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2 October, 21:22

An elevator cab that weighs 27.8 kN moves upward. What is the tension in the cable if the cab's speed is (a) increasing at a rate of 2 1.22 / msand (b) decreasing at a rate of 2 1.22 / ms?

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  1. 3 October, 00:04
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    a) T = 8.63 * 10 ⁴ N, b) T = - 3.239 * 10 ⁴ N

    Explanation:

    Given:

    W = 27.8 KN = 27.8 * 10 ³ N,

    For upward motion: Fnet is upward, Tension T is upward and weight W is downward so

    a) a=21.22 m/s² (not written clearly the unit. if it is acceleration?) then

    Fnet = T - W

    ⇒ T = F + W = ma + W

    T = (W/g) a + W (W=mg ⇒m=W/g)

    T = (27.8 * 10 ³ N / 9.8) 21.22 m/s² + 27.8 * 10 ³ N

    T = 86,263.265 N

    T = 8.63 * 10 ⁴ N

    b) For Declaration in upward direction a = - 21.22 m/s²

    Fnet = T - W

    ⇒ T = F + W = ma + W

    T = (W/g) a + W

    T = (27.8 * 10 ³ N / 9.8) (-21.22 m/s²) + 27.8 * 10 ³ N

    T = - 32395.5 N

    T = - 3.239 * 10 ⁴ N

    as Tension can not be negative I hope the value of acceleration and deceleration is correct.
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