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Kinetic & Potential Energy / Momentum Problem

  1. Nov 29, 2011 #1

    x93

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    1. The problem statement, all variables and given/known data
    From Kleppner and Kolenkow:
    A small cube of mass m slides down a circular path of radius R cut into a large block of mass M, as shown. M rests on a table, and both blocks move without friction. The blocks are initially at rest, and m starts from the top of the path.
    Find the velocity v of the cube as it leaves the block.

    Ans. clue. If m=M, v=√(gR)

    http://img390.imageshack.us/img390/5575/blocksbi2.jpg [Broken]

    2. Relevant equations
    KE=(1/2)mv2
    PE=mgh
    mivi=mfvf
    KEi=KEf


    3. The attempt at a solution
    For m, initial energy PEm=mgR
    Just before m leaves block M, KEm=(1/2)mv2=mgR
    Thus, v=√(2gR).
    From here, I set up equations for conservation of momentum as well as kinetic energy.
    I then used substitution and tried to solve for the velocity of m as it leaves the block, M, but the algebra just isn't working out. Did I make a mistake?
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Nov 30, 2011 #2

    ehild

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    Homework Helper
    Gold Member

    Do not ignore the KE of the large block.


    ehild
     
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