If in a manufacturing company they want to produce a system where the force F1 must be 10% of the output force F2.if the area of the pistol (where F1 is applied)is 450 spuare milimetre.calculate the diameter of the pistol two where F2 is an output force
To calculate the diameter of the piston where F2 is the output force, we need to understand the relationship between force and area in a hydraulic system.
In a hydraulic system, the force is directly proportional to the pressure, and the pressure is inversely proportional to the area. Mathematically, this can be expressed as:
Force = Pressure x Area
In this case, we know that F1 must be 10% of F2. Therefore, we can express it as:
F1 = 0.1 x F2
We also know the area of the piston where F1 is applied is 450 square millimeters. Let's call the diameter of this piston D1, and the diameter of the piston where F2 is applied D2.
The area of a circle is calculated using the formula:
Area = π x (radius)^2
To find the diameter, we need to rearrange the formula:
Diameter = 2 x radius
Let's start solving for the diameter of the second piston:
1. Calculate the area of the first piston:
Area1 = 450 square millimeters
2. Calculate the radius of the first piston:
Area1 = π x (radius1)^2
(radius1)^2 = Area1 / π
radius1 = sqrt(Area1 / π)
3. Calculate the force ratio:
F1 / F2 = 0.1
F1 = Pressure1 x Area1
F2 = Pressure2 x Area2
Since we know the force ratio, we can express Pressure1 in terms of Pressure2:
Pressure1 = Pressure2 / 0.1
4. Calculate the area of the second piston using the force ratio:
Area2 = F2 / Pressure2
5. Calculate the radius of the second piston:
Area2 = π x (radius2)^2
(radius2)^2 = Area2 / π
radius2 = sqrt(Area2 / π)
6. Calculate the diameter of the second piston:
Diameter2 = 2 x radius2
By following these steps, you can calculate the diameter of the second piston where F2 is the output force. Substitute the known values into the equations to get the final result.