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Why is gravity taken as positive?

  1. May 15, 2013 #1
    1. An elevator (mass 4700 kg) is to be designed so that the maximum acceleration is 6.80×10-2. What is the maximum force the motor should exert on the supporting cable?

    Force Diagram:

    Force Tension

    3. FT = ma + mg
    4700[(0.068(-9.8) - 9.8)]
    = -435178.8N
    but the answer should be positive. Why isn't gravity negative?
  2. jcsd
  3. May 15, 2013 #2
    Why is it F = ma + mg? Why not F + ma = mg? Why not F + mg = ma? Why not something else?
  4. May 15, 2013 #3
    Because the ƩF = ma
    ƩF = FT - mg
    So FT - mg = ma
    => FT = ma + mg
  5. May 15, 2013 #4


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    Then in the bolded line, acceleration due to gravity and hence weight is taken as negative whilst tension FT is taken as positive. So the resultant force ma is

    ma =FT + (-mg) = FT - mg
  6. May 15, 2013 #5
    Applying Newton's Second Law:

    g here is just +9.8. The "downward" direction of gravity is already taken care of by the minus sign in :


    Rewriting it as
    Just plug and chug...

    You should get a positive tension force
  7. May 16, 2013 #6
    Since that takes care of the "negative" direction of gravity, you should not further assume that g is negative like you did originally.
  8. May 16, 2013 #7
    Thanks everyone!!!
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