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Snowball problem

  1. May 6, 2009 #1
    1. The problem statement, all variables and given/known data
    "A snowball, initially of mass m, slides down a slope inclined at an angle φ with
    respect to the horizontal. As it moves, the mass of additional snow Δm = αx that it
    accumulates is proportional to the distance travelled x. Write the differential equation
    of translational motion for the snowball, ignoring rotation and friction. [6]"

    I was sure mass was irrelevant in this situation? But judging by the question its not. Could anyone help me out?


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 6, 2009 #2

    gabbagabbahey

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    As always, I'd begin by drawing a picture; what Force(s) act on the snowball, and which direction do they point?
     
  4. May 20, 2011 #3
    F=d(mv)/dt
    F=v dm/dt + m dv/dt

    m=m+ax
    dm/dt=av

    F=mg sin(*)

    mg sin(*)=m dv/dt + a v^2
     
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