Elastic Support
By Charlie on Apr 18, 2010 in Hearing & Orthepedic
If the elastic limit steel is 5.0 x 10^8.Pa what is the min. diameter a steel?
If the elastic limit steel is 5.0 x 10^8.Pa what is the min. diameter a steel wire can have if it is to support a 70-kg circus performer without its elastic limit being exceeded.
Could someone please help me. Please show how you got the answer that you have gotten? thank you
The magnitude of the force exerted by the acrobat is equal to his weight:
F = m · g
The stress in the rod is equal to force divided by cross sectional area:
σ = F/A = m·g / (π·d²/4) = 4·m·g / (π·d²)
The stress shall not exceed the elastic limit:
σ ≤ σ_max
<=>
4·m·g / (π·d²) ≤ σ_max
<=>
d ≥ √(4·m·g / (π·σ_max)
<=>
d ≥ √(4 · 70kg · 9.81m/s² / (π·5×10+8N/m²)) = 1.323×10-3m
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