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Conservation of Energy problem

  1. Mar 22, 2007 #1
    1. The problem statement, all variables and given/known data

    If there is a frictionless circular path with radius R cut into a block of mass M1 and a block of mass M2 slides down the path, what is the velocity of mass M2 as it leaves the block?

    There is no friction between M1 and the ground.

    M2=mass of falling block
    M1=mass of
    v(21)=velocity of M2 with respect to M1
    v(1)=velocity of M1 with respect to the earth
    v(2)=velocity of M2 with respect to the earth

    2. Relevant equations

    I know that this is a conservation of momentum problem, so I used the equations. E(initial)=E(final) and P(initial)=P(final)

    3. The attempt at a solution

    By using conservation of energy, I found the velocity of the mass M2 with respect to M1 as it leaves the circular path. Since it falls a distance R, I set

    (M2)gR=m[v(21)]^2/2

    And found v(21)=SQRT(2gR)

    Since the system began with no momentum and momentum must be conserved:

    0=(M2)(V2)+(M1)(V1)

    What I'm trying to find is V2, I know that V2=V21+V1, so substituting V1=V2-V21 into the momentum equation...

    0=(M2)(V2)+(M1)(V2-V21)=(M2)(V2)+(M1)(V2-[SQRT(2gR)])

    Now the final answer I got was that V2=M1[SQRT(2gR)]/(M1+M2).

    But the answer hint was that if M1=M2, that V2=SQRT(gR) which wasn't what my answer would get.
     
  2. jcsd
  3. Mar 22, 2007 #2
    just kidding, I got it.
     
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