Answer to Question #123502 in Physics for Adebiyi Bisola Deborah

Question

Good day sir/ma,i have read up elasticity in my textbook and solved questions on it,at first I saw it was easy until I came across this question...I would be very happy if you can help me..A steel wire of diameter 2.5mm is clamped between two fixed clamps that are 1.2m apart.Calculate by how much the wire sags when an 8kg load is suspended between the two clamps.(the answer in the textbook was 10.7mm,but I tried solving it but I couldn't get the answer) Thanks in anticipation sir/ma

Answer 1

$$\frac{\Delta l}{l}=\frac{x^2}{2l^2}$$

$$\frac{4mg}{2\pi d^2E}\frac{l}{x}=\frac{x^2}{2l^2}$$

$$\frac{4(8)(9.8)}{2\pi (0.0025)^2(2\cdot10^{11})}\frac{0.6}{x}=\frac{x^2}{2(0.6)^2}$$

$$x=0.026\ m$$