Young modulus diameter question

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Discussion Overview

The discussion revolves around calculating the diameter of a steel cable required to suspend a passenger lift, given specific parameters such as mass, stress, and gravitational acceleration. The focus is on applying the formula for stress and understanding the relationship between force, area, and diameter in a mechanical engineering context.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem of calculating the diameter of a steel cable using the mass of the lift and the stress value provided.
  • Another participant seeks clarification on the meaning of the symbol σ and the load on the cable, indicating a need for understanding stress in this context.
  • A participant outlines the formula for stress (σ=F/A) and attempts to calculate the area needed for the cable, expressing confusion about unit conversions.
  • Further calculations are presented, including the conversion of mass to force using gravitational acceleration, but there is uncertainty about the correctness of the units used in the calculations.
  • One participant corrects another regarding the conversion of mass to force, emphasizing the importance of the gravitational field value used in the calculations.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the calculations, as there are differing interpretations of the gravitational field value and its impact on the force calculation. The discussion remains unresolved regarding the correct approach to determining the diameter of the cable.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about gravitational acceleration and the potential confusion in unit conversions, which have not been fully addressed.

steb4242
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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
 
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Hi steb4242, welcome to PF. What does the symbol σ represent? What is the load on the cable? How about the stress?
 
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?
 
This is fine. What is the relationship between N and kg m s-2?
 
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
 
Last edited:
steb4242 said:
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 [itex]F=ma[/itex] 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?
 

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