A block of wood floats on water. A layer of oil is now poured ontop of the water

Question

A block of wood floats on water. A layer of oil is now poured ontop of the water to a depth that more than covers the block, asshown in the figure below. (a) Is the volume of wood submerged in watergreater than, less than, or the same as before? sameamount of wood is submerged in water as before morewood submerged in water than before lesswood submerged in water than before (b) If 77% of thewood is submerged in water before the oil is added, find thefraction submerged when oil with a density of 735 kg/m^3 covers the block. (Do not neglectthe buoyant force of air before the oil is added.) 2%

Explanation / Answer

same amount of wood is submerged in wateras before
morewood submerged in water than before
less wood submerged in water thanbefore You know that the density of the wood is 0.77g/cc.   And the density of the oil is 0.735 g/cc. Density of water is 1 g/cc. . Also, the forces must be balanced so: .     weight of wood = buoyant forcefrom oil   + buoyant force from water .        0.77 * V *g    =    0.735 * Vo *g     +    1.00 * Vw* g . Where Vo and Vw   are the volumes of oil and waterdisplaced by the block. . Eliminate g everywhere and divide by V, the volume of theblock. You get: .     0.77 =   0.735 *y    +    1.00 *x         . where x = Vw /V        and   y =Vo /V . You are asked to find x, the fraction of the block that is inthe water. And you also know that the two fractions must total toone, so     y = 1 - x    and: .     0.77 = 0.735 ( 1 - x)   +   x    . solving forx:         x =0.132     or    13.2%     of the block is submerged in thewater. You know that the density of the wood is 0.77g/cc.   And the density of the oil is 0.735 g/cc. Density of water is 1 g/cc. . Also, the forces must be balanced so: .     weight of wood = buoyant forcefrom oil   + buoyant force from water .        0.77 * V *g    =    0.735 * Vo *g     +    1.00 * Vw* g . Where Vo and Vw   are the volumes of oil and waterdisplaced by the block. . Eliminate g everywhere and divide by V, the volume of theblock. You get: .     0.77 =   0.735 *y    +    1.00 *x         . where x = Vw /V        and   y =Vo /V . You are asked to find x, the fraction of the block that is inthe water. And you also know that the two fractions must total toone, so     y = 1 - x    and: .     0.77 = 0.735 ( 1 - x)   +   x    . solving forx:         x =0.132     or    13.2%     of the block is submerged in thewater.

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