Physics · Work, Energy And Power · NEET
Group them by topic. WORK: W = F d cos theta; for a variable force W = integral of F dx (area under a force-displacement graph). ENERGY: KE = (1/2) m v^2; KE = p^2 / (2m) where p is momentum; gravitational PE = mgh; spring PE = (1/2) k x^2. THEOREM: W_net = KE_final - KE_initial (work-energy theorem). POWER: P_avg = W/t; P_instantaneous = F.v = F v cos theta. CONSERVATION: KE + PE = constant (only when forces are conservative). COLLISIONS: momentum m1 u1 + m2 u2 = m1 v1 + m2 v2 is always conserved; KE is conserved only in elastic collisions. Coefficient of restitution e = (v2 - v1) / (u1 - u2). These cover almost every NEET question in this chapter.
The work-energy theorem says the NET work by ALL forces (including friction) equals the change in kinetic energy: W_net = change in KE. It always holds. Conservation of mechanical energy is a special case: it says KE + PE stays constant, but ONLY when no non-conservative force (like friction or air drag) does work. So use the work-energy theorem when friction is present, and use energy conservation when the surface is smooth and only gravity or springs act.
Work W = F d cos theta becomes zero in three cases. First, when displacement d = 0 (you push a wall, it does not move). Second, when force is perpendicular to displacement, so theta = 90 degrees and cos 90 = 0 (this is why the centripetal force in circular motion and the normal force do no work). Third, when the force itself is zero. NEET loves the case of a satellite in a circular orbit: gravity is centripetal, perpendicular to velocity, so it does zero work.
Average power is total work divided by total time: P_avg = W/t. Instantaneous power is the dot product of force and velocity: P = F.v = F v cos theta, where theta is the angle between the force and the velocity. If force and velocity point the same way, P = F v. SI unit is the watt (W = J/s), and 1 horsepower = 746 W. Remember kilowatt-hour (kWh) is a unit of ENERGY, not power: 1 kWh = 3.6 x 10^6 J.
Both describe motion but differently. Momentum p = m v (a vector). Kinetic energy KE = (1/2) m v^2 (a scalar). Combine them to get the very useful relation KE = p^2 / (2m), or p = sqrt(2 m KE). NEET often asks: if momentum doubles, KE becomes four times (since KE is proportional to p^2); if KE doubles, momentum increases by only sqrt(2). Keep this link in the sheet because it turns two-line problems into one-line answers.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. The work-energy theorem W_net = change in KE always holds, because W_net already includes the negative work done by friction. Only mechanical-energy conservation fails when friction is present.
Work and energy share the joule (J = N.m = kg m^2 s^-2). Power is measured in watt (W = J/s). Its dimensional formula: work/energy = [M L^2 T^-2], power = [M L^2 T^-3].
Linear momentum is conserved in every collision (elastic or inelastic) because no external force acts during the brief impact. Kinetic energy is conserved only in perfectly elastic collisions.
The potential energy stored in a spring stretched or compressed by x is U = (1/2) k x^2, where k is the spring constant. The spring force is F = -k x (Hooke's law), and the minus sign shows it is restoring.
1 horsepower (hp) = 746 W (often rounded to 750 W in problems). It is a practical unit for engine power; the SI unit is still the watt.
