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Calculating constant velocity using work

  1. Nov 22, 2011 #1
    1. The problem statement, all variables and given/known data
    A 25.6-kg boy pulls a 4.81-kg toboggan up a hill inclined at 25.7º to the horizontal. The vertical height of the hill is 27.3 m and the coefficient of friction of the hill surface is 0.4
    a) Determine how much work the boy must apply on the toboggan to pull it at a constant velocity up the hill? (Hint: An FBD is needed to see all your forces acting on te toboggan)



    2. Relevant equations
    W = F x ∆d
    Eg = mgh
    Ek = 0.5mv^2
    vf^2 - vi^2 = 2a∆d


    3. The attempt at a solution

    [tex]-mgsin25.7º - \mu Kmgcos25.7º = m * a[/tex]
    [tex]-(30.41 x 9.8 x sin 25.7º) - (.4 x 30.41 x 9.8 x cos 25.7) = 30.41 * a[/tex]
    [tex]-129.24 - 106.46 = 30.41a[/tex]
    [tex]a = -7.75 m/s^2[/tex]


    Calculating length of the hill:

    [tex]\frac{27.3}{sin25.7º} = 62.95m[/tex]

    I don't really know what to do after this.
     
  2. jcsd
  3. Nov 22, 2011 #2

    cepheid

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    Staff Emeritus
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    Gold Member

    If the boy is pulling the toboggan up the hill at a constant speed, then what must the acceleration be equal to? Hint: your mistake was that you forgot one of the forces in the force balance equation: the applied force from the boy!
     
    Last edited: Nov 22, 2011
  4. Nov 22, 2011 #3
    The reply above is spot on.

    reconsider your acceleration and add the pulling force from the boy.
     
  5. Nov 23, 2011 #4
    Ooooh thank you! I feel like an idiot now :(:
     
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