Question

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?

Answer 1

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

$\sigma =\frac{My}{l}$

As per the dimensional analysis

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

So the equation becomes

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

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

Part b

$\sigma =\frac{My}{l}\\\sigma =\frac{2000 \times 0.1}{7 \times 10^{-5}}\\\sigma =2857142.857 \, Pa$

Pressure in US customary base units is given in psi so

$1 Pa =1.45 \times 10^{-4}$

So

$\sigma =2857142.857 \times 1.45 \times 10^{-4} psi\\\sigma =414.28 psi$

So the pressure is 414.28 psi.