Question

A wood cube of volume 0.200 cubic meters floats with 30% of its volume above fresh water. How big is the buoyant force

Answer 1

Given that volume of wooden cube is 0.200 cubic meters

Since 30% of its volume is above fresh water that means 70% of its volume would be inside fresh water.

Now whatever is the volume of body inside water an equal volume of fresh water is displaced by it.

i.e. 70% of 0.200= 0.140 cubic meters

Now we can calculate the buoyant force acting on the wooden block using Archimedes' Principle that states:

"The upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces."

Now weight of water displaced can be calculated using mass of water displaced which can be calculated using density equation

Where stands for density of the substance

Since they have given the liquid displaced is fresh water so =1000 kg/cubic meter

therefore mass= *Volume

mass = 1000*0.140

=140 kg

Now weight of the displaced water can be calculated using equation

W = m*g

W=140*9.81

W= 1373.4 N

Hence weight of liquid displaced which also gives measure of buoyant force acting is 1373.4 N