Common Mistakes to Avoid — Work, Energy & Power — Summary

Forgetting friction in work-energy problems: When a surface is rough, W_friction = −μ_k N · d must be included. Omitting it gives an incorrectly high final speed. Always check for "rough" or "μ" in the problem.
Confusing string and rod in vertical circular motion: For a string, v_top(min) = $\sqrt{gR}$ . For a rod, v_top(min) = 0. Applying the string result to a rod is the most common trap in this chapter.
Assuming KE is conserved in inelastic collisions: KE is conserved ONLY in elastic collisions. In perfectly inelastic collisions, KE loss is maximum (not zero). "Inelastic" ≠ "all KE lost" — some KE remains.
Using wrong angle in W = Fd cos θ: θ must be the angle between force and displacement, not between force and the surface, or between force and the vertical. Draw vectors and measure the included angle explicitly.
Applying energy conservation with friction acting: KE + PE ≠ constant when friction is present. Use: KE_i + PE_i − W_friction_dissipated = KE_f + PE_f.
Confusing power formula for inclined planes: At terminal speed on an incline, both gravity component (mg sin θ) and friction (μmg cos θ) resist motion. Total resisting force = mg(sin θ + μ cos θ). P = F_total · v_terminal.
Forgetting normal force changes when force has a vertical component: When a force is applied at an angle below horizontal, N increases; when angled above horizontal, N decreases. This changes friction force f_k = μ_k N.
Using v_bottom = $\sqrt{5gR}$ for a rod: This is the string result. For a rod, v_bottom(min) = $\sqrt{4gR}$ . String = 5, Rod = 4 — memorise the pair.
Sign errors in collision velocity formulas: In elastic collision formulas, u_{2} appears in both v_{1} and v_{2} expressions. When u_{2} = 0, many terms vanish — write out the full formula first, then substitute.