Statics - Parallel coplanar forces — The resultant of parallel coplanar forces

About this lesson

This unit teaches how to find the resultant of parallel coplanar forces. It begins with two like (same-direction) forces, explaining that the resultant has a magnitude equal to the sum of the two forces, acts in the same direction, and its point of action divides the distance between the forces internally in inverse ratio to their magnitudes. It then covers two unlike (opposite-direction) forces, where the resultant has a magnitude equal to the difference of the magnitudes, acts in the direction of the larger force, and its point of action divides the distance externally from the side of the larger force. The unit also proves (though the proof is not required) that the sum of moments of a system of parallel coplanar forces about any point equals the moment of the resultant about that point. Worked examples and exercises involve finding the resultant of two or more parallel forces, locating its point of action, and solving problems where one force or the resultant is unknown. Situations use forces acting on a ruler, a light rod, and points on a straight line, with forces given in Newtons or kg.wt. By the end, a student should be able to compute the magnitude, direction, and point of action of the resultant for systems of parallel coplanar forces, and apply the moment theorem to solve related problems.