Question

1) A 1.6 m long steel piano wire has a diameter of 0.2 cm. How great is the tension in the wire if it stretches 0.25 cm when tightened? Young modulus for steel is 2.00 x 10" N/m?.

Answer 1

We can find the tension in the wire from the definition of the Young's modulus:

$$E=\dfrac{stress}{strain},$$ $$E=\dfrac{F/A}{\Delta L/L_0}=\dfrac{FL_0}{A\Delta L}.$$

From this equation we can find the tension in the wire, F:

$$F=\dfrac{EA\Delta L}{L_0},$$ $$F=\dfrac{2.0\cdot10^{11}\ \dfrac{N}{m^2}\cdot \dfrac{\pi(2\cdot10^{-3}\ m)^2}{4}\cdot 2.5\cdot10^{-3}\ m}{1.6\ m}=982\ N.$$

Answer:

$F=982\ N.$