 9.800 m/s2

[Initial Height(cm)]----------[Bounced Height(cm)]
100.0---------------------------81.00
90.00---------------------------75.00
80.00---------------------------67.00
70.00---------------------------59.00
60.00---------------------------50.00
50.00---------------------------41.00
40.00---------------------------34.00
30.00---------------------------26.00
20.00---------------------------17.00
10.00---------------------------9.000
0-------------------------------0

Homework Equations



I need a formula that can calculate the bounce height of this

The Attempt at a Solution



I calculated the percentage of the bounce height and it averages at about 83% of the height dropped from. Any help would be greatly appreciated
 
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Are you supposed to find an empirical formula for your measurements?
 
I'm not sure, my teacher was pretty vague about it. I guess just an equation that you can use to calculate the bouncing of an object
 
There is no such equation. An ideal ball in ideal conditions must bounce to exactly the height it was dropped from. But it loses energy because its collision with the ground is not completely elastic and because there is air resistance. Accounting for these losses is a very tricky matter, they depends significantly on the material of ball and its size.

So I think you should just assume that the ball loses some fixed percentage of energy. And you should find the best fit for the coefficient of the loss from your measurements.
 
Try plotting the data on a graph and see what you get. Seeing what is happening visually is a very effective way of examining experimental results. If your graphics package has a curve fitting option, have the package fit a straight line to the data. You will find that the slope of the line represents very accurately the "bounce ratio" (also equal to, the ratio of potential energy from one bounce to the next - see voko comment). It will also agree with the average bounce ratio you determined by averaging the values from all the cases.
 

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