4.2 Addition of Forces
In Chapter 2, we learnt about vectors and their representation. Remember that the resultant is the same for any order of addition of vectors. As forces are vectors, forces can also be added by the head-to-tail rule.
To determine the resultant of two or more forces acting in a plane, the following example explains the method.
Example 4.1
Let us add three force vectors F₁, F₂, and F₃ having magnitudes of 200 N, 300 N, and 250 N acting at angles of 30°, 45°, and 60° with the x-axis. By selecting a suitable scale (100 N = 1 cm), we can draw the force vectors as shown in Fig. 4.2(a).
To add these vectors, we apply the head-to-tail rule as shown in Fig. 4.2(b).
The measured length of the resultant force is 7.1 cm. According to the selected scale, the magnitude of the resultant force F is 710 N and its direction is at an angle of 43° with the x-axis.