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Block, wedge and slope

  1. Feb 25, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img187.imageshack.us/img187/9476/dib.th.png [Broken]

    mA = 22kg
    mA = 10kg
    No friction
    At t = 0, at rest

    a.- Find aB
    b.- Find vB/A at t = 0.5s


    2. Relevant equations

    3. The attempt at a solution

    http://img504.imageshack.us/img504/3786/dib3.th.png [Broken] http://img504.imageshack.us/img504/9979/dib2.th.png [Broken]

    I got to the following equations:
    mA·aA = mA·g·cos(30) + NB·sin(50)
    0 = NA - mA·g·sin(30) - NB·cos(50)

    mB·aA·sin(30) = NB - mB·g·cos(20)
    mB·aB/A - mB·aA·cos(50) = mB·g·sin(20)

    There must be something wrong in these because after solving my results are wrong.
    I don't know if I chose the wright base for studying each body (maybe the equations would be simpler with some other base?).

    Thanks for your help!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Feb 25, 2009 #2
    I'm having a little trouble figuring out how you got to those equations - can you tell me a little more of your reasoning?
     
  4. Feb 25, 2009 #3
    I used Newton's 2nd law and then projected the vectors.
     
  5. Feb 25, 2009 #4

    Delphi51

    User Avatar
    Homework Helper

    It seems to me that you have oversimplified. For starters, the acceleration of block B is going to be partly vertical and partly horizontal. It will not be in the direction of the ramp surface because that surface is falling and moving to the left. I think you need both horizontal and vertical accelerations for both blocks.

    I'm thinking of the free body diagrams for A and B. I can write sum of forces = ma in each direction for each block, and get 4 equations with 6 unknowns including the 4 accelerations and the two normal forces.

    NBsin(20) = 10aBx horizontal
    NBcos(20) - 10g = 10aBy vertical
    -NBcos(20) - NAcos(60) = 22aAx horizontal
    -NBsin20 - 22g + NBsin(60) = 22aAy

    Block A can only accelerate along the ramp so aAy = aAx*tan(30)

    Still missing one equation. Must be something to do with B accelerating along its ramp, but it is itself accelerating so awkward to write!
     
    Last edited: Feb 25, 2009
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