Piano wire weighs 77kN/m^3 and breaks at a stress of 3000MPa. Calculate the length of piano wire that can be lowered down a very deep mine before it breaks.
stress = force/area
The Attempt at a Solution
Piano wire = 77 000N/m^3
stress = 3000 000 000Pa(N/M^2)
Area of cross section = (pi)(d^2)/4
Force exerted by x m^3 of piano wire is (x)(77000)
3 000 000 000 = (4)(77000)(x) /(pi)(d^2)
ASSUME d = 0.0002m
x = 0.122399m^3
Volume = (pi)(r)^2 * h
0.122399 = (pi)(0.001)^2 * h
h= 38 960
This seems a bit too much.
My professor is known for throwing out questions that require "engineering intuition for making assumptions."
Not sure if my solution is right or I can do it without making an assumption.
This is a problem set, no solutions please but only tell me if I'm way off (or close and where i made the mistake).
I appreciate it.