2.1 Work Done by Constant and Variable Forces

Work W = Fd cos θ is the fundamental definition. The angle θ must be measured between the force and displacement vectors, not between the force and the surface. For variable forces, W = ∫F dx equals the area under the F–x graph — a graphical approach frequently tested in NEET. The spring force F = kx gives W_spring = ½$kx^{2}$, which is also the spring PE stored.

2.2 Kinetic Energy

KE = ½$mv^{2}$ has the same dimensional formula as work — [M^{1}$$L^{2}$$T^{-2}] — confirming units are joules. The form KE = $p^{2}$/(2m) is crucial: at equal momenta, lighter bodies hold more KE. NEET uses this in collision problems where momentum is stated but mass ratios differ.

2.3 Work-Energy Theorem

W_net = $\Delta K$E is the most applied theorem in mechanics. It applies to every force: gravity (W = −mgh if moving up, +mgh if moving down), friction (W = −f_k · d), applied force (W = F cos θ · d), normal (W = 0 if perpendicular). The theorem bypasses Newton's second law when force is not constant — a significant computational advantage.

2.4 Potential Energy and Energy Conservation

Gravitational PE = mgh and spring PE = ½$kx^{2}$ are the two PE forms tested at NEET. Conservation of mechanical energy (KE + PE = constant) is applied in projectile problems (velocity at height h), vertical circular motion, spring-block systems, and roller-coaster type problems. When friction is present, the energy equation becomes: KE_i + PE_i = KE_f + PE_f + W_friction (heat generated).

2.5 Power

P = W/t and P = Fv cos θ. Instantaneous power is P = F·v. NEET problems on power often involve engines pulling loads up inclines, where at terminal speed the engine power equals (friction force + gravity component) × speed.

2.6 Vertical Circular Motion

Two distinct setups exist: string (tension ≥ 0) and rod (force can be compressive or tensile). The critical condition at the top for a string is T = 0 → v_top(min) = √(gR). Energy conservation from bottom to top (height = 2R) gives v_bottom(min) = √(5gR). For a rod: v_top(min) = 0, v_bottom(min) = √(4gR). Tension at any point can be found by combining the force equation (centripetal) and energy conservation.

2.7 Collisions

Three types: elastic (e = 1, KE conserved), perfectly inelastic (e = 0, bodies stick), partially inelastic (0 < e < 1). Momentum is always conserved. NEET focuses on: equal-mass elastic collisions (velocity exchange), heavy–light elastic collisions (light body moves at ≈ 2u), and perfectly inelastic collisions (find common velocity, compute KE loss). The maximum KE loss formula $\Delta K$E_max = ½ · μ · u_r$el^{2}$ (where μ = m_{1}m_{2}/(m_{1}+m_{2}) is reduced mass) is useful for verification.