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Conservation of Momentum

  1. Jan 25, 2007 #1
    can anyone push me in the right direction with the followin problem, please?

    1. The problem statement, all variables and given/known data
    a cart is moving on a frictionless surface at a speed of [tex]V_0 [/tex]
    the mass of the cart is M.
    it suddenly starts to rain at time t=0. the rain is dropping vertically at a rate of q gk per second.
    the cart collects all the rain drops that hit it.
    express the speed of the cart as a function of time passed since it started raining.

    2. Relevant equations
    [tex]F = {{dp} \over {dt}}[/tex]

    3. The attempt at a solution

    & F = {{dp} \over {dt}} \Rightarrow \cr
    & 0 = {{dm} \over {dt}}v(t) + {{dv} \over {dt}}m(t) \Rightarrow \cr
    & 0 = qv(t) + {{dv} \over {dt}}(M + qt) \Rightarrow \cr
    & qv = - {{dv} \over {dt}}(M + qt) \Rightarrow \cr
    & qvdt = (M + qt)dv


    so i get this equation and i dont know how to solve it for v...

    **how do i add line breaks to the latex??**
    Last edited: Jan 25, 2007
  2. jcsd
  3. Jan 25, 2007 #2
    just like any differential equation, split the variables, put in the initial conditions, and rearrange for the variable you want.

    [tex] \int { \frac {q}{M+qt}} dt = \int {\frac {1}{v}}dv [/tex]

    Try it that way
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