Question

A copper wire, 200 cm long and 1.22 mm diameter, is fixed horizontally to two rigid supports 200 cm long. Find the mass in grams of the load which when suspended at the mid-point of the wire produces a sag of 2 cm at that point. Young modulus of coppe 12.3 x 10^10 Nm^-2.

Answer 1

$$\frac{Mg}{2\sin \theta}=YA\frac{1-\cos \theta}{\cos \theta}$$

$$\theta=\arcsin \frac{2}{100}=1.15\degree$$

$$\frac{9.8M}{2\sin 1.15}=0.25\pi(0.00122)^2(12.3\cdot10^{10})\frac{1-\cos 1.15}{\cos 1.15}\\M=0.119\ kg$$