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Tension, acceleration, pulley

  1. Nov 19, 2015 #1
    1. The problem statement, all variables and given/known data

    A cat is stuck in a tree. You are designated with the job to get it out, yet you do not want to climb the tree, because you may get stuck as well. Instead you set up a pulley system. A rope (consider it massless) runs from the seat you sit on over an ideal pulley and then to your hand. You pull on the loose end of the rope with a force of 348 N. You weigh 612 N and the seat you sit on weighs 16.0 N. (a) What is your acceleration? (b) What force does the seat exert on you?
    2. Relevant equations
    F=ma
    t - mg = ma
    3. The attempt at a solution
    ok so i found the mass to be 64.2 kg
    the combined force weight is 628 N
    i thought the tension would be 348 N but I'm not getting the right answer with that
     
  2. jcsd
  3. Nov 19, 2015 #2

    Doc Al

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    Staff: Mentor

    That is the tension in the rope.

    Careful here. The rope pulls on the person and on the seat.

    (Hint: For part a, treat the person+seat as a single system. What forces act?)
     
  4. Nov 19, 2015 #3
    i did that and i got -4.5 but the answer should be 1.06
     
  5. Nov 19, 2015 #4

    Doc Al

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    Staff: Mentor

    Show what you did. What forces act on "person+seat"?
     
  6. Nov 19, 2015 #5
    well they have a combined force weight of 628 N so 348 N - 628 N = 64.1 (i messed up the first time)a
    which equals -4.3
     
  7. Nov 19, 2015 #6

    Doc Al

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    Staff: Mentor

    You have an upward force of only 348 N. But how many rope segments pull up on the system?
     
  8. Nov 19, 2015 #7
    one
     
  9. Nov 19, 2015 #8

    Doc Al

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    Staff: Mentor

    Nope. The rope pulls up twice. Once on the person; once on the seat.
     
  10. Nov 19, 2015 #9
    ok doubling the force tension gives me the right answer but I'm confused why that is. I don't understand why it pulls up twice even though its only connected to the chair.
     
  11. Nov 19, 2015 #10

    Doc Al

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    Ah, but it's not only connected to the chair. It's also connected to the person, who is pulling up on one end of the rope. (One end connects to the seat; the other end, to the person.)

    Try this: Draw an imaginary box around the "person + seat". How many rope segments connect to that box?
     
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