A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 7.36...

A solid cylinder (radius = 0.150 m, height = 0.120 m) has a mass of 7.36 kg. This cylinder is floating in water. Then oil (ρ = 851 kg/m³) is poured on top of the water until the situation shown in the drawing results. How much of the height of the cylinder is in the oil?

Expert Solution

you need to use Arquimedes :
There is a force that the water and the oil produced to the cylinder, so the weight of the cylinder must be equal to the plus of those two forces :

Force by the water : 1000*9.8*V'
Force by the oil : 851*9.8*V''
V' = Volume of the cylinder in water
V'' = Volume of the cylinder in oil

1000*9.8*V' + 851*9.8*V'' = 7.36*9.8

In other words, the push by the water + the push by the oil must be equal to the weight of the cylinder. Now then : The volumes can be calculated by :

V' = pi*(0.150)^2*a
V'' = pi*(0.150)^2*b

where : a + b = height = 0.12

Replacing on the first equation :
1000*9.8*V' + 851*9.8*V'' = 7.36*9.8
1000V' + 851V' = 7.36
1000*pi*(0.150)^2*a + 851*pi*(0.150)^2*b = 7.36
22,5*pi*a + 19.15*pi*b = 7.36

a + b = 0.12
we need to find "b" , then a = 0.12 - b
8.48 - 70.68b + 60.16*b = 7.36
1.12 = 10.52*b
b = 0.1065 meters
b = height of oil

Hope that helps

genius_generous answered 2 years ago

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