College

An air cylinder has a 2-inch bore and a 1-inch rod. Air is available at 100 psig. What is the maximum extension and retraction force available from the cylinder?

A. 200 lb., 78 lb.
B. 100 lb., 100 lb.
C. 314 lb., 235 lb.
D. 314 lb., 200 lb.

Answer :

To solve the problem of finding the maximum extension and retraction force available from an air cylinder, we need to follow these steps:

1. Calculate the Bore Area:
- The bore of the cylinder is like the circular area where the piston moves. The formula for the area of a circle is [tex]\( \text{Area} = \pi \times (\text{radius})^2 \)[/tex].
- The bore diameter is given as 2 inches, so the radius is [tex]\( \frac{2}{2} = 1 \)[/tex] inch.
- Therefore, the bore area is [tex]\( \pi \times (1)^2 = 3.1416 \)[/tex] square inches (considering [tex]\(\pi \approx 3.1416\)[/tex]).

2. Calculate the Rod Area:
- The rod is also round but smaller, with a diameter of 1 inch. Therefore, its radius is [tex]\( \frac{1}{2} = 0.5 \)[/tex] inches.
- Using the same area formula, the rod area is [tex]\( \pi \times (0.5)^2 = 0.7854 \)[/tex] square inches.

3. Calculate the Extension Force:
- The extension force is simply the force exerted on the entire bore area.
- Given that the air pressure available is 100 psig (pounds per square inch gauge), the extension force is calculated as:
[tex]\[
\text{Extension Force} = 100 \, \text{psig} \times 3.1416 \, \text{square inches} = 314.16 \, \text{pounds}
\][/tex]

4. Calculate the Retraction Force:
- Retraction involves the movement of the rod as well, so we need to subtract the rod area from the bore area for the effective area.
- Therefore, the effective area for retraction is [tex]\( 3.1416 - 0.7854 = 2.3562 \)[/tex] square inches.
- Thus, the retraction force is:
[tex]\[
\text{Retraction Force} = 100 \, \text{psig} \times 2.3562 \, \text{square inches} = 235.62 \, \text{pounds}
\][/tex]

Therefore, the maximum extension and retraction forces available from the cylinder are approximately 314 pounds and 236 pounds, respectively.