🥋 The Move
Free-Body Diagrams (FBD) — isolate the object, replace contacts with forces, choose axes, and write force-balance / motion equations. Use it whenever forces or contact reactions matter. Avoid skipping it when friction or normal reactions are involved.
📘 Canonical Problem
A block of mass \(m\) slides down a rough incline of angle \(\theta\) with kinetic friction coefficient \(\mu_k\). Find the acceleration \(a\) down the incline and the normal force \(N\).
- Given: \(m,\ \theta,\ \mu_k,\ g\)
- Find: \(a,\ N\)
- Assume: uniform plane; kinetic friction acts up the slope, magnitude \(\mu_k N\).
Sketch notes (no figure):
- Choose axes: \(x\) along the plane (downhill positive), \(y\) normal to the plane (outward).
- Forces: weight \(mg\) (vertical), normal \(N\) (perp to plane), friction \(f_k=\mu_kN\) (up the plane).
- Resolve weight: \(mg_x=mg\sin\theta,\ \ mg_y=mg\cos\theta\).
🔎 Setup (Preview)
- Write balances. Normal: \(\sum F_y=0\Rightarrow N-mg\cos\theta=0\). Along slope: \(\sum F_x=ma\Rightarrow mg\sin\theta-f_k=ma\).
- Use \(f_k\). \(f_k=\mu_kN=\mu_k mg\cos\theta.\)
Continue with annotated steps, speed path, and traps at Black Belt.