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17 November, 14:11

By how much does a 64.3 kg mountain climber stretch her 0.910 cm diameter nylon rope when she hangs 32.2 m below a rock outcropping? (For nylon, Y = 1.35 â 10^9 Pa. Enter your answer in centimeters.)

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  1. 17 November, 16:23
    0
    23 cm

    Explanation:

    m = 64.3 kg, diameter = 0.910 cm

    radius, r = 0.455 cm = 4.55 x 10^-3 m

    A = 3.14 x (4.55 x 10^-3) ^2 = 6.5 x 10^-5 m^2

    L = 32.2 m

    Y = 1.35 x 10^9 Pa

    Let the stretched length is l.

    Use the formula for Young's modulus

    Y = mg L / A l

    l = m g L / A Y

    l = (64.3 x 9.8 x 32.2) / (6.5 x 10^-5 x 1.35 x 10^9)

    l = 0.23 m

    l = 23 cm
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