All subjects · Mathematics · M2

WME02 Mechanics 2

Edexcel IAL Mathematics, M2 (A2 unit, usually Year 13). 28 lessons so far, in the suggested order.

Practise this unit in the app: instant marking and a fix for every mistake. Free, no email needed to start.

Practise in the app

Lessons in WME02

  1. Projectiles: the model and horizontal projection
    Horizontal velocity is constant; vertical motion is suvat with a = 9.8 downwards. Time links the two. Combine components for the speed.
  2. Projectiles at an angle: time of flight, range and greatest height
    Vertical: 0 = (U sin α)2 - 2gH for the top, s = 0 for the landing time. Horizontal: distance = U cos α × time. Show each step when asked to derive.
  3. Projectiles in vector form and the trajectory equation
    Vector form: v = pi + (q - 9.8t)j, r = pt i + (qt - 4.9t2)j. Trajectory: y = x tan α - gx2(1 + tan2 α)/(2U2), a quadratic in tan α.
  4. Variable acceleration: differentiating displacement
    Differentiate x to get v, and v to get a. At rest: v = 0. Greatest velocity: a = 0.
  5. Variable acceleration: integrating to find velocity and displacement
    Integrate a for v, integrate v for x, and find each constant from the given conditions. A definite integral of v gives displacement.
  6. Distance travelled when a particle changes direction
    Solve v = 0, split the interval there, and add the sizes of the displacements in each part.
  7. Differentiating position vectors
    Differentiate each component. Speed is the magnitude of v. Parallel to i: j part of v is zero.
  8. Integrating velocity and acceleration vectors
    Integrate each component, add a constant vector, and use the starting velocity or position to find it.
  9. Centre of mass of a set of particles
    x̄ = Σmx/Σm and ȳ = Σmy/Σm. Treat a uniform rod as a particle at its midpoint.
  10. Centres of mass of standard laminas and arcs
    Use symmetry, then the booklet: triangle 2/3 along a median; sector 2r sin α/(3α); arc r sin α/α, with α half the angle, in radians.
  11. Composite laminas and laminas with holes
    Area acts as mass for a uniform lamina. Holes are negative areas. Tabulate area and centre of each part.
  12. Centres of mass of wire frameworks
    Wire: mass ∝ length, each piece at its midpoint (arc: r sin α/α). Lamina: mass ∝ area.
  13. Suspended laminas and equilibrium angles
    Hanging freely from P: PG is vertical. Then tan θ = perpendicular distance / distance along the edge, read from a careful sketch.
  14. Laminas on inclined planes and hinged laminas
    About to topple: the vertical through G passes through the lower corner, so tan α = (distance along) / (height of G). Hinged: moments about the hinge.
  15. Work done, kinetic energy and potential energy
    W = Fs in the direction of motion (Fs cos θ at an angle). KE = (1/2)mv2, PE = mgh: learn both.
  16. Conservation of energy and the work-energy principle
    Only gravity working: KE + PE constant. Otherwise: initial energy + work by driving forces = final energy + work against resistances. Count gravity once.
  17. Power: driving force, maximum speed and acceleration
    P = Fv, so F = P/v. Maximum speed: P/v = R. Otherwise P/v - R = ma.
  18. Power on slopes and with towing
    Uphill: P/v = R + mg sin α + ma. Downhill: P/v + mg sin α = R + ma. Towing: whole system for a, trailer alone for T.
  19. Impulse and momentum as vectors
    I = mv - mu, as vectors. Momentum is conserved component by component. Speed is the magnitude of the final velocity.
  20. Newton's law of restitution and direct impact
    CLM plus NEL (separation = e × approach), with all velocities in one positive direction. 0 ≤ e ≤ 1.
  21. Loss of kinetic energy in collisions
    Loss of KE = KE before - KE after. Impulse on one particle = its change in momentum. Zero loss only when e = 1.
  22. Impacts with a fixed surface and bouncing
    Rebound speed = e × impact speed. Impulse = mu(1 + e). Dropped from h: rebounds to e2 h.
  23. Successive impacts
    Solve each impact in turn with CLM and NEL. Another impact needs the particle behind to be moving faster towards the one in front.
  24. Moments of forces at an angle
    Moment = force × perpendicular distance = (perpendicular component) × distance along the rod. Components along the rod have no moment.
  25. Rods hinged to a wall: reactions at a hinge
    Moments about the hinge for T, then resolve horizontally and vertically for X and Y. R = sqrt(X2 + Y2).
  26. Ladders against a smooth wall on rough ground
    Smooth wall: horizontal reaction only. F = S, R = total weight, moments about the foot. About to slip: F = μR.
  27. Rods on pegs, rough walls and limiting equilibrium
    Peg reaction is perpendicular to the rod. Rough wall: normal plus friction μS. Limiting at both ends: friction = μ × reaction at both.
  28. M2 exam technique
    1 h 30 min, 75 marks, all questions. g = 9.8, answers to 2 or 3 s.f. Learn KE and PE. Follow any specified method and show all working.

Next exams for WME02

From Pearson's final timetables. All exam dates. Always confirm your entries with your exams officer.