Buoyancy - how much does this person drink?

[Terrance]

This is my second question here in several months; I sincerely appreciate the people here and their generosity to help others! Any help is greatly appreciated!

We've been given a question and the answer; it's our duty to determine how to solve this problem and get to the given answer.

Q: A partially full beer bottle with interior diameter 52 mm is floating upright in water, as shown below. A drinker takes a swig and replaces the bottle in the water, where it not floats 28 mm higher than before. How much (mass) beer did the drinker drink?

The diagrams are simple. The first one depicts a beer bottle floating in water, while the second one portrays the same beer bottle (but with less liquid inside) floating higher in the same amount of water. It is less submerged.

A: 59g

Now, I've determined certain things myself.

The forces acting on the bottle are Fg (gravity), Fa (opposes gravity). Fg can be calculated by doing Fg = mass of the bottle x gravity, however, we don't know the mass of the bottle. Fg can also be calculated by doing, density of the bottle x surface area of the bottle x gravity.

After this, I get somewhat stuck. It's as if there are missing certain values. If anyone can help me solve this problem, it would be greatly appreciated

 

[Doc Al]

Since the bottle (before and after the swig) floats, what can you say about the buoyant force compared to the weight of the bottle + beer? Also: What's the relationship between buoyant force and the displaced fluid?

Using the above, set up equations for before and after the swig. Then compare the two equations (try subtracting). Hint: What matters is the difference in the quantities before and after the swig. Try it.

 

[Terrance]

Thank you very much! With your help and little more researching and thinking, I've solved my problem!