Mechanics 1

Worked examples (5)

• 1State and justify modelling assumptions (5 marks, M1)
• 2Distinguishing scalars from vectors and stating units (4 marks, M1)
• 3Force diagram for a particle on a string over a pulley (6 marks, M1)
• 4Position, velocity and displacement in $\\mathbf{i}$, $\\mathbf{j}$ form (6 marks, M1)
• 5When to model as a particle vs a rod (4 marks, M1)

Worked examples (5)

• 1Single-stage suvat — finding final velocity and time (6 marks, M1)
• 2Vertical motion under gravity — ball thrown up (8 marks, M1)
• 3Train: accelerate, cruise, decelerate (10 marks, M1)
• 4Two particles starting at different times (10 marks, M1)
• 5Reading information from a displacement-time graph (6 marks, M1)

Worked examples (5)

• 1Single particle on a horizontal surface (5 marks, M1)
• 2Connected particles over a smooth pulley (10 marks, M1)
• 3Particle on table connected to hanging particle (10 marks, M1)
• 4Lift acceleration and apparent weight (8 marks, M1)
• 5Particle dragged at an angle (8 marks, M1)

Worked examples (5)

• 1Particle decelerating on a rough horizontal surface (6 marks, M1)
• 2Particle sliding down a rough inclined plane (9 marks, M1)
• 3Particle pushed up a rough inclined plane (10 marks, M1)
• 4Particle on the point of slipping — find $\\mu$ (8 marks, M1)
• 5Connected particles with friction (12 marks, M1)

Worked examples (5)

• 1Impulse changes velocity of a single particle (5 marks, M1)
• 2Direct collision of two particles — both continue forward (8 marks, M1)
• 3Coalescence — particles stick together (6 marks, M1)
• 4Direct collision with one particle reversing direction (10 marks, M1)
• 5Explosion: stationary object separates into two pieces (8 marks, M1)

Worked examples (5)

• 1Particle in equilibrium under two strings (8 marks, M1)
• 2Triangle of forces with sine rule (7 marks, M1)
• 3Particle in equilibrium on a rough incline — find $\\mu$ range (10 marks, M1)
• 4Light rod / cable — direction of force matters (8 marks, M1)
• 5Three coplanar forces using Lami's theorem (8 marks, M1)

Worked examples (5)

• 1Uniform rod on two supports — find reactions (8 marks, M1)
• 2Uniform rod with asymmetric supports and load (10 marks, M1)
• 3Non-uniform rod — find centre of mass (8 marks, M1)
• 4Plank about to tip — find maximum overhang (10 marks, M1)
• 5Ladder problem — moments about the foot (10 marks, M1)

Worked examples (5)

• 1Position vector under constant acceleration (7 marks, M1)
• 2Velocity given as speed and bearing (6 marks, M1)
• 3Closest approach of two ships (10 marks, M1)
• 4Do two particles collide? (8 marks, M1)
• 5Finding velocity from two position observations (7 marks, M1)