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Physics

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A person of mass 50.0 kg is at the bottom of a cave. The cave has a depth of 32.5 meters and the person is to be pulled out of the cave vertically by a rope, starting from rest. What is the shortest amount of time that this could take if the rope can withstand a maximum tension of 550.0 N without breaking?

  • Physics -

    I think this is how you tackle this problem:

    Fnet=T-Fg

    Where

    T=550.N
    Fg=m*g
    Fnet=m*a
    m=50.0kg
    g=9.8m/s^2
    and
    a=?

    Solve for a:

    m*a=550.0N-m*g

    50.0kg*a=550.0N-(50.0kg*9.8m/s^2)

    55.0kg*a=550.0N-490N

    55.0kg*a=60N

    a=60N/55.0kg

    a=1.091m/s^2

    You know acceleration, so solve for time (t) using the following kinematic equation:

    d=Vit+1/2at^2

    where

    d=32.5m
    Vi=0m/s^2
    a=1.091m/s^2
    t=?

    Solve for t:

    32.5=0+1/2(1.091m/s^2)t^2

    t=sqrt*(65m/1.091m/s^2)

    t=7.72s

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