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A nylon rope of length 4.5 m and diameter 6 mm hangs from a tree branch. A monkey of weight 100 N jumps onto and holds the free end. Taking Young's modulus of nylon Y = 4.8 x 10¹¹ N/m² and Poisson's ratio sigma = 0.2, find the resulting change in the rope's diameter.

1. 8.8 x 10⁻⁹ m
2. 4.4 x 10⁻⁹ m
3. 1.76 x 10⁻⁸ m
4. 2.2 x 10⁻⁹ m

Correct answer: 1.76 x 10⁻⁸ m

Solution

Longitudinal strain = F/(A Y); lateral strain = sigma times this, so |delta_d| = sigma*F*d/(A*Y) = 0.2*100*0.006/(2.83e-5*4.8e11) approx 1.76 x 10⁻⁸ m.

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