Applied Mechanics and Graphic Statics
A heavy ladder resting on a floor and against a vertical wall may not be in equilibrium, if

Floor and wall both are smooth surfaces
Floor and wall both are rough surfaces
Floor is smooth and the wall is rough
Floor is rough and the wall is smooth

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Applied Mechanics and Graphic Statics
A body of weight ‘w’ placed on an inclined plane is acted upon by a force ‘P’ parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ‘θ’ and angle of friction is ‘φ’, the minimum value of ‘P’, is

w sin (φ - θ)/cos φ
w cos (θ + φ)/cos φ
w sin (θ - φ)/cos φ
w sinθ cos(θ - φ)/sin φ

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