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.
The answer is 25.4 N but I don't know how to go through and get find this.
I really need help with this question please
To find the force exerted by the mercury on the circular plug at the bottom of the tank, you can use the formula for pressure:
Pressure = Force / Area
The pressure exerted by a fluid at a certain depth is given by the equation:
Pressure = Density x Gravity x Height
In this case, the density of mercury is given as 13,600 kg/m3, the acceleration due to gravity is approximately 9.8 m/s2, and the height of the fluid column is given as 37.6 cm.
To find the force, we need to calculate the pressure at the bottom of the tank using the formula above. First, we need to convert the units of height and diameter to meters.
Height = 37.6 cm = 0.376 m
Diameter = 2.54 cm = 0.0254 m
Now let's calculate the pressure at the bottom of the tank:
Pressure = Density x Gravity x Height
= 13,600 kg/m^3 x 9.8 m/s^2 x 0.376 m
= 49,913.6 Pa
Since we have the pressure, we can now calculate the force using the formula:
Force = Pressure x Area
The area of the circular plug can be calculated using the formula:
Area = π x (radius)^2
The radius is half of the diameter, so:
Radius = 0.0254 m / 2 = 0.0127 m
Now we can calculate the area:
Area = π x (0.0127 m)^2
= π x (0.0127^2) m^2
= 0.000508075 m^2
Now, we can calculate the force:
Force = Pressure x Area
= 49,913.6 Pa x 0.000508075 m^2
= 25.37711 N
Rounding to the appropriate number of significant figures, the force exerted by the mercury on the circular plug at the bottom of the tank is approximately 25.4 N.