I need a formula for bouncing balls

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    Balls Formula
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Homework Help Overview

The original poster is investigating the relationship between the height from which a ball is dropped and the height to which it bounces back. The context involves measuring bounce heights under the influence of gravity, with specific data collected from various drop heights.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the possibility of deriving an empirical formula based on the collected data. There is uncertainty regarding the requirements of the task, with some questioning whether a specific equation is needed or if a general understanding of the bouncing behavior suffices. Others suggest methods for analyzing the data, such as plotting it to identify trends.

Discussion Status

The discussion is ongoing, with various suggestions being offered, including the idea of finding a fixed percentage of energy loss and using graphical analysis to determine a bounce ratio. There is no explicit consensus on a single approach, but multiple avenues for exploration are being considered.

Contextual Notes

Participants note that the behavior of the ball may be influenced by factors such as material properties and air resistance, which complicates the formulation of a straightforward equation. The original poster's teacher's instructions are described as vague, adding to the uncertainty in the discussion.

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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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