Mechanics - Paper 4

Worked examples (13)extended set

• 1Particle suspended by two strings
• 2Contact force, Newton's third law and the range of μ
• 3Rope at an angle on rough ground
• 4Resultant of four forces, then a fifth force
• 5Resultant perpendicular to an unknown force
• 6Three forces in equilibrium: find P and θ
• 7Particle on a string held aside
• 8Knot held by strings over two smooth pulleys
• 9Sledge on a slope: smooth model versus reality
• 10On the point of moving down, then up
• 11Horizontal force on a rough plane, then removed
• 12μ in terms of tan θ and the set of possible angles
• 13Force at an angle to the line of greatest slope

Worked examples (14)extended set

• 1Reading a displacement–time graph
• 2Projected upwards, at the same height twice
• 3Times at rest and acceleration at a change of direction
• 4Four-stage journey and average speed
• 5Two consecutive stages with the same acceleration
• 6Total time from a v–t graph, then sketch the s–t graph
• 7v–t graph with negative velocity: returning to the start
• 8Sketch a v–t graph and form a quadratic in T
• 9Total distance with two changes of direction
• 10Maximum velocity with a fractional power
• 11Piecewise motion with continuity of velocity
• 12Two particles meet in the air and coalesce
• 13A car catches a lorry: check the speed limit
• 14Find the constants, then distance between rest times

Worked examples (14)extended set

• 1Momentum and change in momentum
• 2A particle brought to rest by a collision
• 3Coalescing particles moving the same way
• 4Head-on collision where both particles reverse
• 5A moving particle splits into two
• 6Speed after impact: two possible cases
• 7Symbolic masses: show that, then use a KE loss
• 8Mass and speed from momentum and kinetic energy
• 9Unknown mass: show an inequality
• 10Quadratic in the mass, then a rebound from a wall
• 11Friction before and after coalescence
• 12Mid-air collision and coalescence
• 13Collision on a smooth inclined plane
• 14Three particles: is there a further collision?

Worked examples (3)

• 1Newton's 2nd law (5 marks)
• 2Block on rough incline (8 marks)
• 3Connected particles via pulley (10 marks)

Worked examples (14)extended set

• 1Rope at an angle: speed, work done and power
• 2Car on a level road: maximum speed and acceleration
• 3Smooth curved slide: conservation of energy
• 4Angled pull on rough ground: work against friction and speed
• 5Pulled up a rough slope by a rope at an angle
• 6Constant speed up a hill, then freewheeling down it
• 7Up and back down a rough plane: show AB, then return speed
• 8Down a road between two heights: work done by the brakes
• 9Aircraft climbing at constant speed: average power
• 10Uniform acceleration: time, average power, then steady speed
• 11Resistance cv: show c, then the greatest speed up a hill
• 12Connected particles by energy: find the hanging mass
• 13Waterslide: rough straight section then curved section
• 14Resistance kv²: two instants on the same hill