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Conservation of Momentum/Mechanical Energy Question (Fairly Challenging)

  1. Sep 22, 2012 #1
    1. The problem statement, all variables and given/known data
    A small block of mass m is moving on a horizontal table surface at initial speed v0. It then moves smoothly onto a sloped big block of mass M. The big block can also move on the table surface. Assume that everything moves without friction
    xlav4z.png

    Find the speed v of the small block after it leaves the slope.

    2. Relevant equations
    Conservation of Momentum: mv0 = (M+m)v → v=(mv0)/(M+m)
    Conservation of Mechanical Energy: fairly obvious
    The height that it rises to is h = (1/2g)(Mv0^2/M+m), I derived this from conservation of momentum and conservation of mechanical energy
    3. The attempt at a solution
    I set up the conservation of momentum: (M + m)v = -mv1 + Mv2 Is this correct?
    Now I ask, how should I set up the conservation of mechanical energy equation? Should I solve for one variable in terms of the other? The answer should be in terms of v0.
    The answer is v1 = ((M-m)/(M+m))v0
     
    Last edited: Sep 22, 2012
  2. jcsd
  3. Sep 22, 2012 #2

    Doc Al

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    Staff: Mentor

    Don't assume that m & M have the same velocity.
    Don't worry about the height. That's an intermediate point that we don't care about.
    Set initial momentum equal to final momentum. Let v1 and v2 be the final velocities after they separate.
    Intial KE = final KE
    You'll have two equations. Eliminate v2 and solve for v1.
     
  4. Sep 22, 2012 #3
    How would a conservation of kinetic energy equation look like?

    1/2(M+m)v^2 = 1/2mv1^2 + 1/2Mv2^2 ?

    Conservation of momentum: (M+m)v = -mv1 + Mv2 ?

    If I solve for v1 using these equations, it turns out very convoluted and does not resemble the answer. I feel as though it should be cleaner than this. Am I doing something incorrectly?
     
  5. Sep 22, 2012 #4
    Does this problem even meet the criteria to use conservation of kinetic energy? It doesn't seem to be elastic, does it?

    Please help, this problem has been bugging me for awhile.
     
  6. Sep 22, 2012 #5

    Doc Al

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    Staff: Mentor

    OK, except for the left hand side. Initially, only m is moving.

    Same issue as above.

    Clean up the equations as I suggest and try again. A bit of a pain, but you'll get the required answer with a bit of work.
     
  7. Sep 22, 2012 #6
    Wow, it worked! Thanks so much for your help. I greatly appreciate it.
     
  8. Sep 22, 2012 #7

    Doc Al

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    Staff: Mentor

    Excellent! :approve: (And you are most welcome.)
     
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