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Pulley question

  1. Jun 21, 2008 #1
    Hello guys, i have a question i would like to ask.

    A worker of mass 80kg stands in a platform of mass 40kg pulls the platform up with an acceleration of 2.5ms^-2 using a smooth pulley as shown in the figure. what is the tension T in each side of the rope (g = 10 ms^-2).

    The figure : A man standing in a platform, the platform is attached to a string which is over a pulley and the man is pulling the other side of the string.

    I thought of F-mg = ma
    which will be
    F = (120)(2.5) + 1200

    but its wrong @_@.

    Can someone tell me?
  2. jcsd
  3. Jun 21, 2008 #2
    from what i understand you took m=80+40.
    but the man is not accerlerating, only the platform.
    so m should be 40.
    so the equations should look like this:
    1) F=ma
    2) F=T-mg
    from here it's easy:
    notice that i used a capital T to denote the tention in the rope. i used the capital F to denote the total force acting on the platform.

    F=ma is newton's law: ma=total force. this is the reason for eq. (1)
    but the total force is the rope pulling up (T) and gravity pulling down(-mg). this is eq. (2)
  4. Jun 21, 2008 #3


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    Hi crays! :smile:

    Yes, your'e right, the man is accelerating with the platform.

    And your F is correct.

    But T is not equal to F.

    You haven't drawn a proper diagram for yourself, have you?

    Hint: treating the man-and-platform as one object, how many forces upward are there? :wink:
  5. Jun 21, 2008 #4
    oops. looks like i read the data wrong!
    sorry 'bout that :)
  6. Jun 21, 2008 #5
    Thanks !! I've found the answer. But i don't understand why the tension 1500 is distributed to all over the string.
  7. Jun 22, 2008 #6


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    Hi crays! :smile:

    Just look at your diagram:

    it should show that both ends of the string are attached to the man-platform body, both pulling vertically upwards;

    the tension T is the same throughout the string ('cos that's the way strings work),

    so there's a force T upward at both ends of the string, and both those forces are acting on the body. :smile:

    (usually, the other end of the string is attached to something external, like a ceiling, so the force there isn't acting on the body at all)

    Another way of looking at this is that there is gearing: when the man pulls the rope one foot, the platform only moves half a foot doesn't it?

    How come the man exerts a force of T, but the platform moves under a force of 2T … where does the extra energy come from? :confused:

    Because his force T does T foot-pounds of work, while the work done on the platform is 2T times half a foot-pound, which is the same … no extra energy! :smile:
  8. Jun 22, 2008 #7
    Ah, thanks. Much more understandable.
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