A lead brick with volume of 7*10^-4m^3 is floating in bath of liquid mercury. 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?
To find the fraction of the lead brick's volume that is above the surface of mercury, we need to find the volume of the portion of the brick that is submerged in mercury and then compare it to the total volume of the brick.
Given information:
Volume of the lead brick (V_brick) = 7 * 10^-4 m^3
To solve for the fraction, we need to find the volume of the portion submerged in mercury, which is equal to the volume of the brick minus the volume above the surface of the mercury.
Since the brick is floating, the buoyant force acting on it is equal to the weight of the liquid displaced by the brick. This can be found using Archimedes' principle:
Buoyant force (F_buoyant) = weight of liquid displaced
The specific density of mercury (ρ_mercury) is 13.6 g/cm^3, or 1.36 * 10^4 kg/m^3.
The weight of the liquid displaced is equal to the weight of the brick.
Weight (W) = mass (m) * gravity (g)
Where:
m = density (ρ_brick) * volume (V_brick)
g = acceleration due to gravity (approximately 9.8 m/s^2)
Assuming the brick has a uniform density, its density (ρ_brick) can be found using the equation:
ρ_brick = mass / volume
= density * volume / volume
= density
Therefore, ρ_brick = ρ_mercury = 1.36 * 10^4 kg/m^3.
Now, we can calculate the weight of the brick and the buoyant force:
W = ρ_brick * V_brick * g
F_buoyant = W
To find the volume of the portion submerged in mercury (V_submerged), we can use the equation:
V_submerged = V_brick - F_buoyant / ρ_mercury
Now, we can calculate the fraction of the lead brick's volume above the surface of mercury (V_above_surface):
V_above_surface = V_submerged / V_brick
To calculate the force required to hold the lead brick below the mercury surface, we need the weight of the portion submerged in mercury.
Weight submerged = ρ_mercury * V_submerged * g
Therefore, the force required to hold the lead brick below the mercury surface is equal to the weight of the submerged portion.
To summarize the steps:
1. Calculate the weight of the brick (W = ρ_brick * V_brick * g).
2. Calculate the buoyant force (F_buoyant = W).
3. Calculate the volume of the portion submerged (V_submerged = V_brick - F_buoyant / ρ_mercury).
4. Calculate the fraction of the brick's volume above the surface of mercury (V_above_surface = V_submerged / V_brick).
5. Calculate the force required to hold the brick below the mercury surface (Weight submerged = ρ_mercury * V_submerged * g).