Rebound Height vs Air Pressure: A Puzzling Relationship

[innocentasker]

TL;DR

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Hi all
I have a very quick question
I'm trying to understand why a graph of Rebound height (m) vs Air Pressure (x axis) doesn't have a line of best fit which goes through the origin.
I understand a basketball's bounce can be compared to the compression of a mass-spring system but then why doesn't it have a directly proportional relationship between its air pressure and rebound height?

 

[PeroK]

Why should it? The maximum rebound height is the height it was dropped from, so it can't reboubd beyond that however high the pressure.

 

[innocentasker]

My apologies i should've framed my question better...i understand that it can't rebound beyond it's drop height but until that height...could you help me understand why air pressure is not directly proportional to the rebound height?
For example..
a 3 psi ball may bounce to 1.5m
And the same ball at 3.5 psi may bounce to 1.8m
But the same ball at 4 psi may bounce to 2.1m

Does it have anything to do with the COR of the ball?
Thanks in advance

 

[berkeman]

I'm trying to understand why a graph of Rebound height (m) vs Air Pressure (x axis) doesn't have a line of best fit which goes through the origin.

Welcome to PF.

Can you post a link to the graph you are referring to? Also, I would think the rebound height would be zero when you get down below about 0.5psi or so -- that's a pretty flat basketball...

https://www.istockphoto.com/photo/flat-basketball-isolated-gm182481240-11881459

 

[PeroK]

could you help me understand why air pressure is not directly proportional to the rebound height?

Why should it be linear? You'd expect the rebound to be zero until it reaches a minimum threshold. Then, I'd expect it to increase quickly over some relatively small range of pressure until it reaches the next threshold, where it is bouncing normally. I'm not sure about the curve here and how close to linear that would be. Then, the curve would flatten out and any further increase would be minimal.

There's no reason for it to be linear.

 

[innocentasker]

Sure!
I've thrown together some random data to illustrate what i mean
see how the line of best fit doesn't go to (0,0)

Welcome to PF.

Can you post a link to the graph you are referring to? Also, I would think the rebound height would be zero when you get down below about 0.5psi or so -- that's a pretty flat basketball...

View attachment 296009
https://www.istockphoto.com/photo/flat-basketball-isolated-gm182481240-11881459

 

[berkeman]

But you don't have any data below 6psi? I'm pretty sure it will drop like a stone and intersect the x-axis before the origin...

 

[innocentasker]

is this what you mean? i think its a logarithmic fit but i don't understand why

Why should it be linear? You'd expect the rebound to be zero until it reaches a minimum threshold. Then, I'd expect it to increase quickly over some relatively small range of pressure until it reaches the next threshold, where it is bouncing normally. I'm not sure about the curve here and how close to linear that would be. Then, the curve would flatten out and any further increase would be minimal.

There's no reason for it to be linear.

 

[PeroK]

is this what you mean? i think its a logarithmic fit but i don't understand whyView attachment 296014

I wouldn't like to guess the shape, but I imagine the height would drop off far more quickly than that.

Why? Exprience of playing football (soccer) as a child. It only took the ball to lose a bit of air pressure for the game to be ruined. A half-inflated ball was no use. It would just flop around.

You youngsters these days probably spent your childhood sitting indoors playing computer soccer where the ball never goes flat!

 

[berkeman]

I did a Google search on basketball rebound height vs pressure and got lots of hits. But I didn't find any experiments that went below about 5-6psi. Maybe you will be the first to plot that data!

 

[berkeman]

Summary:: -

Hi all
I have a very quick question
I'm trying to understand why a graph of Rebound height (m) vs Air Pressure (x axis) doesn't have a line of best fit which goes through the origin.
I understand a basketball's bounce can be compared to the compression of a mass-spring system but then why doesn't it have a directly proportional relationship between its air pressure and rebound height?

Please do not try to delete your OP and the thread title (and your posts!) -- that is usually a sign that a student is trying to cheat on their homework. Your OP and thread title have been restored, and this thread is now locked.