A tank contains mercury, whose density is 13 600 kg/m3. Find the force exerted by the mercury on a circular plug at the bottom of the tank. The plug has a diameter of 2.54 cm, and is located 37.6 cm below the surface of the mercury.
volume of cylinder above the plug
V=AreaPlug*heightmercury (note volume in cm^3)
change volume to meters cubed
Vm^3=V/1E6
now the weight of the mercury in that cylinder is density*g*volume
force=that weight
To find the force exerted by the mercury on the circular plug at the bottom of the tank, we can use the concept of pressure.
Pressure is defined as the force exerted per unit area. The formula for pressure is:
Pressure = Force / Area
In this case, the force exerted by the mercury can be calculated by multiplying the pressure exerted by the bottom of the tank (due to the weight of the mercury) by the area of the circular plug.
Step 1: Calculate the pressure exerted by the bottom of the tank:
The pressure exerted by a fluid at a certain depth can be found using the formula:
Pressure = Density * Gravity * Depth
Here, the density of mercury (ρ) is given as 13,600 kg/m^3. The acceleration due to gravity (g) is approximately 9.8 m/s^2. And the depth (h) is given as 37.6 cm, which is equal to 0.376 m.
So, the pressure exerted by the bottom of the tank is:
Pressure = 13,600 kg/m^3 * 9.8 m/s^2 * 0.376 m
Step 2: Calculate the area of the circular plug:
The area of a circular plug can be calculated using the formula:
Area = π * (radius)^2
The diameter of the plug is given as 2.54 cm, which is equal to 0.0254 m. Therefore, the radius is half of the diameter, which is 0.0127 m.
So, the area of the circular plug is:
Area = π * (0.0127 m)^2
Step 3: Calculate the force exerted by the mercury:
Now, we can calculate the force exerted by the mercury on the circular plug by multiplying the pressure exerted by the bottom of the tank by the area of the circular plug.
Force = Pressure * Area
Substituting the values:
Force = (13,600 kg/m^3 * 9.8 m/s^2 * 0.376 m) * (π * (0.0127 m)^2)