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A uniform board is leaning against a smooth vertical wall. The board is at an angle above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.710. Find the smallest value for the angle , such that the lower end of the board does not slide along the ground.

  • Phyics - ,

    A = angle of board up
    force up = weight of board = w

    friction force max = .7 w
    equal and opposite horizontal force on wall = .7 w

    length of board = L
    weight of board down = w at L/2
    moment of that weight about foot of board = w(L/2) cos A
    moment of horizontal wall force about foot of board = .7 w (L/2) sin A

    .7 sin A = cos A
    sin A/cos A = 1/.7 = 1.43 = tan A
    so A = 55 degrees

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