Mechanics: Kinematics to Gravitation — The Complete High-Yield Map

Why mechanics decides your Physics score

Mechanics is the single largest block inside the 50 Physics questions of MECEE-BL. Almost every numerical here is a one-formula substitution — the exam rewards students who can pick the right equation in 10 seconds.

Kinematics

For uniform acceleration, the three equations of motion are the backbone:

• v = u + at
• s = ut + ½at²
• v² = u² + 2as

Vertical motion under gravity (take g = 9.8 m/s², or 10 m/s² when options are round numbers):

• Maximum height: H = u²/2g
• Time of flight (up and back): T = 2u/g

Projectile motion launched at angle θ with speed u:

• Range R = u² sin2θ / g — maximum at θ = 45°
• Height H = u² sin²θ / 2g; two angles θ and (90° − θ) give the same range.

Newton's laws and momentum

• First law: inertia — a body keeps its state unless a net external force acts.
• Second law: F = ma, or more generally F = dp/dt (rate of change of momentum).
• Third law: action and reaction are equal, opposite, and act on different bodies (classic example: recoil of a gun).

Momentum p = mv is conserved in every collision. Impulse J = FΔt = Δp explains why a cricketer pulls the hands back while catching — increasing Δt reduces the force.

Friction: limiting friction f = μN. Kinetic friction is slightly less than limiting static friction and is independent of area of contact.

Work, energy and power

• Work W = Fs cosθ — zero when force ⊥ displacement (centripetal force does zero work).
• Kinetic energy KE = ½mv²; potential energy PE = mgh.
• Work–energy theorem: net work = change in KE.
• Power P = W/t = Fv.

In a perfectly elastic collision both momentum and KE are conserved; in an inelastic one only momentum is. For a body falling freely, total mechanical energy stays constant — the exam loves "at what height is KE = PE?" (answer: half the drop height).

Circular motion and gravitation

• Centripetal acceleration a = v²/r = ω²r; centripetal force F = mv²/r.
• Newton's law of gravitation: F = Gm₁m₂/r² with G = 6.67 × 10⁻¹¹ N·m²/kg².
• Variation of g: decreases with height (g' ≈ g(1 − 2h/R) for small h) and with depth (g' = g(1 − d/R)); g is maximum at the poles.
• Orbital velocity v = √(gR) ≈ 7.9 km/s; escape velocity vₑ = √(2gR) ≈ 11.2 km/s. Note vₑ = √2 × v(orbital).
• A geostationary satellite has period 24 h and orbits west-to-east above the equator at ≈ 36,000 km.

Simple harmonic motion

Defining condition: acceleration ∝ displacement, directed toward the mean position, a = −ω²x.

• Time period of a spring–mass system: T = 2π√(m/k)
• Simple pendulum: T = 2π√(L/g) — independent of mass and (for small angles) amplitude. A 1 m pendulum has T ≈ 2 s (the "seconds pendulum" is 0.99 m).
• v(max) = ωA at the mean position; a(max) = ω²A at the extremes.
• KE is maximum at the centre, PE maximum at the extremes; total energy E = ½mω²A² is constant.

Elasticity and fluids

• Stress = F/A; strain = ΔL/L (dimensionless). Hooke's law: stress ∝ strain within the elastic limit.
• Young's modulus Y = (F/A)/(ΔL/L); SI unit N/m² (pascal).
• Pressure at depth h: P = ρgh; Pascal's law underlies the hydraulic press.
• Archimedes' principle: upthrust = weight of displaced fluid. A body floats when its average density ≤ fluid density.
• Excess pressure: soap bubble ΔP = 4T/r (two surfaces), liquid drop ΔP = 2T/r.
• Capillary rise h = 2T cosθ / rρg; Bernoulli's theorem — P + ½ρv² + ρgh = constant — explains aerofoil lift and the venturimeter.
• Terminal velocity (Stokes' law): F = 6πηrv, and v(t) ∝ r².

Exam tip: When a numerical gives u = 0 ("starts from rest") jump straight to v = at, s = ½at², v² = 2as. MECEE-BL mechanics numericals are built so the arithmetic finishes in under 30 seconds — if you are multiplying awkward decimals, you picked the wrong equation.

Key formulae & quick revision

1. v² = u² + 2as — the no-time equation; use whenever time is not mentioned.
2. H = u²/2g and R = u² sin2θ/g — vertical throw and projectile range.
3. F = ma, J = Δp — force and impulse–momentum.
4. W = mgh, KE = ½mv², P = Fv.
5. a = v²/r — centripetal; work done by centripetal force = 0.
6. vₑ = √(2gR) = 11.2 km/s; geostationary period = 24 h.
7. T = 2π√(L/g) (pendulum), T = 2π√(m/k) (spring).
8. ΔP = 4T/r (bubble), h = 2T cosθ/rρg (capillary).