A platform is suspended by four wires at its corner's. The wires are 3m long and have a diameter of 2mm. Young modulus for the material of the wires is 1.8*10^11 N/M^2. How far will the platform drop (due to elongation of the wires) if a 50k load is placed at the center of the platform.

Question

irishboy123 · Answer

start with the definition, re-arrange, and then plug in values....

$ Y =  {\dfrac {\sigma}{\epsilon }} ={\dfrac {F/A_{0}}{\Delta L/L_{0}}}={\dfrac {FL_{0}}{A_{0}\Delta L}} $

$ \implies  \Delta L  ={\dfrac {FL_{0}}{A_{0}Y}}$

Where

$F = 50g \color{red}{ \times  \dfrac{1}{4}} N$ due to the symmetry

$L_o = 3m$

$A_o = \dfrac{\pi (0.002)^2}{4} m^2$

$Y = 1.8\times 10^{11} N/m^2 $

osprey · Answer

This is a brilliant question ... for what the source question hides, and, probably, the poster has not yet learned. The young mod experiment is a very sneaky way of taking the stress tensor, the strain tensor, and the young modulus tensor, and reducing a vast pile/array of numbers to one, simply by making the thing one dimensional. When I first clapped eyes on some other bits of "mechanics", I almost fell out of my nest at the shear number of numbers used in elasticity. it's something like 9 and 9 for the stress and strain, and 27 for the mod, and then a few names, possibly like Poisson chucked in to make the kettle boil over completely. Bon voyage http://perendis.webs.com