WPH14 Further Mechanics, Fields and Particles

Lessons in WPH14

1. Impulse and force as rate of change of momentum
   F = Δp/Δt; impulse FΔt = Δp (N s = kg m/s); area under a force-time graph = impulse; longer contact time, smaller force.
2. Core practical 9: force and change in momentum
   Measure v with light gates, Δp = mΔv; Δp against Δt has gradient F; force-sensor area should equal Δp; compensate for friction.
3. Conservation of momentum in two dimensions
   Resolve momentum into two perpendicular directions, conserve each separately, then recombine.
4. Elastic and inelastic collisions; E_k = p²/2m
   Elastic: E_k conserved. Inelastic: E_k falls. Momentum always conserved. E_k = p²/2m.
5. Core practical 10: analysing collisions with ICT
   Camera overhead with a scale in view; frame rate gives the time; resolve velocities; compare momentum in x and y.
6. Radians and angular velocity
   θ = s/r; 2π rad = 360°; ω = 2π/T = 2πf; v = ωr.
7. Centripetal acceleration and force
   a = v²/r = rω² towards the centre; F = mv²/r = mrω² is the resultant force, supplied by real forces.
8. Electric fields and Coulomb's law
   E = F/Q; F = kQ_1Q_2/r² with k = 8.99 x 10⁹ N m² C^-2; E = kQ/r² for a point charge; inverse square.
9. Electric potential, uniform fields and equipotentials
   V = kQ/r (zero at infinity); W = QΔV; E = V/d between plates; E is the potential gradient; equipotentials are perpendicular to field lines.
10. Capacitance and energy stored
    C = Q/V; W = (1/2)QV = (1/2)CV² = Q²/2C; energy = area under the V-Q graph.
11. Charging, discharging and the time constant
    Q = Q_0e^-t/RC (same for V and I); RC = time to fall to 37%; ln V against t has gradient -1/RC.
12. Core practical 11: capacitor charge and discharge
    Logger or oscilloscope across C; square wave for short RC; time to 37% gives RC; ln V against t has gradient -1/RC.
13. Magnetic flux and magnetic forces
    φ = BA; flux linkage Nφ; F = BIl sin θ; F = Bqv sin θ; Fleming's left-hand rule.
14. Electromagnetic induction: Faraday's and Lenz's laws
    ε = -N dφ/dt: e.m.f. = rate of change of flux linkage; Lenz: the induced effect opposes the change.
15. The nuclear atom and alpha scattering
    A = protons + neutrons, Z = protons. Most alphas pass straight through (empty space); a few bounce back (tiny, dense, positive nucleus).
16. Accelerating and detecting charged particles
    Heated filament releases electrons; eV = (1/2)mv²; r = p/BQ; electric fields accelerate, magnetic fields bend; tracks show charge and momentum.
17. Particle interactions, tracks and probing the nucleon
    Charge, energy and momentum are always conserved. Only charged particles leave tracks. Probing nucleons needs λ = h/p of about 10^-15 m, so very high energies.
18. Mass-energy, particle energy units and relativistic lifetimes
    ΔE = c²Δm; pair production needs at least 2mc²; 1 MeV = 1.60 x 10^-13 J; mass in MeV/c²; fast particles live longer in the lab frame.
19. Quarks, leptons and antiparticles
    u = +2/3, d = s = -1/3. Baryons qqq, mesons q anti-q, leptons fundamental. Antiparticles: same mass, opposite charge and quantum numbers.
20. Conservation laws and particle equations
    Check Q, B and L on both sides. Baryons B = 1, mesons B = 0, leptons L = 1, antiparticles opposite.

Next exams for WPH14

• January 2027: Tue 19 Jan 2027, afternoon, 1h 45m
• Summer 2027: Fri 28 May 2027, afternoon, 1h 45m

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