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Determine the largest angle - wedge

  1. Feb 27, 2012 #1
    1. The problem statement, all variables and given/known data
    A small wedge is placed beneath corner B of the 4000-kg block of marble.
    Determine the largest angle θ for which the wedge is self-locking; that is, the
    wedge will not slide out from under the block. Neglect the mass of the wedge and
    the small angle between surface AB and the horizontal.

    http://screensnapr.com/e/527Zk6.jpg [Broken]

    2. Relevant equations

    using the FBD of the whole composite body.

    summation of forces on x = 0
    0.2Na - 0.2Nc = 0

    summation of forces on y = 0
    -39240 + Na + Nc = 0

    solving, it yields = Na = 19620 Nc = 19620

    3. The attempt at a solution

    now, we take the fbd of just the wedge

    summation of forces along x = 0
    Nb cos(90-θ) -fb cos(θ) - fc = 0

    summation of forces along y = 0
    -Nb sin(90-θ) - fb sin(θ) + Nc = 0

    dividing those 2 eqns yields:

    -tan(90-θ) + tan(θ) - (Nc/fc)
    then since we have Nc and Fc (using f = uN) where u = 0.2

    and θ yields arounds 70 degrees which is incorrect (the book says 18.15 degrees)

    thanks
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
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