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A wire of cross-sectional area 4 x 10⁻⁴ m², Young's modulus 2 x 10¹¹ N/m² and natural length 1 m is fixed horizontally between two rigid vertical poles. A 1 kg mass is hung from its midpoint, causing the wire to sag. Find the angle theta that each half of the wire makes with the horizontal. (Take g = 10 m/s².)
- about 0.9 deg
- about 1.8 deg
- about 0.5 deg
- about 2.5 deg
Correct answer: about 0.9 deg
Solution
Combining 2T*theta = mg with T = Y*A*(theta²/2) gives theta³ = mg/(Y*A), so theta = (mg/(YA))^(1/3) radians, about 0.016 rad ~ 0.9 deg.
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