A 2kg cube of Aluminum is suspended by a rope tied to aballoon which is floating

Question

A 2kg cube of Aluminum is suspended by a rope tied to aballoon which is floating on a fluid of density 1.5x103kg/m3. Assume the balloon has negligible mass.(Al = 2.7x103 kg/m3) What volume of the ballon is submerged in the liquid? Asker's note: rope mass is negligible. Volume of balloon isnot given. Volume/dimensions of aluminum cube is not given. Depthof cube is not given. Any help would be greatly appreciated. Finalexam tomorrow! A 2kg cube of Aluminum is suspended by a rope tied to aballoon which is floating on a fluid of density 1.5x103kg/m3. Assume the balloon has negligible mass.(Al = 2.7x103 kg/m3) What volume of the ballon is submerged in the liquid? Asker's note: rope mass is negligible. Volume of balloon isnot given. Volume/dimensions of aluminum cube is not given. Depthof cube is not given. Any help would be greatly appreciated. Finalexam tomorrow!

Explanation / Answer

Total mass of fluid displaced has to equal the mass of thealuminum. . 2 kg of fluid has a volume of   2kg / 1500kg/m3 =    0.0013333 m3 . The volume of the aluminum is     2 kg /2700   =     0.0007407 m3 . So the aluminum displaces   0.0007407m3 of the fluid, the balloon must displace .       0.0013333 - 0.0007407 =    0.0005926 m3   of the fluid and this isthe volume of balloon submerged . So the aluminum displaces   0.0007407m3 of the fluid, the balloon must displace .       0.0013333 - 0.0007407 =    0.0005926 m3   of the fluid and this isthe volume of balloon submerged

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