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

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Applied Mechanics and Graphic Statics
A point subjected to a number of forces will be in equilibrium, if

Algebraic sum of the moments of the forces about the point is zero
Two resolved parts in any two directions at right angles are equal
Sum of resolved parts in any two directions at right angles, are both zero
Algebraic sum of the forces is zero

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Applied Mechanics and Graphic Statics
The force acting on a point on the surface of a rigid body may be considered to act

At the centre of gravity of the body
On the periphery of the body
On any point on the line of action of the force
At any point on the surface normal to the line of action of the force

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