Lesson 2 · 14 min
Free-body diagrams
The first drawing an engineer makes. If the diagram is wrong, the algebra cannot save you.
One body, every contact, gravity
A free-body diagram isolates one object. You draw it as a point or a block. You draw every force acting on it — not forces it exerts, not accelerations, not velocity. Gravity at the center of mass, downward. Contacts: normal (perpendicular to the surface), friction (tangent, opposing slip or impending slip), tension along a cable, spring along its axis.
Then you choose axes. Aligning an axis with the acceleration — down a ramp, along a cable — is not laziness. It is how you keep the algebra from growing a cosine you do not need.
The usual suspects
Weight always exists (near Earth). The normal force exists only at a contact, and it is whatever magnitude is required to prevent interpenetration — it is not “always mg.” A body in an elevator, on a banked curve, or under a downward push has N ≠ mg. Friction exists only at a rough contact, and static friction is an inequality: it can be anything from zero up to μs N.
Check
A crate sits at rest on a horizontal floor. You push sideways with 5 N; it does not move. Friction on the crate is