A steel wire 1.5m long and of radius 1mm is attached with a load 3 kg at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency 2Hz. Find the elongation of the wire when the weight is at the lowest position: (Y = 2 × 1011N/m2 and g = 10 m/s2)

Engineering

Physics

Stress Strain and Hookes Law New

Circular Motion in Vertical Plane

Acceleration

Question

A steel wire 1.5m long and of radius 1mm is attached with a load 3 kg at one end the other end of the wire is fixed it is whirled in a vertical circle with a frequency 2Hz. Find the elongation of the wire when the weight is at the lowest position: (Y = 2 × 10¹¹N/m² and g = 10 m/s²)

3.17 × 10⁻⁷m

7.17 × 10⁻³m

1.77 × 10⁻³m

1.37 × 10⁻⁷m

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Forces at the lowest point are gravitational force and centrifugal force

F = mg + mω²r = mg + mω²L

Δℓ= \frac{FL}{YA} = \frac{(mg + {mω}^{2} L) L}{Y \times {πr}^{2}}

ω = 2πf = 2π × 2 = 4π

Δℓ = \frac{(30 + 3 \times 16 π^{2} \times 1.5) \times 1.5}{2 \times 10^{11} \times π \times (10^{- 3})^{2}} = 1.77 \times 10^{- 3} m