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Work-Energy Principle

  1. Nov 2, 2007 #1
    [SOLVED] Work-Energy Principle

    1. The problem...
    On an essentially frictionless horizontal ice-skating rink, a skater moving at 3.00 m/s encounters a rough patch that reduces her speed by 45.0 % to a friction force that is 25.0 % of her weight.

    Use the work-energy principle to find the length of the rough patch.

    2. The relevant equation...
    KEi + PEi + W(by friction) = KEf + PEf where i = initial and f = final

    3. My attempt...
    Since Work by friction = -Fd, then you can substitute F for (.25 x mg), correct? that is because the Force of friction (F) is 25% of her weight (mg). Ultimately, this is going to allow m to cancel out. With that, I have the equation:

    .5mv^2 + mgh + (-.25mg)d = .5mv^2 + mgh

    Factoring out the m so it can cancel out I now have:

    m (.5v^2 + gh + (-.25g)d) = m (.5v^2 + gh)

    Since this is all happening on a level surface, then h = 0. Now I am left with:

    .5v^2 + (-.25g)d = .5vf^2

    Now, plug in our known values...

    .5(3^2) + (-.25 x 9.8)d = .5(.45 x 3)^2

    Note: v final = 3 x 45% as stated in the problem

    Solving for d, I get 1.46 meters. But this is wrong...

    I've also tried this same exact setup using a final speed of 0, getting a distance of 1.84 meters. That, too, is wrong.
  2. jcsd
  3. Nov 2, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    The problem states that the speed is reduced by 45%, not reduced to 45%.
  4. Nov 4, 2007 #3
    Yeh, I got that about 5 mins after I posted this (and the forum for down for me, I couldn't access it). Thanks for your help, though. It's much appreciated. :)
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