A mass that has a density of 6.50 x 10 2 kg/m 3 is placed in a container filled

Question

A mass that has a density of 6.50 x 102kg/m3 is placed in a container filled with water. The mass has a length of .500m, a width of .500m and a height of.250m. Assume that the density of water is of 1.00 x103 kg/m3 and find the following: a) Find the masses percentage of the volume that is submergedin the water. b) Another mass with a volume of .0146m3 is placedon top of the original mass. Find the density of the secondmass that would cause the original mass to be completely submergedin the water.

Explanation / Answer

Let the fraction of volume submerged is f from archimedis principle we have Vf*1000=V*650 hence f=0.65 the weight of the mass added should be equal to the difference between the buoyancy force when fully submerged-weightof the block volume of the block=0.0625m3 so the weight of mass added is0.0625m3*1000*9.8-650*0.0625*9.8=214.375N mass=21.875kg density=21.875kg/0.0146=1498kg/m3

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