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Intro Physics question f = ma problem

  1. Feb 21, 2013 #1
    1. The problem statement, all variables and given/known data

    1) An elevator cable can withstand a maximum tension of 19,500N before breaking. The elevator has a mass of 490 kg and a maximum acceleration of 2.24 m/s2. Engineering safety standards require that the cable tension never exceed two-thirds of the breaking tension. How may 65-kg people can the elevator safely accommodate?



    2. Relevant equations


    F = ma


    3. The attempt at a solution

    F = ma

    F = (2/3)*(19,500 N)
    F = 13,000 N

    Then:

    n = { [(13,000 N) / (2.24 m/s^2)] - 490 kg } / 65 kg
    n = 81.7

    n = 81 people
     
  2. jcsd
  3. Feb 21, 2013 #2

    ehild

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    Do not forget gravity. The cable exerts the upward tension T and gravity exerts the downward force mg. The resultant of these forces accelerate the elevator upward.

    ehild
     
  4. Feb 22, 2013 #3

    tms

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    In addition to what ehild said, don't forget that the entire elevator, people plus car, are accelerating.
     
  5. Feb 22, 2013 #4
    This is what I've gotten so far.

    Since "require that the cable tension never exceed two-thirds of the breaking tension" :
    F = ma
    F = (2/3)*(19500)
    F = 13000

    Max Acceleration = 2.24 m/s^2
    Acceleration due to gravity = 9.81 m/s^2
    Acceleration = 2.24 + 9.81 = 12.05 m/s^2

    So,

    F = ma
    13000 = ((490kg)+(65kgx))(12.05m/s^2)
    x = 9.059 people

    Rounded it to 9 people.
     
  6. Feb 22, 2013 #5

    ehild

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    Your "F" is the tension in the cable.

    The elevator is accelerated by the sum of both forces: tension and gravity. The net force on the elevator is T-mg upward. So ma=T-mg.

    Rearranging the equation, it becomes the same you used. T=m(a+g). The result is correct.

    ehild
     
  7. Feb 22, 2013 #6
    Oh that makes sense now ehild.

    Thanks a lot guys, the help is much appreciated.
     
  8. Feb 22, 2013 #7

    ehild

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    You are welcome:smile:

    ehild
     
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