Mechanics (Paper 4) — Courseware Index

W12

Forces & Equilibrium

Six lessons on the mechanics of forces — identifying forces and drawing diagrams, resolving into components and resultants, equilibrium, contact forces under the smooth model, limiting friction, and Newton's third law.

6 LESSONS
240 MIN

01 Identifying Forces & Force Diagrams Weight, normal contact, tension and friction — recognising the forces acting on a particle and drawing a labelled force diagram. FORCE TYPES · FREE-BODY DIAGRAM · LABELS 40′→ 02 Components & Resultants Resolving a force into perpendicular components, and combining two or more forces into a single resultant. RESOLUTION · RESULTANT · COMPONENTS 40′→ 03 Equilibrium — Resolving Forces The equilibrium condition for a particle, using resolution in two perpendicular directions to find unknown forces. EQUILIBRIUM · RESOLVE · UNKNOWNS 40′→ 04 Contact Forces & the Smooth Model Normal reaction on horizontal and inclined planes, and problems solved under the smooth (frictionless) model. NORMAL REACTION · INCLINE · SMOOTH 40′→ 05 Limiting Friction & F = μR The friction law F = μR at the point of sliding, and equilibrium problems on rough planes. FRICTION · μR · ROUGH PLANE 40′→ 06 Newton's Third Law Action–reaction pairs between two bodies, tension in a string, and the forces between connected particles. ACTION–REACTION · TENSION · CONNECTED 40′→

W13

Kinematics

Six lessons on the motion of particles along a straight line — scalars and vectors, displacement–time and velocity–time graphs, the constant-acceleration formulae, the average-velocity formula, and Newton's second law with constant and variable acceleration.

6 LESSONS
240 MIN

01 Distance, Speed, Displacement, Velocity, Acceleration The five quantities of motion: scalars versus vectors, distance versus displacement, and the two averages — with a live particle sliding along a groove. SCALARS · DISPLACEMENT · AVERAGES 40′→ 02 Displacement–Time & Velocity–Time Graphs Reading a whole journey from its graphs: gradient for velocity and acceleration, area for displacement, stage by stage. s–t GRAPH · v–t GRAPH · AREAS 40′→ 03 Constant Acceleration Formulae The four SUVAT formulae, choosing the one that fits the knowns, and entering a deceleration as a negative acceleration. SUVAT · FORMULA CHOICE · DECELERATION 40′→ 04 s = ½(u + v)t — the Average-Velocity Formula The trapezium picture: a distance from two speeds and a time, without the acceleration — and the same formula read in reverse. AVERAGE VELOCITY · TRAPEZIUM · REVERSE USE 40′→ 05 F = ma with Constant Acceleration Newton's second law along a line: from the resultant force to the acceleration, then the kinematic formulae to a speed or a distance. F = ma · RESULTANT · DRIVING & RESISTANCE 40′→ 06 F = ma with Variable Acceleration a(t) When the acceleration changes with time, integration replaces the SUVAT toolkit: a(t) → v(t) → x(t), with constants fixed by initial conditions. CALCULUS · INTEGRATION · INITIAL CONDITIONS 40′→

W14

Momentum

Six lessons on the quantity of motion — momentum and its conservation, impulse and the change in momentum, direct collisions and splitting, the coefficient of restitution, rebound problems, and comprehensive practice.

6 LESSONS
240 MIN

01 Momentum & Its Conservation Momentum as mass × velocity, the sign convention along a line, and the conservation law that keeps the total unchanged through any collision or explosion. p = mv · SIGNS · CONSERVATION 40′→ 02 Impulse & the Change in Momentum Impulse as force × time, equal to the change in momentum, with rebounds making the change the sum of the two speeds and cushioning lowering the force. I = Ft · REBOUNDS · FORCE–TIME AREA 40′→ 03 Direct Collisions & Splitting Writing the before-and-after momentum equation along a line: coalescing bodies, a rebounding particle, a coupling that breaks, and a train that splits in two. BEFORE & AFTER · COALESCE · SPLIT 40′→ 04 The Coefficient of Restitution Separation speed as e times the approach speed, the rebound height e²h of a dropped ball, and the pair of equations that momentum plus restitution supplies. e · REBOUND HEIGHT · TWO EQUATIONS 40′→ 05 Rebound Problems Vertical momentum with one sign convention, two balls meeting and coalescing in mid-air, a ball that loses speed at every bounce, and chains of impacts. VERTICAL MOTION · MID-AIR · REPEATED BOUNCES 40′→ 06 Momentum: Comprehensive Practice Full questions that chain the methods together: friction sets the speed before an impact, momentum fixes the speeds after it, and friction again decides the final distances. CHAINED METHODS · FRICTION · EXAM PRACTICE 40′→

W15

Energy, Work & Power

Six lessons on the energy of motion — work and the work–energy principle, kinetic and gravitational potential energy, power and P = Fv, constant-power journeys against resistance, the full energy audit with friction, and cross-topic practice.

6 LESSONS
240 MIN

01 Work & the Work–Energy Principle Work done by a constant force and by a force at an angle, work against gravity and resistance, and the work–energy principle — with the work of a variable force read as the area under a force–displacement graph. WORK · FORCE × DISTANCE · WORK–ENERGY 40′→ 02 Kinetic & Gravitational Potential Energy The two stores of mechanical energy — ½mv² carried by motion and mgh stored by height — and the conversion between them on smooth slopes, chutes and swings. ½MV² · MGH · ENERGY STORES 40′→ 03 Power & P = Fv Power as the rate of working — P = W/t for a job and P = Fv for a driving force — with top speed fixed where the driving force balances the resistance. POWER · P = FV · TOP SPEED 40′→ 04 Constant Power, Resistance & Acceleration Constant power against constant or speed-proportional resistance: F = P/v at an instant, then F − R = ma, and the steady speed where the acceleration dies away. F = P/V · R = KV · STEADY SPEED 40′→ 05 Energy Conservation & Dissipation The full audit of a journey: potential to kinetic conversion, the work removed by friction, and resistance forces recovered from the energy they take. CONSERVATION · FRICTION · AUDIT 40′→ 06 Energy, Work & Power — Comprehensive Practice Cross-topic practice across the week: choosing between energy, kinematics, F = ma and P = Fv, and chaining the tools where one is not enough. TOOL CHOICE · MIXED PRACTICE · EXAM 40′→

Paper Four Mechanics