Question

A particular human hair has a Young's modulus of 3.18 x 109 N/m2 and a diameter of 145 μm. If a 204 g object is suspended by the single strand of hair that is originally 19.5 cm long, by how much A L hair will the hair stretch? hair - If the same object were hung from an aluminum wire of the same dimensions as the hair, by how much ALAI would the aluminum stretch? ALAI If the strand of hair is modeled as a spring, what is its spring constant khair? N/m hair-

pretty confused on how to solve this, if you could explain it please

Answer 1

a) For hair Y = F L/A Delta L A is cross section Area Y is young modulus F is force applied L is length In present case F = mg F = 0.204 times 9.8 F = 1.992 N A = pi r^2 = 3.14 times (145 times 10^-6/2)^2 A = 0.0165 times 10^-6 m^2 3.18 times 10^9 = 1.9992 times 0.195/0.0165 times 10^6 Delta L_hair Delta L_hair = 0.38898/0.05247 times 10^9 times 10^-6 Delta L_hair = 7.429 times 10^-3 m b) For Aluminum Y = 69 times 10^9 N/m^2 69 times 10^9 = 1.9992 times 0.195/0.0165 times 10^-6 Delta L_Al Delta L_Al = 0.3424 times 10^-3 m \r\n (c) Elongation in spring is Delta L_hair using mg = k Delta L_hair k = mg/Delta L_hair = 0.204 times 9.8/7.429 times 10^-3 k = 0.269 times 10^3 N/m