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Box Hangs From Rope

  1. Oct 19, 2007 #1
    A 61.0kg box hangs from a rope. What is the tension in the rope if:

    (a) The box is at rest?
    (b) The box moves up a steady 5.10m/s?
    (c) The box has v_y = 5.10m/s and is speeding up at 5.10m/s^2? The y axis points upward.
    (d) The box has v_y = 5.10m/s and is slowing down at 5.10m/s^2?

    This problem seems easy, but because I cannot even get part (a) I am confused and need help.

    To me it seems like part (a) should be either 0N or 61N.
    F=ma
    F=61kg(0m/s^2) ---> box at rest means acceleration is zero right?
    F=0N
     
  2. jcsd
  3. Oct 19, 2007 #2

    Doc Al

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    Analyze the forces acting on the box (there are two) and apply Newton's 2nd law (Fnet=ma). You're right that "ma" = 0, but that means that the net force is zero.
     
  4. Oct 19, 2007 #3
    I am still a little confused.
    The two forces are Tension and Weight, which if the Acceleration is zero, doesnt this mean that the force of the tension and weight are the same.
     
  5. Oct 19, 2007 #4
    Gravity....

    So it would be 61kg times 9.8m/s^2 = 597.8N for part (a)
     
  6. Oct 19, 2007 #5
    How do I tackle part (b)?
     
  7. Oct 19, 2007 #6

    Doc Al

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    Exactly. The force equation is: T - mg = ma = 0; so T = mg.

    Using the same method. What's the acceleration in this case?
     
  8. Oct 19, 2007 #7
    5.10 ???
     
  9. Oct 20, 2007 #8

    Doc Al

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    No. 5.10 m/s is the speed, which is steady. (Note that acceleration has units of m/s^2, not m/s.)

    So, what's the acceleration of something moving upward at a steady speed?
     
  10. Oct 20, 2007 #9
  11. Oct 20, 2007 #10

    Doc Al

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    Yep. Next!
     
  12. Oct 20, 2007 #11
    Ok so it 598N again.

    Now part (c)...
    It is accelerating at 5.10m/s^2

    T-mg=ma

    ma= 61(5.1) = 311N
    mg= 598N

    T= ma+mg= 311N+598N = 909N
     
  13. Oct 20, 2007 #12
    Part (d) would then be 598N - 311N = 287N

    Thanks for your help!!!
     
  14. Oct 20, 2007 #13

    Doc Al

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    Perfect! (for b, c, & d!)
     
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