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Homework Help: Relative motion of 2 particles

  1. Jan 28, 2010 #1
    Please help. Im starting to think the answer in the back of my book is wrong. Refer to picture below. Question: Find the speed of the elevator if the winches A and B both pull the rope at 5 m/s. Answer is 2.14m/s. How? I have no idea. Im not the kind to just give up.

    199.png

    Thank you very much!
     
  2. jcsd
  3. Jan 28, 2010 #2

    ehild

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    The length of both ropes changes in a rate -5 m/s. So the sum of the velocities is not zero.

    More: notice that xa=xb, xa=xd+xc.

    ehild
     
  4. Jan 28, 2010 #3
    Thank you for your reply. In class we set these types of equations as:

    Rope 1:

    Step one: Xb+Xc+Xd= length(which is just Some constant)
    Step two: Differentiate both sides to get velocity since previous equation is length or displacement.

    there fore we get Vb+Vc+Vd=0

    Step three: we know Vb=Va=5m/s and we can substitute. 5+Vc+Vd=0 -> Vc+Vd= -5m/s

    Rope 2:
    Step one: Xa+Xa+Xc= length(some constant)
    Step two: differentiate both sides to get 2Va+Vc=0
    Step three: substitute known. 2(5) + Vc = 0 -> Vc= -10m/s

    Finaly
    Solving for the last unknown Vc+Vd=-5 -> -10+Vd=-5 -> Vd = 5m/s

    Somewhere I am not doing something right because the answer is 2.14m/s (sign is disregarded)
    What doesn't make sense is that Vd and Vc are different velocities, and I think they should be the same because how can the elevator go up with a constant velocity. MY GUESS IS THAT I LABELED THE PROBLEM WRONG
     
  5. Jan 28, 2010 #4
  6. Jan 29, 2010 #5

    rl.bhat

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    When the system moves, total changes in each segments of the string must be zero.
    In the blue string
    change in the 1st segment = Xb - Xc
    change in the 2nd segment= Xd - Xc, but Xd = Xb, so
    = Xb - Xc
    change in the 3rd segment =- Xd - y
    So total change in the blue string = (Xb)-2(Xc) - y = 0......(1)
    Now in the purple string
    change in the 1st segment = Xa - Xf
    change in the 2nd segment = y - Xf
    change in the 3rd segment = y - Xg
    So total change in the purple string = Xa - 3Xf + 2y = 0......(2)
    From eq.1 y = (Xb - 2Xc). Substitute it in equation (2). Note that Xf = Xc and Xa = Xb,
    Find Xf in terms of Xa. Put Xa = 5m/s and find Xf.
     
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