A piano wire has a radius of 0.50 mm. One end is fixed and the other is wrapped around a tuning peg, which has a diameter of 3.5 mm and is 80 cm away. After the wire just becomes taut, the peg is given three full turns. What is the tension in the wire? Young's modulus for steel is
20 × 10¹⁰ N/m².

Question

Quizplus · Accepted Answer

The tension in the wire can be calculated using the formula for Young's modulus: $ \Delta L = \frac{FL}{AY} $, where $ F $ is the force (tension), $ L $ is the original length, $ A $ is the cross-sectional area, and $ Y $ is Young's modulus. The change in length $ \Delta L $ is due to the wire being wrapped around the peg. The circumference of the peg is $ \pi \times 3.5 \, \text{mm} $, and three turns increase the length by $ 3 \times \pi \times 3.5 \, \text{mm} $. Solving for $ F $ gives approximately 6.5 kN.

A Piano Wire Has a Radius of 0