Question

What amount of mass (in kg) hung on a 20 gauge steel wire will cause it to experience an elastic strain of 0.10%? (Use Y = 20 x 10^10 N/m^2 for steel and 0.640 mm diameter for 20 gauge wire.)

Answer 1

strain = 0.1% = 0.001

Y = stress/strain

stress = strain x Y = 0.001 x 20x10^10 = 20x10^7 N/m^2

but stress = weight/area

20x10^7 = weight/(3.14 x (0.64x10^-3)^2)

weight = 257.23 N

weight = mg

m = weight/g = 257.23/9.81 = 26.22 kg