The area of the cylinder required for a given pressure is directly
proportional to the applied force.
The correct response;
- The required diameter of the cylinder is approximately 0.26 inches
Method by which the diameter is found:
Given parameters;
The gauge pressure produced by the pneumatic system, P = 75 lb/in²
The force required to complete the given task, F = 4 lb.
Required parameter;
The diameter of the pneumatic cylinder.
Solution:
Derivation of the formula for area;
[tex]\displaystyle Pressure, \, P = \mathbf{\frac{Force, \, F}{Area, \, A}}[/tex]
Therefore;
[tex]\displaystyle Area, \, A= \mathbf{\frac{Force, \, F}{Pressure, \, P}}[/tex]
Plugging in the given values to determine the area of the cylinder;
[tex]\displaystyle Area, \, A= \frac{4 \, lb}{75 \, lb/in^2} = \frac{4}{75} \, in.^2[/tex]
Determining the diameter of the cylinder;
A = π·r²
[tex]\displaystyle r = \sqrt{ \frac{A}{\pi} }[/tex]
[tex]\displaystyle r = \sqrt{\frac{4}{75 \cdot \pi} } \approx 0.13[/tex]
The required diameter, d = 2 × r
Therefore;
d ≈ 2 × 0.13 = 0.26
- The required diameter, d ≈ 0.26 inches
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