The systematic steps involved in solving a problem in mechanics are:
1. Draw a free body diagram
2. Choose convenient coordinate system
3. Consider all the forces acting on the body
4. Resolve the forces in the chosen coordinate system
5. Apply Newton's Laws of Motion
To draw a free-body diagram, we need to draw a schematic diagram showing all the bodies in an environment along with their links and supports. Then we consider a convenient part of this diagram, relevant to the problem at hand, as a system. Then we draw a detailed diagram of this system along with the external forces acting on it. This diagram is known as a free-body diagram. In a free-body diagram, we do not consider the forces applied by the system on the environment.
Next, we choose a convenient coordinate system to resolve the forces involved. Coordinates should be chosen keeping in mind the probable direction of motion of the body. This makes the solution easier.
Then we add details about all the known and given forces on the system, indicating their respective magnitude and direction.
Then we resolve all these forces along the chosen coordinate system.
Finally, we can take the help of Newton’s Laws of Motion to determine the magnitude and direction of unknown forces.
If the problem at hand requires an analysis of multiple systems in an environment, we follow the same procedure for each individual system.