🥋 The Move
Pick the quickest tool. Use Work–Energy when you need speeds/positions and work is path-independent (or easy to compute). Use Newton + kinematics when accelerations/signs/constraints matter step-by-step.
📘 Canonical Problem
A block of mass \(m\) starts from rest on a horizontal surface. A constant horizontal force \(F\) pulls it a distance \(s\) with kinetic friction coefficient \(\mu_k\). Find its final speed \(v\).
- Given: \(m,\ F,\ s,\ \mu_k,\ g\)
- Find: \(v\)
- Assume: constant \(F\), constant \(\mu_k\), straight path.
Sketch notes (no figure):
- Work–Energy: \(W_{\text{net}}=\Delta K\).
- Friction work: \(W_f=-\mu_k m g\,s\).
- Newton route: \(a=(F-\mu_k m g)/m\), then \(v^2=2as\).
🔎 Setup (Preview)
- Energy. \( \tfrac12 m v^2 = F s – \mu_k m g s \Rightarrow v = \sqrt{\dfrac{2s}{m}\big(F-\mu_k m g\big)}\).
- Newton. \(a=(F-\mu_k m g)/m\Rightarrow v^2=2as\) (same result).
Full comparison and speed rules at Black Belt.