Connection between Pressure, Surface Density and Height?

[Whtbrd]

[Mentors' note: moved from technical forums so no template]

Hi All,

Working on a lab write-up, and I need background equations to support the reasoning for my experiment.

To outline briefly, two-part experiment, first part was finding the ideal pressure for a basketball, where I inflated it, dropped it, and used a data-logger to see the height it returned to. This provided me with results that showed 9PSI was ideal, from a test of 8PSI-10PSI (+0.5)

Second part, was using my ideal pressure, dropping the ball on different surfaces, based on their density (g/m^3), this has given me a logarithmic equation, which makes sense, as the higher density, the ball will bounce higher, but won't bounce higher than it started at.

Basically, looking for any supporting equations found by physicists that can prove this should work, particularly for part 2. Guessing it'll look something like displacement=Height/(Pressure, Density), with pressure and density in the denominator.

If anyone has any equations that they think will be helpful, please link to an article on them.

Thanks,

 

[bigfooted]

maybe you can look here for some inspiration:
https://en.wikipedia.org/wiki/Coefficient_of_restitution

 

[haruspex]

dropping the ball on different surfaces, based on their density

How can you be sure they don’t differ in other ways that might be more important? Water is denser than wood, but my guess is it would bounce higher off the wood (depending on temperature).