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Homework Help: Apparent Weight

  1. Nov 7, 2007 #1
    1. The problem statement, all variables and given/known data
    A man with a mass of 85.0 kg rides downward on an elevator.Initially the elevator accelerates downwards at 1.845 m/s^2 and eventually slows at 1.60 m/s^2 as it reaches the ground floor. Find the mans apparent weight as he starts down and as he reaches the ground floor.


    2. Relevant equations

    fn=m(a-g)

    3. The attempt at a solution

    fn= (85.0 kg) (1.85m/s^2--9.81m/s^2)
    =991.1 N

    fn=m(a-g)
    = (85.0 kg) (1.60 m/s^2--9.81 m/s^2)
    =969.85 N

    The question I have is in the second part of the question should th value for a be positive or negative?
     
  2. jcsd
  3. Nov 7, 2007 #2

    Doc Al

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    Staff: Mentor

    This is not quite right: you added instead of subtracted.

    It might be clearer if you wrote it as:
    [tex]\Sigma F = F_n - mg = ma[/tex]

    So:
    [tex]F_n = m(a + g)[/tex]

    But note that the acceleration is downward and thus negative.
     
  4. Nov 7, 2007 #3
    So fn=85.0kg ( -1.85m/s^2 +(-9.81m/s^2)
    =-991.1N

    fn=85.0kg (-1.60 m/s^2 + (-9.81 m/s^2)
    = -969.85N
    Is this correct?
     
  5. Nov 7, 2007 #4

    Doc Al

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    Staff: Mentor

    No, you're making the same mistake. In the expression "a + g", it's "a" (the acceleration of the elevator) that is negative, not g! (g is just a positive constant = 9.81 m/s^2.)

    Always do a sanity check: If the elevator accelerates upward, you'd be squashed against the floor giving a greater apparent weight; if it accelerates downward, you'd be pulled away from the floor, reducing your apparent weight.
     
  6. Nov 7, 2007 #5
    fn =85kg (-1.85 m/s^2 +9.81m/s^2)
    = 676 N

    fn = 85kg ( 1.6m/s^2 + 9.81m/s^2)
    = 969.85 N
    Is this correct?
     
  7. Nov 8, 2007 #6

    Doc Al

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    Staff: Mentor

    Excellent! The wording of the problem was a bit tricky. At first the elevator accelerates downward at a = -1.85 m/s^2. Then it slows down, which means it accelerates upward at +1.6 m/s^2.
     
  8. Nov 8, 2007 #7
    Thanks for the help !
     
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