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marin [14]
2 years ago
7

A pneumatic system is producing 75 lb/in2 of gauge pressure. A cylinder is needed to press an adhesive label onto a product. It

has been determined that 4 lb of force is optimal to complete this task. What is the required diameter of the pneumatic cylinder? Assume standard atmospheric pressure (14.7 psi).
_____ in
(Precision - 0.00)

​

Mathematics
1 answer:
kolbaska11 [484]2 years ago
8 0

The area of the cylinder required for a given pressure is directly

proportional to the applied force.

<h3>The correct response;</h3>
  • The required diameter of the cylinder is approximately <u>0.26 inches</u>

<h3>Method by which the diameter is found:</h3><h3>Given parameters;</h3>

The gauge pressure produced by the pneumatic system, P = 75 lb/in²

The force required to complete the given task, F = 4 lb.

<h3>Required parameter; </h3>

The diameter of the pneumatic cylinder.

<h3>Solution:</h3><h3>Derivation of the formula for area;</h3>

\displaystyle Pressure, \, P = \mathbf{\frac{Force, \, F}{Area, \, A}}

Therefore;

\displaystyle  Area, \, A= \mathbf{\frac{Force, \, F}{Pressure, \, P}}

<h3>Plugging in the given values to determine the area of the cylinder;</h3>

\displaystyle  Area, \, A= \frac{4 \, lb}{75 \, lb/in^2} = \frac{4}{75} \, in.^2

<h3>Determining the diameter of the cylinder;</h3>

A = π·r²

\displaystyle r = \sqrt{ \frac{A}{\pi} }

\displaystyle r = \sqrt{\frac{4}{75 \cdot \pi} }  \approx 0.13

The required diameter, d = 2 × r

Therefore;

d ≈ 2 × 0.13 = 0.26

  • The required diameter, d ≈ <u>0.26 inches</u>

Learn more about the formula for pressure here:

brainly.com/question/13373498

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