# Problem: Minimum Pressure

What would be the minimum pressure required to hold the given load on the pneumatic cylinder?

Think you know the answer? Submit it at http://ifps.org/docs/education_training/fluid_power_math_teaser/answer.aspx

**Special thanks to Chad Grimmer, who suggested this Air Teaser. *

##### See the Solution

This problem has a clockwise moment (torque) that is equal to the CCW moment. We call this a “state of equilibrium.” The CW moment can be calculated figuring the perpendicular distance to its force. If we made a triangle with the 500 lbs. being the opposite side, and the 144″ is the hypotenuse side of a triangle, we can use the cosine to determine the horizontal perpendicular distance to the load back to the pivot. (See diagram “A”.) Cosine of 45° = adjacent / hypotenuse. Cosine of 45°x 144″ = 101.8″. Our CW moment (torque) is now 101.8″ x 500 lbs. = 50,911.6 lb. inches.

Now for the reaction (cylinder force), we need to find the CCW moment. Looking a diagram “B”, I have drawn a triangle representing a perpendicular distance to the center of the cylinder back to the pivot point. The triangle that we are looking at has the opposite side of a 35°angle. This time we will use the sine function because we have the opposite side and the hypotenuse. Sine of 35° x 72″ = a perpendicular distance of 41.3″. Our CCW moment is 41.3″ x F(unknown force). Now we are ready to write our equilibrium equation where the CCW moment = the CW moment. Note that our cylinder force is our only unknown and I called it “F”. Remember that a moment is a force and a perpendicular distance. Therefore 101.8″ x 500 lbs. = 41.3″ x F (lbs.). F = 101.8 x 500 / 41.3

F = 1232.4 lbs. on our cylinder.

Now we need calculate the cylinder pressure with F = P x A. A = D²x .7854, A = 4²x .7854 or 12.566.

1232.4 / 12.566 = **98 PSI**

### Deadline past. Not available for submissions.

*Winner:*

**Harry Pawluk, Jr., **Hanco, Ltd, Ardara, PA

By Ernie Parker, AI, AJPP, AJPPCC, S, MT, MM, MIH, MIP, MMH, Fluid Power Instructor, Hennepin Technical College, EParker@Hennepintech.edu

This teaser is printed in the *Fluid Power Journal.* Those who submit the correct answer before the deadline will have their names printed in the *Society Page* newsletter and in *Fluid Power Journal.* The winners will also be entered into a drawing for a special gift.