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

Part a : The SI unit of σ is Pascal.

Part b : The pressure is 414.28 psi.

Step-by-step explanation:

Part a

The equation is given as

`\sigma =(My)/(l)`

As per the dimensional analysis

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

So the equation becomes

`\sigma =([N-m][m])/([m^4])\\\sigma =([N][m^2])/([m^4])\\\sigma =([N])/([m^(4-2)])\\\sigma =([N])/([m^(2)])\\`

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

Part b

`\sigma =(My)/(l)\\\sigma =(2000 * 0.1)/(7 * 10^(-5))\\\sigma =2857142.857 \, Pa`

Pressure in US customary base units is given in psi so

`1 Pa =1.45 * 10^(-4)\\`

So

`\sigma =2857142.857 * 1.45 * 10^(-4) psi\\\sigma =414.28 psi`

So the pressure is 414.28 psi.