Work, Energy and Power

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Work, Energy & Power — Key Facts Work: W = F·d cosθ = Fd_parallel; SI unit: Joule (N·m); can be negative (angle >90°) Kinetic Energy: KE = ½mv²; scalar, always ≥ 0 Potential Energy: PE = mgh (gravitational), PE = ½kx² (spring); depends on frame Conservation of Mechanical Energy: total KE + PE = constant (only if no non-conservative forces Power: P = W/t = F·v (instantaneous); SI unit: Watt (J/s); 1 hp ≈ 746 W ⚡ Exam tip: Work-Energy theorem W_net = ΔKE is valid even with friction — use it!

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Work, Energy & Power — NEET/JEE Study Guide Conservative forces: gravity, spring, electrostatic — path independent, have potential energy Non-conservative: friction, air resistance — mechanical energy dissipated as heat Work-Energy theorem: net work done = change in KE; W_net = ΔKE Potential energy: U = -∫F·dr; for gravity U = mgh (near Earth’s surface); for spring U = ½kx² Collisions: elastic (KE conserved, e=1), inelastic (KE lost, 0<e<1), perfectly inelastic (objects stick, e=0) Coefficient of restitution: e = v_separation/v_approach = √(KE_lost/KE_initial) for 1D

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Work, Energy & Power — Comprehensive Notes Variable force work: W = ∫F·ds; integrate force-displacement graph = area under curve Power-velocity: P = Fv; for vehicle with constant power: v = (Pt/m)^(1/3), a = (P/(2mv)) Vertical circular motion: minimum speed at top of circle v_min = √(gr) for rope; for complete circle v_bottom ≥ √(5gr) Center of mass frame: momentum = 0; kinetic energy in CoM frame = KE_total - KE_CoM Rocket propulsion: Tsiolkovsky equation Δv = v_e ln(m₀/m_f); thrust = -v_e dm/dt Collision in 2D: conserve momentum in x and y separately; for equal masses at 90° → right angle

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