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Homework Help: Elevator question

  1. Jul 3, 2010 #1
    100 kg elevator acclerates up at rate avg a*. What's the avg force acting on the elevator if it covers a distance X over a period of 10s?

    a* denotes average accleration
    a. 2X + 1000
    b. 100(a* + 1)
    c. 2a* + 1000
    d. 2a*X

    I set up a free body diagram to show all the forces acting on the elevator. There's a downward force due to gravity, Fg, the net upward force, Fn, causing the accleration.

    Fn - Fg = ma*
    Fn = ma* + Fg

    The question states that it travels a distance of X over 10 sec

    a* = delta V/delta t
    delta V = X/t , which the question gives me
    delta V = x/10s, i substituted this into the a* equation and got
    a* = x/100s

    when i plug this into my net force equation:

    Fn = ma* + Fg
    Fn = m(a* + g)
    Fn = 100kg(x/100s + 10m/s^2)
    Fn = X + 1000

    I can't seem to figure out why my answer doesn't match any of the answer choices. Can someone please point out what i'm doing wrong?
    Thanks
     
  2. jcsd
  3. Jul 3, 2010 #2
    You used the wrong kinetic equation. You calculated your final velocity incorrectly.
     
  4. Jul 3, 2010 #3
    avg velocity comes to mind since the question says the elevator travels a distance x over a period of 10s. If i solve the problem using this information, the answer comes out to be 2X + 1000.
    But avg accleration is equal to delta v/ delta t, not avg velocity. And also, using avg velocity would mean i have constant acceleration and i don't.

    I really think this is a ridiculous question, very loosely termed.
     
    Last edited: Jul 3, 2010
  5. Jul 3, 2010 #4

    Doc Al

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    Staff: Mentor

    OK.
    No, X/t gives the average speed, not the change in speed.
     
  6. Jul 3, 2010 #5
    ok, so does that mean avg speed is = 2X/t?
    if so, then the answer is a. 2X + 1000

    I still don't see the relationship between avg speed and avg acceleration.
     
  7. Jul 3, 2010 #6

    HallsofIvy

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    Science Advisor

    There isn't any. And average speed is irrelevant. Force= mass * acceleration, not mass* speed. If the speed were constant over the trip, there would be no force.
     
  8. Jul 3, 2010 #7
    ok, if the acceleration were constant and the initial velocity were given to be 0, then i see some sense in solving this problem. And even then the answer wouldn't match any of the given answers.
     
    Last edited: Jul 3, 2010
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