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P=F/A IS A BASIC FORMULA FOR MECHANICAL DESIGN.

P*A=F,
WHERE F=Force
(measurements of force:
1 dyne = 10-5 newtons
1 kgf (kilopond kp) = 9.80665 newtons
1 metric slug = 9.80665 kg
1 lbf = 32.174 poundals
1 slug = 32.174 lb
1 kgf = 2.2046 lbf )
P/A IS NOT VALID.

2007-01-25 20:05:39 · answer #1 · answered by Anonymous · 4 0

I'm not completely sure what you're asking, but here goes anyway: If you know that the radius is one/half the diameter, or r = D/2 you can just plug this into the equation for area given the radius: A = PI * r**2 or A = PI * (D/2)**2 squaring D/2 gives A = PI * D**2/4 If you need to actually prove that the area of a circle is A = PI * r**2, You can do it using what is called an integral. You have to start by measuring angles in radians, not degrees, and assume that 360 degrees = 2* PI radians That is, there are 2 *PI radians in a circle of 360 degrees. Now take a small triangle which has two sides of length r, the radius of your circle. Define "alpha" as the angle between the two sides, measured in radians. By the definition of what a radian is, the length of the third side is just one of the two sides (r) times an angle of one radian in size (alpha) or Base = r * alpha The area of such a traingle is one half the base times the height, or Area = 1/2 * Base * r Substituting for "Base" gives Area = 1/2 * (r * alpha) * r Combining r terms gives Area = 1/2 * alpha * r**2 Subsituting the size of alpha as 1 radian gives Area = 1/2 * (1) * r**2 or Area of triangle = 1/2 * r**2 Now add up the areas of all of these triangles it takes to fill up your circle. Start by placing the first triangle in the circle with the "top" of the triangle (where the two sides of length r come to a point) on the center. Now add another triangle right next to it, with its point on the center of the circle, and keep going until you have added triangles all the way "around" the circle and are back at the first triangle. You've effectively "swept out the area", or "taken the integral" of a circle from 0 to 2*PI radians. Now add up all the areas of the traingles. Since there are 2*PI radians in a circle, the total area of all the triangles is Area of circle = 2*PI * 1/2 * r**2 the "2" terms cancel to give Area of circle = PI * r**2 Obviously this is a self-referencing proof, because it only works if you define an angle of 1 radian to be 1/(2*PI) of a circle; but it's valid as long as you're consistent in your use of the definition of the radian in all applicable branches of Cartesian geometry and trigonometry.

2016-05-24 00:09:38 · answer #2 · answered by ? 4 · 0 0

It is common in structural engineering for P to represent the load and A as the effective area carrying the load.

When expressed that you have force/ unit area which is pressure or if a structural or mechanics of materials application would be stress which is also expressed as force / unit area.

2007-01-25 13:04:24 · answer #3 · answered by Roadkill 6 · 0 0

If a bar is under tension or compression, Load applied is "P" and the cross-sectional area of bar is "A".
Then Normal stress= P/A.

2007-01-27 00:22:40 · answer #4 · answered by Krishna 1 · 1 0

i think you mean P x A, which equals force.

(pressure = force / area)

2007-01-25 12:39:17 · answer #5 · answered by Critical Mass 4 · 0 0

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