SOLUTION: Engineers use complex mathematical formulas when designing aircrafts. For example, stringers used in the wing of an air plane must be able to support a certain load. Engineers have

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Question 426518: Engineers use complex mathematical formulas when designing aircrafts. For example, stringers used in the wing of an air plane must be able to support a certain load. Engineers have to use a stringer with the right diameter for the job. Using a smaller size poses a safety hazard. Using a larger size is a waste of material and will result in increased cost to the plane's operator.
Let's assume that the stress S on a rod is given by the formula,
S = (load)/(cross sectional area).
Let's assume that the air plane uses an aluminium rod with diameter 20mm to support a load of 5 x 10^4 Newton. Engineers know that maximum stress on Aluminium is 1 x 10^ 8 Newtons/m^2. How do we determine whether the rod can withstand the load?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The cross sectional area of a rod = %28pi%29r%5E2
Therefore A = %28pi%29%2810%29%5E2+=+314.16 mm^2
Convert the area to square meters: 314.16 mm^2*(1 m/1000 mm)^2 = 3.1416 x 10^-4
We are given S = 1 x 10^8, and L = 5 x 10^4
For the rod to withstand the load, we need the stress to be less than 1 x 10^8
Since S = L/A, we have S = 5 x 10^4/3.1416 x 10^-4 = 1.59 x 10^8 N/m^2.
This value is greater than the maximum stress of 1 x 10^8, so the rod will not withstand the load.