You will float a wood block in a container filled with water. Derive a formula p

Question

You will float a wood block in a container filled with water. Derive a formula predicting the percentage of the block submerged. (Hint: This is a problem in fluid statics. The weight of the block must be balanced by the buoyant force). The formula should be expressed as a ratio in terms of the volume of the block, V_block, and the volume of displaced water, V_water. The result should be given in terms of the density of the block, _block, and the density of water, _water.

Explanation / Answer

You will float awood block in a container filled with water. Derive a formula predicting the percentage of the block submerged. (Hint: This is aproblem in fluid statics. The weight of the block must be balanced by thebuoyant force). The formula should be expressed as a ratio in terms of the volumeof the block, V_block, and the volume of displaced water, V_water. Result shouldbe given in terms of the density of the block, _block, and the densityof water, _water. If wood block is floating in water,its weight (due to gravity "g") must be balanced by the buoyant force of displaced water. The latter is given by the weight of displaced water. Further,the volume of displaced water willequal the volume of woodblock submerged: {Weight Of WoodBlock} = {Buoyant Force Of Displaced Water} ---->   {Weight Of WoodBlock} = {Weight Of Displaced Water} ---->  (Mass_block)*g = (Mass_displaced_water)*g ---->   (V_block)*(_block)*g = (V_water)*(_water)*g ---->  (V_block)*(_block) = (V_water)*(_water) ---->  (V_water)/(V_block) = (_block)/(_water) ---->  (V_submerged_block)/(V_block) = (_block)/(_water) ---->  (100)*(V_submerged_block)/(V_block) = (100)*(_block)/(_water) ---->  {PercentBlock Submerged} = (100)*(_block)/(_water) .

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