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Material point and curve wedge

  1. Jul 1, 2014 #1
    1. The problem statement, all variables and given/known data

    I think that the image is clear.
    There isn't friction, not the material point with wedge, not the wedge with the floor.

    At time t=0 the material point start to move, I need to find the final speed of the two objects at time [itex]t\rightarrow\infty[/itex].

    2. Relevant equations

    I have used conservation of energy and momentum.

    3. The attempt at a solution

    So I have two equation:
    [itex]\frac{1}{2}m{v_m}^2+\frac{1}{2}M{v_M}^2 = mgR[/itex]

    [itex]m{v_m}+M{v_M}=0[/itex]

    And the solution is [itex]{v_m}=\sqrt{\frac{mgR}{\frac{1}{2}m+\frac{1}{2}\frac{m^2}{M}}}[/itex]

    Am I wrong?
     

    Attached Files:

  2. jcsd
  3. Jul 1, 2014 #2

    tms

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    It can be simplified, but it looks okay. What about the velocity of the other object?
     
  4. Jul 1, 2014 #3
    Well, if [itex]V_m[/itex] is right is very simple to find [itex]V_M[/itex], so I haven't written it.
     
  5. Jul 2, 2014 #4
    I have also a similar problem, you can see the image.

    In this the mass m, start with an initial speed [itex]v_0[/itex], you have to find [itex]v_0[/itex] so that the material point has maximum height R.

    I think that is right to use the two equations:

    [itex]\frac{1}{2}m{v_m}^2+\frac{1}{2}M{v_M}^2+mgR=\frac{1}{2}m{v_0}^2[/itex] energy

    [itex]m{v_m}+M{v_M}=mv_0[/itex] momentum

    for the point of maximum height, and then you have [itex]{v_m}={v_M}[/itex] , because the two bodies are in contact.
     

    Attached Files:

  6. Jul 2, 2014 #5

    tms

    User Avatar

    Next time, you should put a new problem in a new thread.

    That appears correct.
     
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