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Homework Help: Find the upward acceleration of the man

  1. Feb 9, 2014 #1
    1. The problem statement, all variables and given/known data
    A man of mass m stands on a platform of equal mass m and pulls himself by two ropes passing over pulleys.If he pulls each rope with a force to half its weight,his upward acceleration would be

    a)g/2
    b)g/4
    c)g
    d)0



    3. The attempt at a solution
    force exerted by man=1/2mg*2=mg
    total force exerted downwards=mg+mg=2mg(weight of man and platform)
    then 2mg-mg=2ma=>a=g/2
    But answer given is 0.How?
     

    Attached Files:

  2. jcsd
  3. Feb 9, 2014 #2

    Doc Al

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    Consider the man + platform as a single system. How many upward forces act on that system?
     
  4. Feb 9, 2014 #3
    Cant find it .please help.
     
  5. Feb 9, 2014 #4
    Ok.downward force is mg+mg=2mg
     
  6. Feb 9, 2014 #5
    2 upward force act.
     
  7. Feb 10, 2014 #6

    Doc Al

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    No. Draw an imaginary box around the 'man + platform'. How many rope segments attach to (and thus pull up on) that system?
     
  8. Feb 10, 2014 #7

    BvU

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    Let me also ask a "helping" question: Consider the man by himself. He is pulling straight down on two ropes, each with a force equal to half his weight X g. How much force does he exercise on the platform in a static situation ?
     
  9. Feb 10, 2014 #8
    2 rope segments.
     
  10. Feb 10, 2014 #9

    BvU

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    Ah, posts cross. You want me to pick up on doc's line of approach?
     
  11. Feb 10, 2014 #10
    both your and doc's.
     
  12. Feb 10, 2014 #11

    BvU

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    I would say four. A segment would be something that exercises a force. A piece of rope slung around a pulley attached to a ceiling can exercise two upward forces, so it's convenient to speak of two segments.
     
  13. Feb 10, 2014 #12
    @Bvu,he exercise mg force.
     
  14. Feb 10, 2014 #13
    @Bvu,then each rope has two segments,right?
     
  15. Feb 10, 2014 #14

    BvU

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    Now the fun thing about a segment of rope in physics is that a) it's weightless ;-) and b) tension forces at each end are equal. That way a piece of rope can be treated as one, but I just talked myself into looking at them as two segments. Doc will decide what's wisdom here. We don't let this hold us back.

    So we have four segments pulling up, each with mg/2 (m = man's mass). Right ?
     
  16. Feb 10, 2014 #15

    BvU

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    Now we have to complete the man+platform picture. What other forces play a role ?
    (rhetorical, you already answered) mg down for the man, mg down for the platform (m=mass platform=mass man)
     
  17. Feb 10, 2014 #16
    @Bvu,if there are two pulleys then will the segments be 2?
     
  18. Feb 10, 2014 #17
    @Bvu,I do not understand that why do we need to consider the mg/2 two times in a single rope?
     
  19. Feb 10, 2014 #18

    BvU

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    My reasoning would be 4. So yes, here you could claim that there are 8 segments and we only see 6 chunks of rope. Talked myself in a corner there....

    In the picture the two pulleys on the left do exactly the same as one pulley would do. Same for the two on the right. Drawing two each is somewhat sadistic on the part of the composer of the exercise.

    My argument for the sections is that a section can exercise a force in a direction. Two sections of a chunk of rope slung around a pulley exercise two forces of equal magnitude but different directions. (Viz. the pulley at the top of the 30 degree ramp earlier).

    Here e.g. the leftmost pulley pulls up on the platform and pulls to the left on the second pulley.
    The second pulley pulls to the right on the first and pulls up on the man.

    This way I bluf my way into considering the piece of rope between the two pulleys as two sections. Others might beg to disagree.
     
  20. Feb 10, 2014 #19

    BvU

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    This is starting to look like a typing contest... I'm old and I'm slow typing with only two fingers...

    The idea is already in my preceding post: it can exercise two forces, one at each end. Because of pulleys the directions can be equal or different.
     
  21. Feb 10, 2014 #20

    BvU

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    Ah, you fell for the trick question. Half his weight on each of the ropes leaves nothing for the platform !
     
  22. Feb 10, 2014 #21

    BvU

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    So here's the drawing doc hoped you would make. The imaginary box is the dotted ellipse ;-).
    And you see straight away why I adopted that working definition of a segment. I start liking it more and more!

    Now back to business and an answer to the question you deftly circumnavigated: what other forces play a role on the system in the dotted ellipse ?
     

    Attached Files:

  23. Feb 10, 2014 #22
    and why tension will be equal to mg/2?
     
  24. Feb 10, 2014 #23

    BvU

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    That's what it said in the original problem, right ?

    I see, it said half its weight, which is half the weight of the platform which is half the weight of the man.

    edited:
    [strike]Your part of the world may be handicapped by thinking weight and force have the same dimension. They do not.Weight = mass,[/strike]
    On second thought -- or rather after thinking -- a bigger part of the world is handicapped by this weight/mass difference that daily language use ignores. Let me speak for myself only in the future!
    Force = mass X acceleration.

    In decent units: My [strike]weight[/strike] mass is 100 kg, sadly. If I hang from a rope attached to a firm branch, the tension in the rope is 100 kg * 9.81 m/s2. At my position (either hands or feet, rather not: neck) that force is pulling up, at the branch it is pulling down.
     
    Last edited: Feb 10, 2014
  25. Feb 10, 2014 #24

    Doc Al

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    Because you are told that the man pulls each rope with a force of mg/2. That means the rope must be pulling back on him with an equal force (Newton's 3rd law) and thus that the tension in the rope must equal mg/2.
     
  26. Feb 10, 2014 #25

    BvU

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    Hi doc. You take over, please.
     
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