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

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