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Elevators and Acceleration

  1. May 24, 2004 #1
    This should be a simple problem, but I think I'm making it harder than it is.

    In this problem, I am interested in maximum acceleration for an elevator during normal operation. While the elevator is at rest, on the ground floor, I get in, put down my bathroom scale and stand on it. I continue standing while the elevator is going up. During my trip to the 45th floor, the scale reading increases by a max of 25lbs.

    It doesn't matter what floor you go to.
    When the elevator accelerated upward, the apparent weight is greater than mg by the amount ma. It's as if gravity were increased from g to g+a.

    According to an equation I found in my textbook...
    Fn-mg=ma (where a is in the y direction)
    Fn=mg+ma (where Fn is the reading on the scale, the apparent weight)

    Since the reading is given in lbs, I am going to use 32.2ft/s^2 for gravity.
    I am going to start with an arbitrary weight of 100lbs, which would give a max weight of 125lbs.
    And W=mg so....100lbs=(m)(32.2ft/s^2)=3.11slugs

    125lbs=(3.11slugs)(32.2ft/s^2)+(3.11slugs)(a ft/s^2)
    125lbs-100.14lbs=(3.11slugs)(a ft/s^2)
    24.86lbs=(3.11slugs)(a ft/s^2)

    If I did the problem right...
    Is 7.99ft/s^2 my answer for max acceleration? Or do i add that to 32.2ft/s^2 for a max acceleration of 40.19ft/s^2?

    Thanks! Kelli :yuck:
  2. jcsd
  3. May 24, 2004 #2

    Doc Al

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    Staff: Mentor

    You did the problem correctly. (But see my steps below.) You calculated the max acceleration (assuming a 100 lb weight). Why would you add it to g? (g is the acceleration of a freely falling body--the elevator isn't falling, is it?)

    Here's how I'd do it:

    Fn - mg = ma
    (mg + 25) - mg = ma
    25 = ma

    a = 25/m = 25 (32.2/100) = 8.05 ft/s^2 (upwards)
  4. May 25, 2004 #3
    Do I need to even assume a 100lb weight? What if i used a weight different than 100lbs, wouldn't that affect the acceleration?
  5. May 25, 2004 #4

    Doc Al

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    Staff: Mentor

    Yes it would. The same net force (25 lbs) acting on a different mass would yield a different acceleration.
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