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Finding the speed with kinetic friction

  1. Feb 6, 2009 #1
    1. The problem statement, all variables and given/known data
    You and your friend Peter are putting new shingles on a roof pitched at 20degrees . You're sitting on the very top of the roof when Peter, who is at the edge of the roof directly below you, 5.4 m away, asks you for the box of nails. Rather than carry the 2.1 kg box of nails down to Peter, you decide to give the box a push and have it slide down to him.

    If the coefficient of kinetic friction between the box and the roof is 0.51, with what speed should you push the box to have it gently come to rest right at the edge of the roof?
    2. Relevant equations
    normal force up y-axis
    mg down y-axis
    angle left of -y
    friction positive x
    not 100% sure if these are right

    n-mg*cos O=may
    fk+mg(sin O)=max
    vf=vi+at
    xf=xi+vi*t+.5at^2

    3. The attempt at a solution
    first get normal force which solve for 1st equ.
    n=2.1(9.8)cos20=19.34
    then find kinetic friction
    19.34*.51=9.86
    put into next equation
    9.86+2.1(9.8)sin20=2.1*a
    a=8.047

    plug into kinematic equ.
    5.4=0+0*t+.5(8.047)t^2
    t=1.15
    vf=8.047*1.15
    vf=9.3

    obviously not right cause Im not sure about the free-body diagram any help would be fantastic.
     
  2. jcsd
  3. Feb 6, 2009 #2

    LowlyPion

    User Avatar
    Homework Helper

    What will the acceleration (deceleration) be?

    It will be the gravity component down the slope less the frictional slowing = g*sinθ - μ*g*cosθ = a

    Since the final velocity is 0, now you can simply use the V2 = 2*a*x
     
  4. Feb 6, 2009 #3
    thank you my friend...that was much easier then I thought it was.
     
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