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.
closed as off topic by Georg, David Zaslavsky♦ May 13 '11 at 20:51
Questions on Physics Stack Exchange are expected to relate to physics within the scope defined in the FAQ. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about closed questions here.
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.
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.
2943 mm^3 equals 2.943 cc. This is the equivalent force of submerging a 0.7 inch diameter ball in water. It will give about 0.002943 kg * (9.8N/kg) of bouyant force in fresh water. You say it weighs 800 grams = 0.800 kg * (9.8N/kg). 0.800 kg is a lot more than 0.002943 kg. Unless the enclosure is built of something less dense than water, this bouy is going to drop like a rock without any load at all.
Perhaps you meant 2943 cc? That is a volume of just under 3 liters, and equates to a sphere of exactly 7 inches diameter. In that case, assuming negligible added volume of the construction material, then your net bouyant force in fresh water will be about (2943 grams - 800 grams)(1kg/1000g)(9.8N/kg) = 2.143 kg * (9.8N/kg) = 21.00N = 4.71 lbs.
To explictly answer your exact question; the equation is:
Net_Bouyant_Force = ((Total_Volume_of_bouy) * (Density_of_displaced_liquid)) - Weight_of_bouy
Make sure you keep your units straight. Density is often given as mass/volume. In the above equation you want to convert to weight/volume.