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Small block with velocity inside a large block at rest

  1. Nov 2, 2015 #1
    1. The problem statement, all variables and given/known data

    D4sOhC4.png

    2. Relevant equations

    (Conservation of momentum)
    (Conservation of energy)

    3. The attempt at a solution

    I know linear momentum must be conserved on the X-axis, so

    mvo=mv1x+Mv2

    where v1 is the final velocity of the small mass and v2 is the final velocity of the large mass. Also, M=2m.

    Energy is also conserved, so

    (1/2)mvo2=(1/2)mv12+(1/2)Mv22+mgR

    Since the problem stipulates that the 2 blocks never lose contact with each other, I'm guessing the momentum in the x direction would actually be

    mvo=(m+M)v2

    and v2=v1x

    But I'm not sure if that is right, and so I'm not totally sure where to go from here.
     
  2. jcsd
  3. Nov 2, 2015 #2
    It looks like you have all the physics in place to solve it. Keep going with the algebra ...

    When I solved it I wrote everything in terms of the velocity ##\vec{v}## of the small block, so that

    ##v^{\ 2}=v_x^{\ 2}+v_y^{\ 2}.##
     
    Last edited: Nov 2, 2015
  4. Nov 5, 2015 #3
    I don't think that momentum is conserved in the x-direction.
    What can one say about conservation of momentum in the y-direction?
    Also, the two blocks do not form an isolated system because of the normal
    force on the larger block by the frictionless surface.
     
  5. Nov 5, 2015 #4
    There are no external forces in the x-direction.
    There are external forces in the y-direction.

    That normal force is one of the external forces in the y-direction.
     
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