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WME01 Mechanics 1

Edexcel IAL Mathematics, M1 (AS unit, usually Year 12). 27 lessons so far, in the suggested order.

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Lessons in WME01

  1. Constant acceleration (suvat)
    List s, u, v, a, t; choose the equation without the unwanted letter; keep one positive direction.
  2. Modelling assumptions in mechanics
    Light means no mass (same tension), inextensible means same acceleration, smooth means no friction, uniform means weight at the centre. Use g = 9.8 and give 2 o
  3. Vectors: magnitude, direction and resultants
    Add components to find a resultant; magnitude by Pythagoras; direction by tan and a sketch.
  4. Resolving vectors and finding resultant forces
    Along the direction: F cos θ; perpendicular: F sin θ. Then add components or use the triangle of forces.
  5. Position vectors and constant velocity
    r = r_0 + vt; speed = |v|; v = (r_2 - r_1)/t. Due north: i part zero; due east: j part zero.
  6. Vectors with constant acceleration and meeting problems
    v = u + at and r = r_0 + ut + (1/2)at2 in vector form. To meet, both components must match at the same t.
  7. Vertical motion under gravity
    Pick up as positive, so a = -9.8. Top: v = 0. Below the start: negative s. Reject negative times.
  8. Multi-stage motion and two moving objects
    End velocity of one stage = start velocity of the next. Two objects: same clock, same origin, then equate positions.
  9. Velocity-time graphs
    Gradient = acceleration; area = displacement. Trapezium area = (1/2)(a + b)h. Below the axis counts as negative displacement.
  10. Displacement, speed and acceleration-time graphs
    s-t gradient = velocity; v-t gradient = acceleration and area = displacement; a-t area = change in velocity; speed-time never goes negative.
  11. Newton's laws of motion
    Resultant force = ma along the motion; forces balance perpendicular to it. Weight = mg.
  12. F = ma with vectors
    Add the forces, then F = ma component by component. The acceleration points the same way as the resultant force.
  13. Connected particles in a line: lifts and towing
    Whole system for the acceleration, one body for the internal force. Negative tension means thrust.
  14. Particles connected over a pulley
    Same T both sides, same size of acceleration. One F = ma for each particle, then add.
  15. Pulleys and pegs at the edge of a table
    Each particle: F = ma along its own line of motion, same T and same size of a. Force on a corner pulley is T sqrt(2).
  16. When the forces change part-way through
    New forces mean a new acceleration. Link stages by velocity. In the ground, R - mg = ma (deceleration a).
  17. Motion on a smooth inclined plane
    Along the slope: mg sin α; into the slope: mg cos α. Resolve along for F = ma, perpendicular for R.
  18. Friction and the coefficient of friction
    Resolve perpendicular for R, then F = μR when sliding, opposing the motion. Then F = ma along the motion.
  19. Motion on a rough inclined plane
    Friction μmg cos α opposes motion: up the slope it adds to mg sin α, down the slope it subtracts. Slides back only if tan α > μ.
  20. Momentum and impulse
    Momentum = mv, impulse = mv - mu = Ft. Choose a positive direction: a rebound changes the sign of v.
  21. Conservation of momentum in collisions
    Total momentum is conserved. Use a positive direction and draw before and after. Impulses in a collision are equal and opposite.
  22. Equilibrium of a particle
    Equilibrium: resolve in two perpendicular directions and set each sum to zero (or add the vectors to 0).
  23. Equilibrium on slopes and with rods
    Resolve along and perpendicular to the slope. Parallel holding force: mg sin α. Horizontal holding force: mg tan α.
  24. Friction in equilibrium and limiting friction
    At rest: F ≤ μR. Limiting (on the point of moving): F = μR, opposing the way it would move.
  25. Moments of forces
    Moment = F × perpendicular distance. Equilibrium: forces balance and moments balance about any point. Take moments where an unknown acts.
  26. Beams on supports and hanging rods
    Moments about one support for the other reaction; then forces up = forces down.
  27. Non-uniform rods and rods about to tilt
    Non-uniform: let the weight act at x and find x. About to tilt about one support: the other reaction is zero; take moments about the tilting support.

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