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Q & A: pressure and buoyancy

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Most recent answer: 10/22/2007
Q:
Hello! Im doing a project on air pressure and was wondering how the amount of air pressure in a basketball affects its buoyancy??
- Jennifer (age 16)
Stanton College Preparatory School, Jacksonville, Florida
A:
Hi Jennifer- This should be a pretty easy experiment to do, since all you need is a pump, a basketball, and a tub of water. Here's what I bet you'll find.
If the pressure inside the ball is just the same as the outside (atmospheric) pressure, the ball can be either fully inflated to a sphere or only partly inflated. Since it's only the air part inside that's lignter than water, you'll find that the ball is more buoyant if it's fully inflated. By that I mean that a higher fraction of the ball's volume will float above water. I bet if you squish too much air out of the ball, it may sink. (it depends on whether the rubber, leather, and other ingredients of the basketball are lighter than water or not).

Now we get more to the part you were asking about. What happens if you pump up a fully inflated ball from say one atmosphere of pressure to about two atmospheres of pressure? Ordinary air at ordinary pressure weighs a little more than one gram per liter (a thousand cubic centimeters). A basketball looks like it holds about 10 liters. (You can measure that by pushing the ball under water and seeing how much it displaces.) So that would be around 10 grams of air. If you double the pressure at room temeperature, you have twice as much air inside, or another 10 grams or so. The buoyancy will go down a little.
Archimedes figured out that the volume of the ball below the water line is just big enough to hold enough water weigh as much as the ball weighs. So the ball would sink just enough to make part below water pick up about 10 cubic centimeters of volume, since the density of water is one gram per cubic centimeter. That means the ball will sink a small fraction of a millimeter, because the area of the water-level slice of the ball is hundreds of square centimeters. (The volume change is the height change times that area.) Observing that will be hard, because when you increase the pressure much the ball starts to expand a little too. My guess is that it will be very hard for you to see the effect of the extra pressure on the ball's buoyancy. If you had a very rigid tank and could pressurize it to many times atmospheric pressure, then the effect would be easier to see.

Alternatively, you could push the ball into the water with a scale that you don't mind if it gets wet or not, and measure the upward force just when the ball is fully submerged. It should be about ten grams' worth of force less than the force of the less-inflated ball (if your scale is that accurate). It is much easier however just to weigh the ball with different amounts of air in it when it is dry.

Mike

(published on 10/22/2007)

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