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Flashcards · YPH11 · Topic 4
Further Mechanics, Fields and Particles flashcards
33 cards on Topic 4, subtopics 4.3 to 4.5. Pick a subtopic or study them all.
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4.3 Further Mechanics
- How is momentum conserved in a two-dimensional collision?
- Momentum is a vector, so it is conserved separately in each of two perpendicular directions. Resolve, apply conservation to each, then recombine.
- Kinetic energy in terms of momentum
- Ek = p²/2m
- 0.15 kg at 8.0 m/s hits a stationary 0.25 kg ball and rebounds at 2.0 m/s. Velocity of the second ball?
- 1.2 = −0.30 + 0.25v, so v = 6.0 m/s. KE before 4.8 J, after 0.3 + 4.5 = 4.8 J, so the collision is elastic.
- Angular velocity
- ω = θ/t = 2π/T = 2πf, in rad s⁻¹. Angles must be in radians. v = rω.
- Centripetal acceleration and centripetal force
- a = v²/r = rω² F = mv²/r = mrω²
- Is centripetal force a separate force?
- No. It is the resultant of the real forces present (tension, gravity, friction, normal contact or magnetic force), directed towards the centre.
- Why does an object in uniform circular motion accelerate but keep the same kinetic energy?
- Its direction, and so its velocity, changes continuously. The resultant force is perpendicular to the velocity, so it does no work.
- Minimum speed at the top of a vertical circle on a string
- When the tension is zero, gravity alone provides the centripetal force: mg = mv²/r, so v = √(gr).
- Core Practicals 9 and 10
- 9: investigate the relationship between force and change of momentum. 10: use ICT (such as video analysis) to analyse collisions between small spheres.
- Impulse (Newton's second law in Unit 4)
- Impulse = FΔt = Δp, in N s (equal to kg m s⁻¹). It is the area under a force–time graph. Example: a 0.16 kg ball hit from rest to 45 m s⁻¹ receives an impulse of 0.16 × 45 = 7.2 N s.
4.4 Electric and Magnetic Fields
- Electric field strength
- E = F/Q: force per unit positive charge (N C⁻¹ or V m⁻¹). Field lines run from positive to negative.
- Coulomb’s law, and the radial field of a point charge
- F = Q₁Q₂ / (4πε₀r²) E = Q / (4πε₀r²): an inverse-square field.
- Field between parallel plates
- Uniform: E = V/d, the same everywhere between the plates.
- Electric potential of a point charge, and equipotentials
- V = Q / (4πε₀r). Equipotentials are always perpendicular to field lines.
- Path of a charged particle entering a uniform field at right angles: electric vs magnetic
- Electric field: a parabola (constant force in a fixed direction, like a projectile). Magnetic field: a circle (force always perpendicular to the velocity).
- Radius of a charged particle’s circular path in a magnetic field
- BQv = mv²/r, so r = mv/BQ = p/BQ.
- Capacitance, and energy stored by a capacitor
- C = Q/V W = ½QV = ½CV² = Q²/2C (the area under a Q–V graph).
- Capacitor discharge equation and time constant
- Q = Q₀ e^(−t/RC). Time constant RC: after one time constant the charge has fallen to about 37% of its initial value.
- A 220 μF capacitor at 9.0 V discharges through 47 kΩ. Time constant, and p.d. after it?
- RC = 220 × 10⁻⁶ × 47 × 10³ = 10.3 s V = 9.0 × e⁻¹ = 3.3 V
- Force on a current-carrying conductor and on a moving charge in a magnetic field
- F = BIl sin θ F = BQv sin θ Zero when parallel to the field, maximum when perpendicular.
- Magnetic flux and flux linkage
- Flux φ = BA (Wb). Flux linkage = Nφ.
- Faraday’s law and Lenz’s law
- Faraday: the induced e.m.f. is proportional to the rate of change of flux linkage, ε = −d(Nφ)/dt. Lenz: the induced current opposes the change producing it (the minus sign), as conservation of energy requires.
- Core Practical 11
- Use an oscilloscope or data logger to display and analyse the p.d. across a capacitor as it charges and discharges through a resistor.
4.5 Nuclear and Particle Physics
- Quark composition of a proton and a neutron, with charges
- Proton: uud, charge (+⅔) + (+⅔) + (−⅓) = +1. Neutron: udd, charge (+⅔) + (−⅓) + (−⅓) = 0.
- Hadrons, baryons, mesons and leptons
- Hadrons feel the strong force: baryons are three quarks; mesons are a quark and an antiquark. Leptons (electron, muon, tau and their neutrinos) are fundamental and do not feel the strong force.
- Antiparticle
- A particle with the same mass as its partner but with opposite properties such as charge.
- What must be conserved in a particle interaction?
- Charge, baryon number, lepton number, energy and momentum. To reject an interaction, name the rule it breaks.
- Mass–energy, and the electronvolt
- ΔE = c²Δm. 1 eV = 1.60 × 10⁻¹⁹ J, so 1 MeV = 1.60 × 10⁻¹³ J and 1 GeV = 1.60 × 10⁻¹⁰ J. Masses can be given in MeV/c².
- Electron–positron annihilation at rest
- The mass becomes two photons travelling in opposite directions (so momentum is conserved), each of energy 0.511 MeV.
- Why are very high energies needed to probe the inside of nucleons?
- Resolving very small distances needs a very short de Broglie wavelength, which means high momentum and so high energy. Kinetic energy can also become the mass of new particles.
- How does a linear accelerator work?
- An alternating p.d. across successive drift tubes is timed so the particle is accelerated at each gap. The tubes get longer because the particle is moving faster.
- How does a cyclotron work?
- Two dees in a magnetic field with an alternating p.d. across the gap. The field keeps the particle circling; it is accelerated at each crossing of the gap and its radius grows (r = mv/BQ).
- What does a particle track in a magnetic field tell you?
- The radius of curvature gives the momentum (r = p/BQ); the direction of curvature gives the sign of the charge.