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WPH11 Mechanics and Materials

Edexcel IAL Physics, Unit 1 (AS unit, usually Year 12). 21 lessons so far, in the suggested order.

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Lessons in WPH11

  1. Stress, strain and the Young modulus
    σ = F/A; ε = Δx/x; E = σ/ε, the gradient of the linear part of a stress-strain graph.
  2. Equations of uniformly accelerated motion
    List s, u, v, a, t; pick the equation without the unwanted quantity; one positive direction; g = 9.81 m/s2.
  3. Displacement, velocity and acceleration graphs
    s-t gradient = velocity; v-t gradient = acceleration, v-t area = displacement; a-t area = change in velocity.
  4. Scalars, vectors, resolving and resultants
    Vectors have direction. Components: F cos θ (next to the angle) and F sin θ. Right angles: Pythagoras and tan.
  5. Projectile motion
    Split the motion: horizontal velocity constant, vertical acceleration g. Time links the two.
  6. Free-body force diagrams
    One object, every force acting on it, arrows from the object, weight from the centre of gravity.
  7. Newton's first and second laws
    ΣF = ma with the resultant force; W = mg with g = 9.81 N/kg; zero resultant means constant velocity.
  8. Core practical 1: acceleration of free fall
    From rest h = (1/2)gt2: plot h against t2, g = 2 x gradient. Time electronically; use a small dense ball.
  9. Newton's third law
    Third-law pairs: equal size, opposite direction, same type, on different bodies.
  10. Momentum and its conservation
    p = mv (a vector). With no external resultant force, total momentum before = total momentum after.
  11. Moments and equilibrium
    Moment = force x perpendicular distance. In equilibrium: resultant force zero and clockwise moments = anticlockwise moments.
  12. Work, kinetic energy and gravitational potential energy
    W = FΔs cos θ; E_k = (1/2)mv2; ΔE_grav = mgΔh.
  13. Conservation of energy
    Energy in = energy out. Without friction mgΔh = (1/2)mv2; with friction, the difference is work done against resistance.
  14. Power and efficiency
    P = E/t = W/t; efficiency = useful output / total input (energy or power).
  15. Density and upthrust
    ρ = m/V. Upthrust = weight of fluid displaced = ρ_fluid V g. Floating: upthrust = weight.
  16. Viscosity and Stokes' law
    F = 6πηrv for small spheres, low speed, laminar flow. Viscosity falls as a liquid warms. Terminal velocity: W = U + F.
  17. Core practical 2: viscosity by the falling-ball method
    Time the ball between marks once it is at terminal velocity; η = 2r2 g (ρ_s - ρ_l) / (9v). Record the temperature.
  18. Force-extension graphs and deformation
    ΔF = kΔx up to the limit of proportionality. Beyond the elastic limit, deformation is plastic (permanent).
  19. Stress-strain graphs and breaking stress
    Gradient of the linear part = E; UTS is the maximum stress; brittle materials break with little plastic deformation, ductile ones stretch a lot first.
  20. Core practical 3: determining the Young modulus
    Long thin wire; micrometer for diameter; F against Δx; E = gradient x original length / area.
  21. Elastic strain energy
    Strain energy = area under the force-extension graph; for a straight line E = (1/2)FΔx = (1/2)k(Δx)2.

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