A hollow cubical box is 0.30 meters on an edge. This box is floating in a lake with 1/3 of its height beneath the surface. The walls of the box have a negligible thickness. Water is poured into the box. What is the depth of the water in the box at the instant the box begins to sink?
The answer from the book that i got the problem from is 0.2 meters.
buoyancy force = (density of the water)(volume of displaced water)(gravity)
The Attempt at a Solution
First I did the buoyancy force, which i think is: (1000 kg/m^3)(1/3)(0.3)^3 m^3)(9.8 m/s^2) = 88.2 N.
But what I don't get is, if the walls of the box have negligible thickness, wouldn't that mean the mass of the box is basically zero? So how can the box even have 1/3 of its volume in the water when it has no weight?
Also if the buoyancy force is 88.2 N just holding the box in equilibirium, wouldn't that mean the box weighs 88.2 N...
Any help at all would be really appreciated..!