Greater the air pressure, higher the ball bounces?

Question

Ok, so I have this ball that I have heated up that is made of an elastic material. Regardless of the material the ball is made of, im really just curious about the air inside it itself.
I understand the rise in temperature will increase the air pressure by giving the particles more kinetic energy thus increasing the force the air exerts on the ball's wall, but my question really is

"would the air pressure have a large enough effect on the rate that the ball changes shape from when it hits the ground to when it bounces back?"

i.e. would an increase in air pressure cause the ball to bounce higher?

Hope someone understands. :)

Answer 1

I think most of us have experienced the effect of an underinflated ball...like a soccer (football) ball or baskeball. It doesn't bounce very high does it? But, when you pump it up ("increase in air pressure") to full recommended pressure, it bounces just fine...up to where you expect it to bounce. I think you can answer your own question here.

As to why more pressure means more bounce, think of a ball as like a spring. When the ball hits the cement (or whatever), it compresses like a spring would compress. It compresses because the ball changes direction (the rebound) and that takes force. When the impact force compresses the ball, it builds up potential energy (PE) in the ball.

Then the ball decompresses (expands) because of that PE and converts the PE into kinetic energy. And that kinetic energy (KE) is what propels the ball back into the air upon rebounding. How much PE and consequent KE is created depends mostly on how much air pressure the ball contains.

Recall the force on a compressed spring is F = k dx; where k is spring constant and dx is the amount of compression from a neutral point. Well, k = F/dx; so for a given dx, the more force generated, the higher k will be. Similar for the ball.

If the ball is at high interior pressure, the force F on the walls will be high. At low pressure, the force f will be low. Therefore, using the spring analogy K = F/dx and k = f/dx for the same depression of the ball's wall upon impact. In other words, like a spring, more force is created on a ball at high pressure than on a ball with low pressure. And more force means the ball will bounce higher than the lower pressure, lower force ball.

Answer 2

Balls with more air will reach the necessary internal pressure faster so that the force needed to push outward on the surface against the weight and impact force of the ball is reached sooner than when there is less air inside the ball. As consequence the higher inflated ball is less deformed when it reaches sufficient force to spring it back upward. And deformation loses a lot of energy through friction and heat. So, bottom line, the more air in a ball reduces the amount of kinetic energy (KE) lost to friction so that it has more kinetic energy than the under-inflated ball to bounce back upward. And, as you well know, the height of the ball on rebounding can be found from h = KE/mg; where h is the max rebound height, m the ball's mass, and g ~ 10 m/sec^2. KE is the kinetic energy the ball has just as it leaves the ground heading upward. There is, of course, a point where the ball will just go splat and lie there if it's really under-inflated. At that point the deformation is so great that there is little force and resulting kinetic energy left to send the ball skyward.

Answer 3

when I was a child, I would inflate the soccer ball to an extend that it bounced back about 2/3 of the height I dropped it from. Too little pressure would cause it to bounce back less. So experimentally, the answer is yes.
As for the theory behind it, I assume a firmer ball spends less time in contact with the ground, as well as bends less, so less heat is generated and more is left for bouncing.
Disclaimer:
I am not sure this is a GENERAL true statement, and there maybe materials that will behave differently.

Answer 4

Ever dribble a basketball that has a slow leak...i rest my case

Answer 5

I agree with your statement.