Question

8.0 kg stone at the end of a steel wire (Y = 2.0×1011) is being whirled in a horizontal circle

at a constant tangential speed of 12 m/s. The wire is 4.0 m long and has a radius of 1.0 × 10-3m.

Determine the strain in the wire.

Answer 1

$F=m\frac{v^2}{r}=8\cdot\frac{12^2}{4}=288\ (N)$

$A=\pi r^2=3.14\cdot(1\cdot10^{-3})^2=3.14\cdot10^{-6}\ (m^2)$

$E=\frac{Fl}{A\cdot\Delta l}\to\Delta l=\frac{Fl}{AE}=\frac{288\cdot4}{3.14\cdot10^{-6}\cdot2\cdot10^{11}}=$

$=0.0018\ (m)=1.8\ (mm)$