A large, 64.0 kg cubical block of wood with uniform density is floating in a freshwater...
A large, 64.0 kg cubical block of wood with uniform density is floating in a freshwater lake with 20.0% of its volume above the surface of the water. You want to load bricks onto the floating block and then push it horizontally through the water to an island where you are building an outdoor grill.
a) What is the volume of the block?
b) What is the maximum mass of bricks that you can place on the block without causing it to sink below the water surface?
Homework Answers
Bouyancy = rho*submerged volume*g
submerged volume = a^2*x
x=0.8a as 20%is above water
submerged volume = 0.8a^3
balancing weight and buoyancy
mg = rho*0.8a^3 g
a^3 = 64/800
a = 0.43m
(b) for fully submerged body buoyancy generated = rho*a^3*g = 80g
hence 80-64 = 16 kg of bricks can be carried before sinking
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