Finding Mass and Distance using apparent Weight

  1. 1. The problem statement, all variables and given/known data
    Henry gets into an elevator on the 50th floor of a building and it begins moving at t=0s The figure shows his apparent weight over the next 12s.

    [​IMG]

    What is Henry's mass?
    How far has Henry traveled at t =12s

    2. Relevant equations

    F=ma
    w=mg
    weight apparent = w(1+ a/g)


    3. The attempt at a solution

    Well so far, all I know is that the elevator is moving down since the apparent weight has gone up. I have no idea how to approach the problem and I have tried using the third formula that I have listed but no luck. Do I even use the apparent weight equation? Because I need the acceleration, and no information has been given on that.
     
    Last edited: Oct 6, 2007
  2. jcsd
  3. Astronuc

    Staff: Mentor

    Chegg
    Well the way I would read that, is that the elevator accelerates downard initially for 2 seconds, since Henry is lighter, then descends at constant speed (from which one can get Henry's weight), then decelerates (Henry is heavier), and then stops (from which one again get's Henry's weight).

    One needs to determine when to apply W = m(g-a) and W = m(g+a).
     
  4. Oh, I see, so you would you would use 750 N as his weight when determining the mass. Thanks for explaining the graph to me. Even our prof never explained this kinda graph to us. To me this is new material. k, Lemme try to find the distance now. I would need to find the acceleration first right?
     
    Last edited: Oct 6, 2007
  5. ouch, ok nevermind... Anyone have any tips on how to approach this when finding distance?
     
  6. Astronuc

    Staff: Mentor

    For an approximation, one could assume constant acceleration.

    Then there are three parts of the problem to find distance - the initial drop at constant acceleration, the descent at constant velocity, and the descent during deceleration.

    See this reference - http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html
     
  7. but wouldn't i need the velocity as well? i have acceleration as 1.962 m/s.
     
  8. Astronuc

    Staff: Mentor

    Start with an initial velocity of zero at t = 0s.

    Use the acceleration to find the distance and velocity at t = 2s. That velocity is the initial velocity and constant velocity for the period t =2 s to t = 10 s.

    Determine the distance for that period.

    Then use that intial velocity and deceleration for the final period 10 s to 12 s, when velocity goes to zero because the elevator stops.
     
  9. Do i add all the distances up?
     
  10. Astronuc

    Staff: Mentor

    Sure, why not?
     
  11. Argh, i dunno what im doing wrong but the answer i keep getting is wrong. Is my acceleration correct?
     
  12. Astronuc

    Staff: Mentor

    About 1.96 m/s2 is correct. Here I'm assuming a step change in acceleration. From the curve, it looks like it changes rapidly from 1.96 to 0 between 2 and 2.2 s, so that could be a source of error, but it should be relatively small.

    Please write out the formulas one is using.
     
    Last edited: Oct 6, 2007
  13. ok well i got 62.784 m as the total distance traveled after 12 secs. Is that correct?
     
  14. oh well I used the formula i mentioned in the beginning

    Apparent Weight = mg(1+a/g)
     
  15. Basically for t=0 to t=2 i got 3.924 m
    t=2 to t=10 i got 31.392m
    t=10 to t=12 i got 27.468m

    and i got the total to be 62.784m

    whoops i should start editing my posts instead of continuously posting. Sorry.
     
  16. Astronuc

    Staff: Mentor

    It seems you've done that part correctly.

    Please write the formulas for distance and velocity at 2 s, and then at 10 s, and then at 12 s, so we can see how you determine the cumulative distance.
     
  17. k well i did for

    t=0 to t=2

    x = (0)(2) +1/2 (1.962)(2)^2

    x = 3.924m

    Vf^2 = (0)^2 +2(1.962)(3.924)
    Vf = 3.924

    is that correct so far?
     
  18. then for t = 2 to t = 10 Constant Velocity so a = 0

    x = 3.924 (8) + 1/2 (0)(8)^2 Took t=8 since 10-2 = 8

    x = 31.392m

    then for t=10 to t=12

    x = (3.924)(2) + 1/2 (-1.962)(2)^2

    x = 3.924m

    and the total i got was 39.24 m ( Realized i had an error in there so i changed it)
     
  19. oh cool it was right. Thanks Astronuc.
     
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