Work, Energy & Power is one of the most formula-rich and conceptually layered topics in NEET Physics. It draws together scalar quantities, vector dot products, energy conservation, and collision mechanics — making it a consistent source of 2–3 questions per year.
Work Done by a Force
Work is defined as the scalar product of force and displacement: W = F d cos θ, where θ is the angle between the force vector and displacement vector. The SI unit is the joule (J) with dimensional formula [M^{1}$$L^{2}$$T^{-2}]. Work is positive when θ < 90° (force aids motion), zero when θ = 90° (force perpendicular to motion — normal force, centripetal force), and negative when θ > 90° (force opposes motion — friction). For a variable force, work equals the area under the F–x graph: W = ∫F dx. This integral interpretation is critical for spring-related problems.
Kinetic Energy and the Work-Energy Theorem
Kinetic energy KE = ½ = /(2m), where p is linear momentum. The momentum form is indispensable when comparing KE of objects with equal momenta — the lighter object always has greater KE. The Work-Energy Theorem states: W_net = E = ½ − ½. This must include work done by ALL forces — gravity, friction, normal force, applied force — without exception. A common NEET trap is omitting friction work, which leads to an inflated final speed.
Potential Energy and Conservative Forces
Gravitational PE = mgh (h measured above chosen reference). Spring PE = ½, where k is the spring constant [M^{1}$$L^{0}$$T^{-2}] (N/m) and x is extension or compression. Conservative forces (gravity, spring) do path-independent work; the potential energy function exists only for conservative forces. Non-conservative forces (friction, air resistance, viscosity) are path-dependent and dissipate mechanical energy as heat. The Law of Conservation of Mechanical Energy — KE + PE = constant — applies only when all acting forces are conservative. When friction acts, total energy (KE + PE + thermal) is conserved, but mechanical energy decreases.
Power
Power P = W/t = Fv cos θ, with SI unit watt (W) and dimensional formula [M^{1}$$L^{2}$$T^{-3}]. Instantaneous power P = F·v (dot product). Conversion: 1 horsepower (hp) = 746 W. Engine power problems at NEET often involve finding terminal velocity or maximum speed on an inclined road where driving force equals resistive force: P = Fv → v_max = P/F.
Vertical Circular Motion
For a body tied to a string moving in a vertical circle of radius R:
- Minimum speed at the top: v_top = √(gR) — obtained by setting tension T = 0 at the top. Here mg provides all centripetal force.
- Minimum speed at the bottom: v_bottom = √(5gR) — derived using energy conservation from bottom to top.
- At any angle, energy conservation gives: ½ = ½mv_to + mg(2R), yielding v_botto = v_to + 4gR.
For a rigid rod (unlike a string, a rod can push):
- Minimum speed at the top: v_top = 0 (rod exerts compressive force).
- Minimum speed at the bottom: v_bottom = √(4gR) = 2√(gR).
The string–rod distinction is a high-frequency NEET conceptual trap.
Collisions
Momentum is conserved in all collisions. For elastic collisions (KE also conserved, e = 1):
Special case — equal masses: velocities exchange. Heavy body hitting a stationary light body: light body moves at ≈ 2u. For perfectly inelastic collisions (bodies stick together, e = 0): common velocity v = (m_{1}u_{1} + m_{2}u_{2})/(m_{1} + m_{2}). KE lost = ½ · m_{1}m_{2}/(m_{1}+m_{2}) · (u_{1}−u_{2})^{2} — maximum possible KE loss. The coefficient of restitution e = (v_{2}−v_{1})/(u_{1}−u_{2}) encodes the collision type: e = 1 (elastic), 0 < e < 1 (partially inelastic), e = 0 (perfectly inelastic).
NEET Strategy
Always check: (1) Is it a string or rod in vertical circular motion? (2) Is the collision elastic or inelastic? (3) Are all forces included in the work-energy calculation? These three checks resolve the majority of NEET errors in this chapter.