# Maxiumum weight a buoy can float [closed]

I have a buoy that can hold 2943.02 cubic millimeters of non-pressurized air, I need and equation to work out the maximum weight that the buoy can float.

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## closed as off topic by Georg, David Z♦May 13 '11 at 20:51

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Well, it depends how heavy the buoy is. –  TonyK May 13 '11 at 12:20
The buoy is 0.8kg but I was hoping that, that could be incorporated into the weight floating. –  Alexander 'Bambi' Sadler May 13 '11 at 12:29
The Buoy is 0.8kg –  Alexander 'Bambi' Sadler May 13 '11 at 12:30
Buoyancy is related to the weight of the volume of material displaced. In your case this means the max weight would be equal to $3943mm^3$ of water, minus the 0.8kg weight of the buoy.. –  qftme May 13 '11 at 12:50
@qftme That volume of "pressurized air" is meaningless. One needs the Volume of the "buoy" (total volume!) –  Georg May 13 '11 at 13:11

The buoyancy is the weight of water displaced. Usually for problems like this we assume 1 g/cm^3 (which is fresh water at 4C). That is the weight it can support, but you have to count its own weight as part of what is supported.

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Seems like a very tiny buoy! Also, the amount of air is given to surprising precision.

As a first (and excellent) approximation, you can assume that air is weightless. Water weighs roughly $1$ gram per cc, you have about $3$ cc of air, so the air can support about $3$ grams.

Not an awful lot, compared to your estimated weight of the buoy.

An important consideration would be the density of the material that the buoy is made of. If it is substantially greater than the density of water, the buoy will sink and support nothing. But if the buoy is bulky and made of material of low density, the solid material of the buoy could contribute a lot more to the buoyancy than the air. Imagine for example a buoy made of very lightweight wood with a tiny $3$ cc bubble of air in the middle. This bubble will contribute virtually nothing to the buoyancy. The "solid" material of the buoy will make a much greater contribution.

Please do check your units. As mentioned above, $2943.02$ cubic millimetres is really really tiny. Do you mean $2943.02$ cc? That would be more realistic, though still smallish. And the density of the "solid" part of the buoy is relevant.

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