Question

A particular human hair has a Young's modulus of 3.80 x 10 N/m² and a diameter of 150 um. If a 234 g object is suspended by the single strand of hair that is originally 15.0 cm long, by how much AL hair will the hair stretch? AL hair = m If the same object were hung from an aluminum wire of the same dimensions as the hair, by how much ALA would the aluminum stretch? ALAI = ALA = m If the strand of hair is modeled as a spring, what is its spring constant khair? khair = N/m

Answer 1

given
Y_hair = 3.80*10^9 N/m^2
d = 150 micro m

r = d/2 = 75 micro m
L = 15 cm = 0.15 m
m = 234 g

= 0.234 kg

a) use, Y = (F/A)/(delta_L/L)

delt_L/L = F/(A*Y)

delta_L = L*F/(A*Y)

= L*m*g/(A*Y)

= 0.15*0.234*9.8/(pi*(75*10^-6)^2*3.8*10^9)

= 5.12*10^-3 m <<<<<<<------------------------------Answer

b) for aluminimum, Y = 68.9*10^9 N/m^2

delta_L_al = L*m*g/(A*Y)

= 0.15*0.234*9.8/(pi*(75*10^-6)^2*68.9*10^9)

= 2.83*10^-4 m <<<<<<<------------------------------Answer

c) k_hair = m*g/delta_L

= 0.234*9.8/(5.12*10^-3)

= 448 N/m <<<<<<<------------------------------Answer