Question

a 450 kg weight is hung from a copper wire that is 1.5m long. The wire strecthes by 1.2mm. What is the radius of copper wire?

Answer 1

Write down the Young's modulus of copper. This is -

Y = 1.17 x 10^11 N/m^2

Expression for the Young's modulus is -

Young modulus (E) = Stress/strain.

Stress is calculated by Force (F)/Area (A)

Strain is extension (e)/lenght(L)

So -

(F/A)/(e/L) = FL/Ae = Y

rearrange to get -

A = FL / (Y*e)

Standard units are metres for lengths and N for forces.
450 kg = 450 x 9.81 = 4414.5 N
Elongation = e = 1.2 mm = 1.2 x 10^-3 m

Put the values -

A = (4414.5 x 1.5) / (1.17 x 10^11 x 1.2 x 10^-3) = 4716 x 10^-8

=> pi*r^2 = 4716 x 10^-8

=> r^2 = 1501.4 x 10^-8 m^2

=> r = 38.75 x 10^-4 m = 3.875 x 10^-3 m

=> r = 3.875 mm

Hence, radius of the copper wire = 3.875 mm (Answer).

Hope, you understand the solution !