2. A piece of wood has a mass of 20 g and when placed in water it floats. That i

ID: 1342635 • Letter: 2

Question

2. A piece of wood has a mass of 20 g and when placed in water it floats. That is, if totally

immersed its buoyant force is more than enough to overcome its weight. Therefore a sinker is

attached to the block of wood. Since only the buoyant force of the wood when totally

immersed is required and not that of the wood and sinker combination, first the sinker is

immersed with the wood out of water as in figure 1 to obtain an apparent mass of 40 g. Then

the water in the container is raised to cover the wood as in figure 2 and the apparent mass is 16g

a) What is the buoyant force on the wood when immersed (show calculations)?

b) What is the specific gravity of the wood (show calculations)?

figure 1 igure 2

a) appranet weight is the net force acting when immersed.

so if actual weight is W and buyoant force F,
then apparent weight is W-F.

apparent weight/acceleration due to gravity=apparent mass

so when the wood is not immersed, apparent mass=40 grams

==>actual weight=0.04*9.8=0.392 N

when the wood is immersed, buyoant force acts and reduces the apparent mass to 16 grams

then apparent weight=0.016*9.8=0.1568 N

then buoyant force=actual weight-apparent weight=0.2352 N

b)let volume of wood be V.

then buyoant force when fully submerged=V*density of water*9.8

=V*1000*9.8=9800*V

as we found out that , buoyant force is 0.2352 N

then 9800*V=0.2352

==>V=24.7578*10^(-6) m^3
hence density of wood=mass/volume=0.02/V=807.823 kg/m^3

hence specific gravity=density of wood/density of water=807.823/1000=0.8078

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