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Newton's laws -- Block sliding on a Prism

  1. Apr 18, 2016 #1
    1. The problem statement, all variables and given/known data
    All the surfaces shown in fig. are assumed to be frictionless. The block of mass m slides on the prism of mass M which in turn slides backwards on horizontal surface with acceleration of ao. Find the acceleration of smaller block with respect to prism.
    IMG_20160418_185846.jpg


    2. Relevant equations


    3. The attempt at a solution
    As we are working from the frame of reference of prism which is non inertial
    we have to include a pseudo force in opp. direction of acc of prism.
    Now , forces on the block are
    1)mg downwards
    2)Normal force N
    3)pseudo force (mao)
    When I resolved these forces using force body diagram , it gave me 2 equations
    maocosθ+mgsinθ=ma
    i.e aocosθ+gsinθ=a
    and
    N+maosinθ=mgcosθ

    I m stuck here...
    How to eliminate N and ao ??
    Please help
    Ans is
    (M+m)gsinθ / M + msin2θ
     
    Last edited by a moderator: Apr 18, 2016
  2. jcsd
  3. Apr 18, 2016 #2
    how the prism M moves Ma0 = some force, think about it
    i feel a component of N must be responsible for its motion.
     
  4. Apr 20, 2016 #3
    Is it Nsinθ??
     
  5. Apr 20, 2016 #4
    please draw a free body diagram

    i think you are correct - M.acceleration of the prism=Nsin (theta)
     
  6. Apr 23, 2016 #5
    I am not sure, but here's my two cents:
    The angle between the line of acceleration of the prism and the line of acceleration of the block is equal to 90+theta degrees. Use vectors to work out the acceleration of the block with respect to the prism.
     
  7. Apr 23, 2016 #6
    so it can be written
    -M* a (0) = N sin ( theta)
     
  8. Apr 24, 2016 #7

    ehild

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    No, M*a0=Nsin(theta).

    The block and the prism interact with the normal force of magnitude N. See picture. If ##\vec N## is the normal force acting on the block, then it is ##-\vec N## acting on the prism.
    The normal force exerted on the prism has a backward component, accelerating the prism horizontally, to the left. @Prathamesh was right.
     

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  9. Apr 24, 2016 #8
    if a0 is taken as +ve directed on the right side , then naturally
    -Ma0 can be seen as vector going to the left.
     
  10. Apr 24, 2016 #9

    ehild

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    The force causing this acceleration of the block is -N. -Mao=-Nsin(theta), and you can eliminate the minuses.
     
  11. Apr 25, 2016 #10
    Try to do without pseudo forces, which will enhance your understanding further.
     
  12. Apr 25, 2016 #11
  13. Apr 25, 2016 #12

    ehild

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    You missed the parentheses from the answer. Correctly it is (M+m)gsinθ / ( M + msin2θ)

    Together with the equation for the block,
    Mao=Nsin(θ)
    you have three equations with three unknowns. Just go ahead.
     
  14. Apr 25, 2016 #13

    ehild

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    The problem wants the acceleration of the block with respect to the prism. The OP's method is correct and the solution is easy that way.
     
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