Question

An 9.26-kg stone at the end of a steel (Young's modulus 2.0 x 1011 N/m2) wire is being whirled in a circle at a constant tangential speed of 17.7 m/s. The stone is moving on the surface of a frictionless horizontal table. The wire is 4.66 m long and has a radius of 2.01 x 10-3 m. Find the strain in the wire.

Answer 1

Tangential velocity of the stone, v = 17.7 m/s

Mass of the stone, m = 9.26 kg

Now, the centripetal force F needed to keep a mass m moving in a circular path of radius r with a tangential velocity v is given by:

F = mv²/r

F = 9.26 * 17.7^2 / 4.66 = 622.5 N

Cross sectional area A of a wire of radius R is given by:
A = πR²
A = π * (2.01 * 10^-3)²
A = 1.27 * 10^-5 m²

Stress = F / A
Stress = 622.5 / (1.27 * 10^-5)
Stress = 4.90 * 10^7 N/m²

Young's modulus = [stress] / [strain]

=> Strain = [stress] / [Young's modulus]

Strain = (4.90 * 10^7) / (2.0 * 10^11) = 2.45 x 10^-4 (Answer)