This is my lab project and i need help in how to start to solve this problem.

Determine the buoyant force on a balloon(filled with air) as a function of depth. At what depth does neutral buoyancy occur.

3 answers

depth of what?

depth of water

first you need to determine the volume of the balloon and the internal pressures. Using those you can use archimedes principle to figure out how much water is displaced and therefore the bouyant force. Then you must determine how much the water pressure will cause the balloon to shrink. Also the "downward" force, the force opposing the bouyant force I believe should be equal to the weight of the column of water above the balloon you therefore need to know the surface area as you look down at the balloon from above to determine the volume of the column pressing down on the balloon.