Free-Body Diagrams (FBD)
Overview
A FBD shows ALL forces acting on a single object as arrows from the object's centre. Standard forces: Weight (W = mg, downward), Normal force (N, perpendicular to surface), Friction (f, opposing motion), Tension (T, along string/rope), Applied force. Each force must be labelled with magnitude and direction. Resolve along axes, then apply F_net = ma.
Drawing a correct Free-Body Diagram
A Free-Body Diagram (FBD) shows one object as a dot or box, with all forces acting ON it drawn as arrows pointing away from the object. Rules: (1) Include ONLY forces acting on the chosen object. (2) Each arrow should show the force's direction. (3) Label each force (W, N, T, f, etc.). (4) Show the approximate relative magnitudes by arrow length. Common forces to consider: weight (W = mg, always downward), normal force (perpendicular to surface), tension (along string/rope), friction (opposing motion), applied force.
FBD for an inclined plane
For a block on a slope at angle θ: Weight W = mg acts vertically downward (not perpendicular to slope). Resolve weight into components parallel and perpendicular to the slope: W_∥ = mg sin θ (down the slope), W_⊥ = mg cos θ (into the slope). Normal force N = mg cos θ (perpendicular, away from slope). Friction f (if present) acts up the slope if the block slides or tends to slide down.
- ⚠Drawing forces on the wrong object — in an FBD, only forces ON the chosen object go in
- ⚠For inclined planes: using mg (not mg sin θ or mg cos θ) as the component along the slope
- ⚠Forgetting friction when the surface is described as 'rough'