A lead brick with volume of 7*10^-4m^3 is floating in bath of liquid mercury.
a) What fraction of the lead brick’s volume is above the surface of mercury?
A student uses a stick to push the lead brick below the mercury surface so that it is completely submerged. What force is required to hold the lead brick below the mercury surface?
You need to know the specific gravity (or density) of both lead and mercury to answer this question.
Lead has a specific gravity of 11.35, so it is 11.35 times as dense as water. It's density in SI units is
rho1 = 11.35*10^3 kg/m^3
Mercury has a specific gravity of 13.56 and density
rho2 = 13.56*10^3 kg/m^3
The buoyancy force is (rho2)*g*V'
where V' is the displaced volume of mercury. The brick's weight is W = (rho1*g*V)
where V is the volume of the brick.
Setting them equal,
V' = (rho1/rho2)*V = 0.837
The fraction above the surface must be 0.163 or 16.3%
To hold it all beneath the surface, the force required is (rho2 - rho1)*g*V =
2.21*10^3*9.8*7*10^-4 = 15.2 N
Thanks a lot
To answer the first question, we need to determine the fraction of the lead brick's volume that is above the surface of the mercury.
The principle involved here is Archimedes' principle, which states that any object partially or completely submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces.
Since the lead brick is floating in the mercury, it experiences an upward buoyant force equal to its weight. Therefore, the fraction of the lead brick's volume above the mercury surface is equal to the ratio of the buoyant force to the weight of the brick.
Now, let's calculate it step by step:
1. Calculate the weight of the lead brick:
The weight of an object can be calculated using the formula weight = mass x acceleration due to gravity. The mass of the lead brick can be determined using the density formula, density = mass / volume.
Let's assume that the density of lead is 11,340 kg/m^3. Therefore, the mass of the lead brick can be calculated as follows:
mass = density x volume
2. Calculate the buoyant force:
The buoyant force acting on the lead brick is equal to the weight of the fluid (mercury) displaced by the brick. The density of mercury is approximately 13,600 kg/m^3.
The weight of the fluid displaced can be calculated using the formula weight = mass x acceleration due to gravity.
mass_displaced = density_fluid x volume_displaced
3. Calculate the fraction of the lead brick's volume above the mercury surface:
The fraction above the surface can be calculated as follows:
fraction_above_surface = (buoyant_force / weight_of_brick)
To find the force required to hold the lead brick below the mercury surface, you need to calculate the net force acting on the brick. It is the difference between the buoyant force and the weight of the brick.
Now, let's proceed with the calculations:
1. Calculate the weight of the lead brick:
mass = density x volume
mass = 11,340 kg/m^3 x 7 x 10^-4 m^3
Calculate the mass of the lead brick.
2. Calculate the buoyant force:
mass_displaced = density_fluid x volume_displaced
mass_displaced = 13,600 kg/m^3 x 7 x 10^-4 m^3
Calculate the weight of the fluid (mercury) displaced.
3. Calculate the fraction of the lead brick's volume above the mercury surface:
fraction_above_surface = (buoyant_force / weight_of_brick)
Calculate the fraction.
To find the force required to hold the lead brick below the mercury surface, subtract the weight of the lead brick from the buoyant force.
I hope this explanation helps in solving the problem!