D′ALEMBERT'S PRINCIPLE - Application to System of Particles:

While a number of particles are connected by a system, the solution of such problems is bit complexes. The equations and methods developed in the preceding section may be utilized in these cases also. While applying this method, the following points should be followed :

1. We should draw free-body diagram for each body involved indicating all known and unknown forces. If the direction of any unknown force (except frictional forces) is incorrectly assumed the solution shall yield its correct magnitude but with a negative sign. We must remember that however frictional forces always must be in the direction opposite to motion.

2. To mark correctly the frictional forces, it is essential to determine the direction of motion. If the same is not specified, indicate the same by a dashed arrow near each free-body diagram. This shall be helpful in deciding positive direction of equation of motion.

3. Kinematic relationships for different bodies involved should be determined.

4. Select x axis positive in the direction of initial motion and apply equilibrium equations for curvilinear motion and corresponding dynamic equilibrium equations should be used.

5. By using additional kinematic equations, solve for unknown.