A pipe contains water at 4.80 105 Pa above atmospheric pressure. If you patch a 3.55 mm diameter hole in the pipe with a piece of bubble gum, how much force must it be able to withstand?
To calculate the force that the bubble gum must be able to withstand, you need to use the concept of pressure, which is defined as force per unit area. Here's how you can find the required force:
1. Start by calculating the area of the hole using the formula for the area of a circle:
Area = π * (radius)²
Given that the diameter of the hole is 3.55 mm, the radius (r) can be calculated as:
radius = diameter / 2 = 3.55 mm / 2 = 1.775 mm
Convert the radius to meters by dividing it by 1000 (1 mm = 0.001 m):
radius = 1.775 mm / 1000 = 0.001775 m
Now, calculate the area of the hole:
Area = π * (0.001775 m)²
2. Next, calculate the pressure difference between the water inside the pipe and atmospheric pressure. Given that the water pressure is 4.80 * 10^5 Pa above atmospheric pressure, subtract the atmospheric pressure (approximately 1.013 * 10^5 Pa) from it:
Pressure difference = 4.80 * 10^5 Pa - 1.013 * 10^5 Pa
3. Finally, calculate the force using the formula:
Force = Pressure difference * Area
Insert the values into the formula:
Force = (4.80 * 10^5 Pa - 1.013 * 10^5 Pa) * Area
Substitute the value of the area calculated previously.
Force = (4.80 * 10^5 Pa - 1.013 * 10^5 Pa) * π * (0.001775 m)²
Now, you can solve this equation to find the force the bubble gum must withstand.
To determine the force the bubble gum must be able to withstand, we can use the equation for pressure:
Pressure = Force / Area
We can rearrange this equation to solve for the force:
Force = Pressure x Area
First, let's calculate the area of the hole using the diameter given:
Radius = Diameter / 2 = 3.55 mm / 2 = 1.775 mm = 0.001775 m
Area = π x (Radius)²
Area = π x (0.001775 m)² = 9.8927 x 10^(-7) m²
Now we can calculate the force:
Force = Pressure x Area
Given Pressure = 4.80 x 10^5 Pa (above atmospheric pressure)
Force = (4.80 x 10^5 Pa) x (9.8927 x 10^(-7) m²)
Force = 4.74 N
Therefore, the bubble gum must be able to withstand a force of 4.74 Newtons.