Rebound Height vs Air Pressure: A Puzzling Relationship

In summary, the conversation discusses the relationship between air pressure and rebound height in a basketball. The question is raised as to why the graph of rebound height vs air pressure does not have a line of best fit through the origin. It is noted that a basketball's bounce can be compared to a mass-spring system, but it is not directly proportional to air pressure. The conversation also touches on the potential impact of the coefficient of restitution and personal experiences with partially inflated balls. The conversation concludes with a request for more information and data on the subject.
  • #1
innocentasker
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OP tried to delete his post and the thread title, but they have been restored by the Mentors
TL;DR 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?
 
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  • #2
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.
 
  • #3
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
 
  • #4
innocentasker said:
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. :smile:

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...

1643124498616.png

https://www.istockphoto.com/photo/flat-basketball-isolated-gm182481240-11881459
 
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  • #5
innocentasker said:
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.
 
  • #7
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...
 
  • #8
is this what you mean? i think its a logarithmic fit but i don't understand why
1643126380865.png

PeroK said:
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.
 
  • #9
innocentasker said:
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! :smile:
 
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  • #10
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! :smile:
 
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  • #11
innocentasker said:
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.
 
Last edited:
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Likes vanhees71, gmax137 and russ_watters

1. What is the relationship between rebound height and air pressure?

The relationship between rebound height and air pressure is an inverse one. This means that as air pressure increases, rebound height decreases and vice versa. This relationship is known as Boyle's Law.

2. Why does air pressure affect rebound height?

Air pressure affects rebound height because it determines the amount of air molecules present inside the ball. When air pressure is high, there are more air molecules inside the ball, making it harder for the ball to compress and resulting in a lower rebound height.

3. How does temperature affect the rebound height vs air pressure relationship?

Temperature also plays a role in this relationship. As temperature increases, air molecules inside the ball gain more energy and move around more, resulting in an increase in air pressure. This means that at higher temperatures, the ball will have a lower rebound height compared to when it is at a lower temperature.

4. Is there a limit to how high or low the rebound height can be affected by air pressure?

Yes, there is a limit to how much air pressure can affect rebound height. This limit is determined by the elasticity of the ball and the amount of air inside it. If the air pressure is too low, the ball will become too soft and will not be able to bounce at all. On the other hand, if the air pressure is too high, the ball may burst due to the pressure being too much for the elasticity of the ball to handle.

5. How can the relationship between rebound height and air pressure be useful?

The relationship between rebound height and air pressure can be useful in various applications, such as in sports where the performance of a ball is important. By understanding this relationship, manufacturers can design balls with the optimal air pressure to achieve the desired rebound height. It can also be used in scientific experiments to study the properties of gases and their behavior under different pressures.

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