18   17 A cosmic ray, consisting of a fast‑moving proton, collides with a proton within the nucleus of an atom in the upper atmosphere. Three particles, a proton, a neutron and a pion result from the collision. (a) Write a particle equation for this collision. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (b) The table shows the properties of two quarks. Quark Charge / e u +2 / 3 d −1 / 3 Give the quark structure for each of the particles produced by this collision. 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(c) The mass of a pion is 140 MeV / c2 . Calculate the mass of the pion in kg. 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Mass = ....................................................... kg Turn over 19   (d) The mass of a neutron is about the same as the mass of a proton. A student suggests that the minimum kinetic energy the cosmic ray proton would need to create the pion in this collision is 140 MeV. Discuss whether this suggestion is correct. Your answer should include reference to the laws of conservation of momentum and conservation of energy. 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(Total for Question 17 = 12 marks) 20   18 A potential divider circuit may contain a component known as a potentiometer. One type of potentiometer consists of a track with terminals X and Y at either end. There is a sliding contact that can move along the track connected to a terminal Z as shown. t 5.0 mm end view of track track 5.0 mm 115 mm Z sliding contact Y X The length of the track is 115 mm and the width is 5.0 mm. (a) The resistance of the track between terminal X and terminal Y is 12.0 kΩ. Calculate the thickness t of the track. resistivity of track material = 0.49 Ω m (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... t = ....................................................... Turn over 21   (b) The potentiometer is used to monitor the displacement of a moving tool on a machine in a production line. The tool is attached to the sliding contact. The potentiometer is connected to a resistor of resistance R and a potential difference is applied as shown. The tool moves through a maximum displacement of 60 mm from end X, producing a maximum potential difference of 5.0 V between Z and X. 12 V 0 V Z X Y R (i) Show that the potential difference between X and Y is about 10 V. 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(ii) Calculate the value of R. 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R = ....................................................... 22   (iii) When the circuit is assembled, using the correctly calculated resistance value and a battery of e.m.f. 12 V, it is found that the maximum output from the potentiometer is slightly less than 5.0 V. Explain why the maximum output is slightly less than predicted. 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(iv) The tool on the machine should not travel with a speed any larger than 0.8 m s−1 . The graph shows how the displacement varies with time for the downward stroke of the moving tool. Displacement / mm Time / s 0.2 0.1 0 60 23   Deduce whether this speed is exceeded by the moving tool. 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(Total for Question 18 = 15 marks) TOTAL FOR PAPER = 90 MARKS 24   List of data, formulae and relationships Acceleration of free fall g = 9.81 m s−2 (close to Earth’s surface) Boltzmann constant k = 1.38 × 10−23 J K−1 Coulomb law constant k = 1 4πε0 = 8.99 × 109 N m2 C−2 Electron charge e = −1.60 × 10−19 C Electron mass me = 9.11 × 10−31 kg Electronvolt 1 eV = 1.60 × 10−19 J Gravitational constant G = 6.67 × 10−11 N m2 kg−2 Gravitational field strength g = 9.81 N kg−1 (close to Earth’s surface) Permittivity of free space ε0 = 8.85 × 10−12 F m−1 Planck constant h = 6.63 × 10−34 J s Proton mass mp = 1.67 × 10−27 kg Speed of light in a vacuum c = 3.00 × 108 m s−1 Stefan-Boltzmann constant σ = 5.67 × 10−8 W m−2 K−4 Unified atomic mass unit u = 1.66 × 10−27 kg Mechanics Kinematic equations of motion s =  (u + v)t 2 v = u + at s = ut + 1 2 at2 v2 = u2 + 2as Forces ∑F = ma g =  F m W = mg moment of force = Fx Momentum p = mv Work, energy and power ΔW = FΔs Ek = 1 2 mv2 ΔEgrav = mgΔh P = E t P =  W t efficiency = useful energy output total energy input efficiency =  useful power output total power input Turn over 25   Electric circuits Potential difference V =  W Q Resistance R = V I Electrical power and energy P = VI P = I 2R P = V 2 R W = VIt Resistivity R =  ρl A Current I = ΔQ Δt I = nqvA Materials Density ρ =  m V Stokes’ law F = 6πηrv Hooke’s law ΔF = kΔ x Young modulus Stress σ =  F A Strain ε = Δ x x E =  σ ε Elastic strain energy ΔEel = 1 2 FΔ x Waves and particle nature of light Wave speed v = f λ Speed of a transverse wave on a string v = T μ Intensity of radiation I =  P A Power of a lens P =  1 f P = P1 + P2 + P3 + … Thin lens equation 1 u  +  1 v  =  1 f Magnification for a lens m =  image height object height =  v u Diffraction grating nλ = d sin θ Refractive index n1 sin θ1 = n2 sin θ2 n = c v Critical angle sin C = 1 n Photon model E = h f Einstein’s photoelectric equation hf = ϕ + 1 2 mv2 max de Broglie wavelength λ = h p 26   Further mechanics Impulse FΔt = Δp Kinetic energy of a non-relativistic particle Ek =  p2 2m Motion in a circle v = ωr T = 2π ω F = ma =  mv2 r a = v2 r a = rω2 F = mrω2 Fields Coulomb’s law F =  Q1Q2 4πε0r2 Electric field strength E =  F Q E = Q 4πε0r2 E =  V d Electric potential V = Q 4πε0r Capacitance C = Q V Energy stored in a capacitor W = 1 2 QV W = 1 2 CV 2 W = 1 2 Q 2 C Capacitor discharge Q = Q0e−t/RC I = I0e−t/RC V = V0e−t/RC ln Q = ln Q0 −  t RC ln I = ln I0 −  t RC ln V = ln V0 −  t RC In a magnetic field F = BIl sin θ F = Bqv sin θ Faraday’s and Lenz’s laws E =  −d(Nϕ) dt Root-mean-square values Vr ms =  V0 √2 Ir ms =  I0 √2 27   Nuclear and particle physics In a magnetic field r =  p BQ Thermodynamics Heating ΔE = mcΔθ ΔE = LΔm Molecular kinetic theory 1 2 mác2ñ = 3 2 kT pV = 1 3 Nmác2ñ Ideal gas equation pV = NkT Stefan-Boltzmann law L = σAT 4 L = 4πr2σT 4 Wien’s law λmaxT = 2.898 × 10−3 m K Space Intensity I =  L 4πd 2 Redshift of electromagnetic radiation z = Δλ λ  ≈ Δf f  ≈ v c Cosmological expansion v = H0d Nuclear radiation Mass-energy ΔE = c2Δm Radioactive decay A = λN dN dt  = −λN λ =  ln 2 t½ N = N0 e−λt A = A0 e−λt Gravitational fields Gravitational force F = Gm1m2 r 2 Gravitational field strength g = Gm r 2 Gravitational potential Vgrav = −Gm r Oscillations Simple harmonic motion F = −k x a = −ω2x x = A cos ωt v = −Aω sin ωt a = ‒Aω2 cos ωt T = 1 f  =  2π ω ω = 2π f Simple harmonic oscillator T = 2π m k T = 2π l g 28   BLANK PAGE