The equation sigma = My/l is used in the mechanics of materials to determine normal stresses in beams. When this equation is expressed in terms of SI base units. M is in newton-meters (N-m), y is in meters (m), and l is in meters to the fourth power (m^4). What are the SI units of sigma? If M = 2000 N-m v = 0.1 m, and l = 7 times 10^-5 m^4, what is the value of sigma in U.S. Customary base units?

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danialamin danialamin · Answer 1 · 2020-02-01T15:33:56+01:00

Answer:

Part a : The SI unit of σ is Pascal.

Part b : The pressure is 414.28 psi.

Explanation:

Part a

The equation is given as

[tex]\sigma =\frac{My}{l}[/tex]

As per the dimensional analysis

[tex]M=[N-m]\\y=[m]\\l=[m^4][/tex]

So the equation becomes

[tex]\sigma =\frac{[N-m][m]}{[m^4]}\\\sigma =\frac{[N][m^2]}{[m^4]}\\\sigma =\frac{[N]}{[m^{4-2}]}\\\sigma =\frac{[N]}{[m^{2}]}\\[/tex]

As the dimensions are of pressure so the SI unit of σ is Pascal.

Part b

[tex]\sigma =\frac{My}{l}\\\sigma =\frac{2000 \times 0.1}{7 \times 10^{-5}}\\\sigma =2857142.857 \, Pa[/tex]

Pressure in US customary base units is given in psi so

[tex]1 Pa =1.45 \times 10^{-4}\\[/tex]

So

[tex]\sigma =2857142.857 \times 1.45 \times 10^{-4} psi\\\sigma =414.28 psi[/tex]

So the pressure is 414.28 psi.