Initial height of a bouncing ball and energy lost

[tink7718]

I am doing a lab in my senior physics class (IB HL Physics 3-4) and I am very confused about a relationship that I found. For my experiment I dropped a racquetball from different heights and then used video analysis to find the height of the ball on its final bounce. I used this data to calculate the initial and final gravitational potential energy and then found the difference between these value to find the energy lost during the ball's bouncing. I graphed the initial height (x) and the difference in energy (y). I had a perfectly linearly correlated graph (r value of 1) with an equation of E=0.379h-0.006. Because the equation is so correlated I feel like there must be a relationship between these two variables, but I am yet to find it.

Can anyone help with this?

Thank you!

 

[Simon Bridge]

Well your relationship is the equation of the line.
But it may help understand what you've discovered if you look up "coefficient of restitution".

 

[tink7718]

Well your relationship is the equation of the line.
But it may help understand what you've discovered if you look up "coefficient of restitution".

For our labs we have to equate the equation we found for our graphs to one that we learned in class. I looked up the coefficient of restitution, but saw that it related more to kinetic energy and velocity than to potential energy and height. Does it relate to GPE as well?

 

[Simon Bridge]

The coefficient of restitution gives initial kinetic energy after the bounce... this will be related to the final potential energy. Hint: conservation laws.

However, the project suggests you are supposed to have learned something in class related to this.
Since I wasn't there, I don't know what you are supposed to have learned.
You should check you class material to see if anything stands out... it may be indirect.