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Homework Help: Velocity of a trolley on an inclined plane with a twist

  1. Mar 2, 2010 #1
    A friend asked me how to solve this problem:

    There is a trolley of mass M[tex]_{o}[/tex]kg on a fixed inclined plane, whose angle of inclination is [tex]\theta[/tex]. The block is at a height Hmetres, at the top of the inclined plane. Coefficient of friction is [tex]\mu[/tex]. It is also known that it is raining, and the rain drops are falling with a velocity ums[tex]^{-1}[/tex] at the rate of [tex]\eta[/tex] kgs[tex]^{-1}[/tex]. The rain is also falling, making an angle [tex]\alpha[/tex] with the ground. The trolley is released from rest at t=0. Find the velocity v of the trolley when it reaches the bottom.

    I solved this question and ended up with a big differential equation in terms of dv and dt. However, part of the equation contains a dx (displacement along the plane) with t in the denominator that I am unable to get rid of. The only way I can do so is by means of a relation between displacement and time. Could someone help me with this part?

    The problems I'm facing are:
    (i) acceleration is varying
    (ii) velocity is varying
    (iii) I'm unable to get a constraint independent of velocity of the trolley.

    I've attached a .bmp of the figure. Hope it helps.
     

    Attached Files:

  2. jcsd
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