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An elevator's cable can handle a tension of 95,500N. Assuming the car has a mass of 2950 kg and it is carrying a full load of passengers whose combined mass is 3750 kg, what is the minimum time required for the elevator to rise 50.0 m from rest?

4.74 s

2.65 s

3.35 s

5.96 s

  • Physics -

    Assume that the elevator accelerates at a constant rate a while going up X = 50 m in time t. (Assume it doesn't slow down until it gets to higher floors). The acceleration, a, will be given by
    (1/2)at^2 = X
    a = 2X/t^2

    Cable tension at the breaking point is
    95,500 = M(g + a) = 65,660 + M*a
    M*a = 29840 N
    a = (29840)/6700 = 4.45 m/s^2

    Minimum time t = sqrt(2X/a) = 4.74 s

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