Free Body Diagrams

A free body diagram is a simplified sketch used to analyse the forces acting on one single, chosen body in a mechanics problem, in isolation from everything else around it. To draw one correctly:

1. Isolate the body. Choose exactly one body to analyse (a block, a car, a person), and represent it as a simple point or a small shape, mentally removing everything else it touches or interacts with (the ground, a string, another block) from the picture.
2. Identify every external force acting ON this body, and only on this body -- never a force the body itself exerts on something else. These typically include: its weight $mg$ (always vertically downward, due to gravity, a non-contact force); the normal reaction $N$ from any surface it touches (always perpendicular to that surface, pushing away from it); tension $T$ in any string or rope attached to it (always directed along the string, away from the body, pulling it); friction $f$ from any rough surface it is in contact with (always along the surface, opposing the body's actual or tendency-to motion); and any other applied push or pull explicitly given in the problem.
3. Draw each force as an arrow from the point representing the body, with its length loosely suggesting relative magnitude and its direction exactly as identified in step 2.
4. Choose convenient coordinate axes (often, for a body on an incline, axes running along and perpendicular to the incline rather than purely horizontal and vertical) and resolve any forces not already along an axis into components along the two chosen axes.
5. Apply Newton's second law along each axis separately -- $\sum F_x = ma_x$ and $\sum F_y = ma_y$ -- using $a = 0$ along any axis in which the body is known to be in equilibrium.

The worked figure for this section applies exactly this method to a block of mass $m$ resting on a frictionless incline of angle $\theta$, held in place by a light string running parallel to the incline surface. Three forces act on the block: its weight $mg$ (vertically down), the normal reaction $N$ (perpendicular to the incline), and the string tension $T$ (up along the incline). Choosing axes along and perpendicular to the incline, the weight resolves into two components: $mg\sin\theta$ acting down the slope, and $mg\cos\theta$ acting into the incline surface. Since the block is held in equilibrium (at rest), applying Newton's second law with zero acceleration along each of the two chosen axes gives the two governing equations directly: …