How can I calculate the amount of bubbles needed to lift a submerged body?

Question

Our teacher had us come up with our own thermodynamics experiments, so I put a glass of water inside a vacuum-capsule. Inside the glass of water I have placed a non-floating object, a small plastic ball. If I enable the vacuum, the water will begin to develop bubbles of vapor. Those bubbles attach themselves to the plastic ball and it floats.

What I want to figure out now, is how I can approximate the amount of bubbles that are necessary to lift the object. Also, does the vacuum make it easier to lift it, as the pressure on the water surface is lower?

Answer 1

In order for the object to float, the density of the object-bubbles system must fall below the density of water. Therefore you must determine the mass and volume of your object, and the mass of a bubble for every unit of volume. Presumably the vapor bubbles will have much lower density than the surrounding water, so keep adding volume (and minuscule mass) to the volume and mass of your object. Once you have reached the density of water you have reach the floating/nonfloating critical point. Any more vapor bubbles will cause the object to float.