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Potential Energy & Conservative Forces #21

  1. Sep 30, 2006 #1
    In the figure below a 1.24 kg block is held at rest against a spring with a force constant k = 700 N/m.

    Initially, the spring is compressed a distance d. When the block is released it slides across a surface that is frictionless, except for a section of width x = 4.85 cm that has a coefficient of kinetic friction μk = 0.357. Calculate d such that the block's speed after crossing the rough patch is 2.23 m/s.


    Sorry I can't post the picture. This was how I was figuring out the problem, but that isn't working.


    k ( L_1 + x)^2 - coefficient sign (u_k)mgx = 1/2mv_f^2 + mg(0)

    since d= L_1 + x and F= kd

    substitute values to get L_1 and then find d

    That is how i was doing it but I can't figure it out. Is there a more simple explanation or way to figure out this problem? Thanks.
     
  2. jcsd
  3. Sep 30, 2006 #2

    Doc Al

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    Staff: Mentor

    What's "L_1 + x" supposed to be?

    The spring is compressed a distance "d": What's the energy stored in it?

    Except for the spring energy term, your energy equation should work fine.
     
  4. Sep 30, 2006 #3
    I get 0.0641 m when i figure it out my way and that answer is incorrect. Maybe I am doing some math wrong, but I double checked? What answer do you get if you use my above equation?

    Are you sure it is the right equation to use?
     
  5. Sep 30, 2006 #4

    Doc Al

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    First correct the spring energy term. It should be: 1/2 k d^2.
     
  6. Sep 30, 2006 #5
    1/2kd^2 - u_k(mgx) = 1/2mv_f^2 +mg(0)

    Solve for d

    I got d= 0.090595

    incorrect answer

    can anyone else help me with this one?
     
  7. Sep 30, 2006 #6

    Doc Al

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    That's not the answer I get. Check your arithmetic. (Did you use the proper units for distance?)
     
  8. Sep 30, 2006 #7
    yeah, my math was off. Thanks, i figured it out.
     
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