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Homework Help: Elevator decelerating down vs accelerating up

  1. Feb 12, 2010 #1
    This is not an actual problem from my class. All our problems involved an elevator going upward (both accelerating and decelerating). But I am curious if an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

    2. Relevant equations

    Elevator Up: FT - mg = ma
    so: FT = m (a + g)

    so I figure that:
    @ a<0 FT< FG
    @ a=0 FT= FG
    @ a>0 FT > 0

    I was curious what the values are when the elevator is going down.
    I used this equation: mg - FT = ma
    so: FT = m ( g - a )

    so I figure that:
    @ a<0 FT> FG
    @ a=0 FT= FG
    @ a>0 FT< FG

    3. The attempt at a solution

    Is it true that an elevator cable would have the same FT if the elevator was decelerating downward at -3 m/s2 as it would accelerating upward at 3 m/s2 ? I am having a hard time conceptualizing why that is true in my mind's eye.

    Thanks
     
  2. jcsd
  3. Feb 12, 2010 #2

    PhanthomJay

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    Science Advisor
    Homework Helper
    Gold Member

    you let the plus and minus sign sting you (it happens quite often)!
    In your second set of equations for the downward acceleration, you assumed that the downward direction was positive (g is positive), and therefore, the downward acceleration is positive. Thus, FT is less than the elevator weight in this case, and greater than the elevator weight in the first case. Draw a sketch, and look at it over and over and over again, and don't let that minus sign bite you any more:mad:
     
  4. Feb 12, 2010 #3
    Thanks for the help.
     
  5. Jun 10, 2012 #4
    any advice or solution? showthread.php?t=612910
     
  6. Jun 10, 2012 #5
    If you want to compare, the convention of positive or negative direction must be consistent.
     
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