Young modulus diameter question

[steb4242]

I have started a home study course in mechanical engineering, I now realize that I should have started with a math’s course but any way I have a question that I could do with some help with. A designer wishes to calculate the thickness (diameter) of a steel cable for suspending a passenger lift.
mass=1200kg
σ=1100 MN ¯²
g=10 ms¯²

 

[Mapes]

Hi steb4242, welcome to PF. What does the symbol σ represent? What is the load on the cable? How about the stress?

 

[steb4242]

Hi I have the formula for stress which is σ=F/A the figure given for that is 1100MN m¯² and the force which is 1200kg x 10ms¯² as the formula F= m x g
when i rearange the formula to A=F/σ A=12000Nms¯²/1100MN m¯²
i then get a bit lost as what to with the units to get a figure for the area
if i can get the area of the steel rope i can rearange the formula πr² r=√area/π
am i totally off the mark?

 

[Mapes]

This is fine. What is the relationship between N and kg m s^-2?

 

[steb4242]

hi using 1kg=9.8N i have worked out a figure to 11.67 but i am not sure about the units

σ=12000kgms¯² x 9.8 = 117600 Nms¯²

σ=F/A rearranged A=F/σ

A=117600Nms¯²/1100NM m¯²
A=106.9
πr²=106.9 rearranged r = A/π then √answer
106.9/π =34.03
√34.03 = 5.83
r=5.83 x 2 =11.67
diameter = 11.67

 

[Mapes]

1kg=9.8N

Not quite. A mass of 1 kg corresponds to a downward force of 9.8 N in a gravitational field of 9.8 m s^-2 downward acceleration, because $F=ma$ and 1 N = 1 kg m s^-2. But here you're given a gravitational field of 10 m s^-2. Know what I mean?