Bouyant force on a cube floating at the surface between water and oil?

AI Thread Summary
A cube measuring 15 cm is floating at the interface of water and oil, with the oil's density at 810 kg/m3. It is submerged 52% in water and 48% in oil, leading to a calculated buoyant force of 30 N. Using Archimedes' Principle, the mass of the cube is determined to be approximately 3.33 kg. The buoyant force is derived from the combined density of the fluids and the volume of the cube submerged. This analysis illustrates the application of buoyancy principles in mixed fluid scenarios.
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Homework Statement


A cube of 15 cm is floating at the surface between water and oil. The oil has a density of 810 kg/m3. If the cube floats so that it is 52% in water and 48% in the oil, what is the mass of the cube and what is the buoyant force on the cube?


Homework Equations


Archimede's Principle
Fb= densityfluidvfluidg



The Attempt at a Solution


Not sure how to find the mass of the cube when only the height of one side is given?
 
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The cube is displacing it's own weight in oil and water.
it might be simpler to think of it as two (almost ie 0.52/0.48) half cubes immersed in oil and water.
 
fb = (1000*0.52+810*0.48)*0.15^3*9.8
=30 N

mass=fb/g
=30/9=3.33
 
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