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16 December, 12:12

2) A window washer pulls themselves upward using a bucket pulley apparatus. A) How hard must

pull downward to raise herself slowly at a constant speed? B) If she increases this force by 15%, what

will her acceleration be? The mass of the person plus the bucket is 72 kg. Ignore friction.

How should I solve this

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Answers (1)
  1. 16 December, 13:48
    0
    A) F = 705 N

    B) a = 1.23 m/s²

    Explanation:

    Given that,

    The mass of the person and bucket, m = 72 Kg

    The tension, T = 0

    The bucket pulley apparatus works with the principle of Atwood's machine

    The upward acceleration is equal to the downward acceleration. It is denoted by 'a '

    The acceleration due to gravity is 'g'

    The net force in the upward direction, f = T - mg (f = ma) N

    The net force in the downward direction is, F = Mg - T (F = Ma) N

    The upward acceleration is equal to the downward acceleration. It is denoted by a

    Adding the above equations

    Mg - mg = ma + Ma

    Where,

    mg = 72g N

    = 105 N

    To remain equilibrium or to raise herself slowly at a constant speed, the upward force should be equal to the downward force.

    Mg = mg

    Therefore, the force required to raise herself slowly at a constant speed is 705 N

    If she increases this force by 15%,

    (100/72g) x 15 %

    = 20.83g

    Therefore, the total downward force, F = 62g+20.83g

    = 92.83g N

    Substituting the values in the equation

    Mg - mg = Ma + ma

    92.83g - 72g = (92.83g + 72g) a

    a = 92.83g - 72g / 92.83 + 72g

    = 0.126g

    = 1.23 m/s²

    Hence the acceleration will be, a = 1.23 m/s²
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