HOW TO FIND THE RESULTANT OF A FORCE SYSTEM?

For a force system i.e. a system of several forces acting on an object, it is possible to get the same effect on the object by the force system replacing it by a single force, that will be equivalent to the summation of the component forces acting on the object. The single force that will produce exactly the same effect on the object in stead of the force system is called Resultant of the force system.

We know that two forces acting on an object lying on a plane can be added together by

• (i) Triangle's Law or
• (ii) Parallelogram Law.
  For more than two vectors we use
• (iii) Polygon Law of Force Addition.
• (iv) Force Resolution Method.

The resultant of a force system is the Force which produces same effect as the combined forces of the force system would do. So if we replace all components of the force by the resultant force, then there will be no change in effect.

The Resultant of a force system is a vector addition of all the components of the force system. The magnitude as well as direction of a resultant can be measured through analytical method.

THE STEPS TO FIND A RESULTANT OF A CON-CURRENT FORCE SYSTEM:

STEP 1:

RESOLVE ALL THE COMPONENT FORCES ALONG X-AXIS AND Y-AXIS.

If a force F acts on an object at an angle ß with the positive X-axis, then its component along X-axis is F cosß, and that along Y-axis is F sinß.


STEP 2:

ADD ALL THE X-COMPONENTS OR HORIZONTAL COMPONENTS AND IT IS DENOTED BY ΣF_x AND

ADD ALL THE Y-COMPONENTS OR VERTICAL COMPONENTS AND IT IS DENOTED BY ΣF_y.

STEP 3:

FIND THE MAGNITUDE OF THE RESULTANT R

We know from Geometry that

R = √{(ΣF_x)² + (ΣF_y)²}

STEP 4:

FIND THE DIRECTION (α) OF THE RESULTANT FORCE (R)

We know that

tan α = (ΣF_y/ΣF_x)

hence,

α = tan^-1(ΣF_y/ΣF_x)