Question

A light fitting of mass 54 kg is suspended from a copper wire 4 mm in diameter. (UTS=415 MPa and E = 112000 MPa) Calculate the stress in the wire. Calculate the factor of safety.

Answer 1

42.17 MPa, 9.83

Step-by-step explanation:

We have given mass m=54 kg

Diameter d =4 mm so radius
`r=(d)/(2)=(4)/(2)=2 mm=2* 10^(-3)m`

UTS = 415 MPa

E =112000

Weight = mg =54×9.81=529.74 N

Area
`A=\pi r^2=3.14* (2* 10^(-3))^2=12.56* 10^(-6)m^2`

We know that
`stress=(load)/(area )=(529.74)/(12.56* 10^(-6))=42.176* 10^6\ N/m^2=42.176MPa`

`factor\ of\ safety=(UTS)/(stress)=(415)/(42.17)=9.83`