a tire inflated to a gauge pressure of 2 bars has a nail 3mm in diameter embedded in it. what is the force tending to push the nail out of the tire?
To determine the force pushing the nail out of the tire, you can use the principle of pressure.
First, let's convert the gauge pressure from bars to Pascals (Pa), since pressure is commonly expressed in Pa.
1 bar = 100,000 Pa
So, the gauge pressure of 2 bars is:
2 bars * 100,000 Pa/bar = 200,000 Pa
Next, let's calculate the area of the circular surface where the nail is embedded:
The radius of the nail is 3mm/2 = 1.5mm = 0.0015m
The area of a circle is given by: Area = π * radius^2
So, the area of the circular surface is:
Area = π * (0.0015m)^2
Now, we can calculate the force pushing the nail out of the tire using the formula:
Force = Pressure * Area
Force = 200,000 Pa * π * (0.0015m)^2
Simplifying the calculation:
Force ≈ 141.37 N
Therefore, the force tending to push the nail out of the tire is approximately 141.37 Newtons.
To determine the force tending to push the nail out of the tire, we need to consider the pressure inside the tire and the area over which the force is distributed.
1. First, let's convert the gauge pressure from bars to Pascals (Pa). 1 bar is equal to 100,000 Pa. Therefore, 2 bars is equal to 200,000 Pa.
2. The force pushing the nail out of the tire can be calculated using the formula:
Force = Pressure × Area
To find the area, we need to determine the surface area of the nail where it is in contact with the tire. Since the nail is cylindrical, we can calculate its area using the formula for the area of a circle:
Area = π × (radius)^2
Given that the diameter of the nail is 3 mm, we can find the radius by dividing it by 2:
Radius = 3 mm ÷ 2 = 1.5 mm = 0.0015 m
Therefore, the area can be calculated as:
Area = π × (0.0015 m)^2
3. Once we know the area, we can calculate the force:
Force = 200,000 Pa × (π × 0.0015 m)^2
Plugging in these values, the force tending to push the nail out of the tire can be calculated.
F=Pressure*area
= 2*10^5(N/m^2)*pi*1.5*10^-6(m^2)
= 3*pi*10^-1 N