Work–Energy Theorem
W_net = ΔKE — apply a force and watch kinetic energy change exactly by the work done.
Key Notes
Work-energy theorem: net work done on a body equals its change in kinetic energy.
W_net = K_f − K_i = ½m(v_f² − v_i²).
Applies to any net force — constant, variable, gravity, friction, spring, etc.
Derived directly from Newton's 2nd law integrated: F = m·a ⇒ ∫F·dx = ∫ma·dx = ∫mv·dv = ½m·Δ(v²).
Useful for solving problems WITHOUT explicit time analysis — only initial and final states matter.
If multiple forces act, W_net = sum of works done by each (or work by the net force).
Power form: P = dW/dt = F·v.
Used in projectile, pendulum, spring-block, collision, friction-on-incline problems.
Formulas
Work-energy theorem
Universal — applies to any force.
Net work from multiple forces
Sum of works = net work.
Instantaneous power
Rate at which force does work.
Important Points
W-E theorem is a BOOKKEEPING shortcut: skip time-dependent analysis when only KE matters.
ALL forces contribute to W_net — gravity, normal, friction, applied, spring. Watch signs.
If only conservative forces act: W = −ΔU ⇒ ΔK + ΔU = 0 ⇒ energy conservation.
Friction does NEGATIVE work — slows objects, dissipates energy as heat.
Cars accelerating: engine does positive work; air drag and rolling resistance do negative; net work = ΔKE.
Common mistake: forgetting that NORMAL force does no work in flat motion (perpendicular to v).
Work–Energy Theorem notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.