a quarter sits at the bottom of a wishing well where the gauge pressure reads 294 kPa. If the quarter has a diameter of 24mm, what is the total force acting on the top surface of the quarter? Note: Atmospheric pressure = 101.3
To find the total force acting on the top surface of the quarter, we first need to calculate the absolute pressure exerted on the quarter at the bottom of the well. Then we can use this absolute pressure along with the quarter's dimensions to determine the force.
Step 1: Calculate the absolute pressure
Absolute pressure is the sum of gauge pressure and atmospheric pressure. Given that the gauge pressure reads 294 kPa and the atmospheric pressure is 101.3 kPa, we can calculate the absolute pressure:
Absolute pressure = Gauge pressure + Atmospheric pressure
Absolute pressure = 294 kPa + 101.3 kPa
Absolute pressure = 395.3 kPa
Step 2: Calculate the area of the quarter's top surface
To calculate the area of the quarter's top surface, we need the diameter of the quarter, which is given as 24 mm. The formula for calculating the area of a circle is:
Area = π * (radius)^2
Since the diameter is given, we can divide it by 2 to get the radius:
Radius = Diameter / 2
Radius = 24 mm / 2
Radius = 12 mm
Now we can plug the radius into the area formula:
Area = π * (12 mm)^2
Step 3: Convert the area to square meters
The area is currently in square millimeters (mm^2), but we need it in square meters (m^2) to be consistent with the pressure unit (Pascals = N/m^2). Since 1 m = 1000 mm, we can convert the area:
Area = (Area in mm^2) / (1000^2)
Step 4: Calculate the total force
Now that we have the absolute pressure and the area, we can calculate the total force exerted on the top surface of the quarter using the formula:
Force = Pressure * Area
Plugging in the values:
Force = (395.3 kPa) * (Area m^2)
After following these steps, you should have the solution to the problem.