Coefficient of Friction between slide/girl

  1. 1. The problem statement, all variables and given/known data
    A 36kg girl slides down a slide that is 4.5m long. At the bottom of slide she is moving at 3 m/sec. If slide is inclined at 35 degrees find the coefficient of friction between slide and girl.

    2. Relevant equations

    Ff = μ*Force normal
    Total energy = KE + PE
    KE = 1/2 mv^2
    PE = mgh
    Total energy = F cosθ

    3. The attempt at a solution

    KE = 162 using above formula, PE = 911.15. Total energy = 1073.15
    F = 1310.32 using the cosθ formula.

    And that is where I am stuck - is the F the normal force or the Ff (from friction) how would I solve for the coefficient from this point? And have I even approached it in the right way so far?
  2. jcsd
  3. PeterO

    PeterO 2,319
    Homework Helper

    Firstly; how did you get that PE figure - not enough to say using the formula above as I need to know what values you used for m, g and h.

    Secondly; why did you add KE and PE together? Surely we had pE at the top and KE at the bottom, but never both at the same time [perhaps half and half on the way down, but you were considering the top and the bottom, I hope]
    You said,
    Total energy = KE + PE

    At the top that would be Total energy = 0 + PE
    At the bottom that would be Total energy = KE + 0

    And those two totals are different, due to the friction.

    Edit: Total energy = F cosθ makes you group of formulas look like a grab-bag of possibilities, rather than a reasoned list of what actually applies.
  4. gneill

    Staff: Mentor

    At the top of the slide the girl has PE = 911 J. At the bottom, her KE is only 162 J. What happened to the rest of the PE? How much work was done by friction?
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