Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting on an object or system. The object or system is represented by a single isolated point (or free body). Only those forces acting on it that originate outside of the object or system—the external forces—are shown. The forces are represented by vectors extending outward from the free body. Imagine a person sitting on a chair. Here, the free-body diagram consists of two forces. The normal force of the chair is directed upwards, and the gravitational force is directed downwards.
Taking another example, consider a rocket sled moving on a horizontal surface. The sled experiences a rocket thrust that accelerates it, with each rocket creating an identical thrust, T. The system here is the sled, its rockets, and its rider, so none of the forces between these objects are considered. The free-body diagram consists of thrust acting in the positive x-direction, friction acting in the negative x-direction, the normal force acting in the positive y-direction, and its weight acting in the negative y-direction. Although forces are acting both vertically and horizontally, the vertical forces cancel out each other because there is no vertical acceleration. This leaves us with only horizontal forces and a simpler one-dimensional problem. Directions are indicated with plus or minus signs, with the right side taken as the positive direction.
If we were to look at a free-body diagram of a skier on a slope, the normal force would be shown perpendicular to the slope, and the frictional force parallel to the slope. However, the weight of the skier has components along both axes, namely Wx and Wy.
This text is adapted from Openstax, University Physics Volume 1, Section 5.7 Drawing Free-Body Diagrams.
