Question

1. A 1.60 m long steel piano wire has a diameter of 0.20 cm. How great is the tension in the wire if it stretches 0.25 cm when tightened?

Answer 1

$E=\frac{\sigma}{\epsilon}=\frac{F/A}{\Delta l/l}\to F=\frac{E\cdot A\cdot\Delta l}{l}$

$A=\frac{\pi\cdot d^2}{4}=\frac{3.14\cdot0.002^2}{4}=3.14\cdot 10^{-6}m^2$

The Young's modulus of steel is $E=200 MPa$

$F=\frac{E\cdot A\cdot\Delta l}{l}=\frac{200\cdot10^{11}\cdot3.14\cdot10^{-6}\cdot0.0025}{1.6}=981N$