24 (A420U30-1) © WJEC CBAC Ltd. 24 10. A rectangular coil rotates at a constant angular velocity within a uniform magnetic field of 0.114 T. The coil has 270 turns and cross-sectional area 420 cm2. The diagram below is a simplified 3D diagram of the coil. N S axis of rotation This second diagram is a 2D representation of the coil looking along the axis of rotation. normal coil uniform B-field of 0.114 T The flux linkage of the coil for the angles θ = –5° and θ = +5° is 1.29 Wb turn in each case. normal θ –5° +5° uniform B-field of 0.114 T (A420U30-1) Turn over. 25 © WJEC CBAC Ltd. 25 (a) Show clearly how this value for the flux linkage is obtained. [2] (b) Explain why the induced emf is zero when θ = 0. [1] (c) The flux linkage of the coil for the angles θ = 85° and θ = 95° are 0.11 Wb turn and –0.11 Wb turn respectively. The coil rotates 10° in a time of 5.8 ms. Calculate the mean induced emf when rotating between θ = 85° and θ = 95°. [2] Examiner only 5 26 (A420U30-1) © WJEC CBAC Ltd. 26 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE (A420U30-1) Turn over. 27 © WJEC CBAC Ltd. 27 SECTION B: OPTIONAL TOPICS Option A – Alternating Currents Option B – Medical Physics Option C – The Physics of Sports Option D – Energy and the Environment Answer the question on one topic only. Place a tick (√) in one of the boxes above, to show which topic you are answering. You are advised to spend about 25 minutes on this section. 28 (A420U30-1) © WJEC CBAC Ltd. 28 Examiner only Option A – Alternating Currents 11. (a) Derive the expression for the resonance frequency, f0, of a series RCL circuit. [3] (b) Consider the following RCL circuit. Variable frequency a.c. supply, Vrms = 15 V 28 Ω 24 mH 8.2 nF (i) Calculate the rms current at the resonance frequency (f0). [1] f0 = 1 2π LC (A420U30-1) Turn over. 29 © WJEC CBAC Ltd. 29 Examiner only (ii) Calculate the rms current at twice the resonance frequency (2f0). [4] (iii) Calculate the Q factor of the RCL circuit. [2] (iv) Sketch a graph of the rms current in the RCL circuit versus applied frequency of the a.c. supply on the axes provided. Label this graph 28 Ω. [3] rms current / A Frequency f0 2f0 (v) The 28 Ω resistor is replaced by a 56 Ω resistor. On the same axes, sketch and label a second graph showing the rms current versus frequency for the new circuit. [2] 30 (A420U30-1) © WJEC CBAC Ltd. 30 Examiner only (c) Morgan claims that the rms output pd (Vout) in the following circuit is greater than 4.25 V when the frequency is greater than 82.5 Hz but less than 4.25 V below 82.5 Hz. Investigate whether or not Morgan is correct. [5] Vout 28 Ω 54 mH Vin = 6.0 V (rms) (Variable frequency) 20 (A420U30-1) Turn over. 31 © WJEC CBAC Ltd. 31 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE 32 (A420U30-1) © WJEC CBAC Ltd. 32 Examiner only Option B – Medical Physics 12. (a) (i) Sketch graphs to show how the intensity of X-rays from an X-ray tube varies with wavelength for a tube operating at two different voltages. Label the main features of the graphs and indicate which curve represents the higher voltage. [4] Wavelength Intensity (ii) The lower voltage tube operates at 20 kV. Determine the velocity with which the electrons strike the target. [2] (iii) Calculate the minimum wavelength of the X-ray photons produced by these electrons. [2] (A420U30-1) Turn over. 33 © WJEC CBAC Ltd. 33 (b) (i) Ultrasound can be used to carry out either an amplitude scan (A-scan) or a brightness scan (B-scan). Explain which of these two methods you would use to determine the depth of the tumour. Justify your answer. [2] (ii) An ultrasound scan can be used to indicate the thickness of fat on a person’s body. Typically fat has a density of 930 kg m–3 and an acoustic impedance of 1.35 × 106 kg m–2 s–1. If the time delay for the ultrasound pulse is 0.040 ms. Determine the thickness of fat. [3] Examiner only 34 (A420U30-1) © WJEC CBAC Ltd. 34 Examiner only (c) (i) Explain two properties of a radioactive isotope used as a tracer in medicine. [2] (ii) A small volume of Human Serum Albumin (HSA) labelled with iodine-125 of activity 160 Bq is injected into the bloodstream of a patient. A sample of 0.8 cm3 of blood was taken a few hours later and was found to have an activity of 0.025 Bq. If the half-life of iodine-125 is 60 days, calculate the volume of blood in the patient. State any assumptions you make. [3] (d) In a magnetic resonance imaging (MRI) scanner a large magnetic field of 1.5 T is used along with short pulses of radio waves. Dr Francis suggests that radio waves of wavelength approximately 5 m would be suitable for this MRI scanner. Determine whether or not Dr Francis is correct. [2] 20 (A420U30-1) Turn over. 35 © WJEC CBAC Ltd. 35 BLANK PAGE PLEASE DO NOT WRITE ON THIS PAGE 36 (A420U30-1) © WJEC CBAC Ltd. 36 Examiner only Option C – The Physics of Sports 13. (a) The diagram shows the forces acting on an athlete’s arm as she holds a discus. Calculate the magnitude of the tension, T, provided by the deltoid muscle. [3] 18° 0.14 m 0.35 m 0.80 m Tension, T Wdiscus = 19.6 N Warm = 39.0 N Deltoid (A420U30-1) Turn over. 37 © WJEC CBAC Ltd. 37 (b) (i) Define angular acceleration. [1] (ii) When thrown, the discus experiences an angular acceleration. It accelerates from rest to 2.3 revolutions per second in a time of 0.27 s. Calculate the angular acceleration of the discus. [2] (iii) Calculate the mean torque applied to the discus of mass 2.0 kg and radius 11 cm. The moment of inertia is given by the equation I = . [3] mr2 2 Examiner only 38 (A420U30-1) Examiner only © WJEC CBAC Ltd. (c) (i) Calculate the maximum height attained by the discus if it is thrown with a velocity of 24 m s–1 and an angle of 38° from a height of 1.2 m. Ignore the effects of air on the motion of the discus. [4] 38 38° 1.2 m 24 m s–1 (A420U30-1) Turn over. 39 Examiner only © WJEC CBAC Ltd. 39 (ii) Taking the effects of air into account, evaluate whether the horizontal distance travelled by the discus will increase, decrease or remain approximately the same. The diagram shows the speed of air relative to the upper and lower surfaces of the discus. The density of air = 1.3 kg m–3. [5] Speed of air = 21 m s–1 Speed of air = 22 m s–1 (iii) A wind tunnel is used to examine the motion of the discus in a wind speed of 20 m s–1. Calculate the factor by which the drag force increases if the speed of the wind is increased to 30 m s–1 and all other factors are kept constant. [2] 20 40 (A420U30-1) Examiner only © WJEC CBAC Ltd. 40 Option D – Energy and the Environment 14. (a) (i) Solar energy resources are considered to be renewable resources. State what is meant by a renewable energy resource. [1] (ii) The proton-proton chain is a set of reactions that take place in our Sun and can be summarised in the following equation. Use data to show that the percentage mass loss is approximately 0.7%. [2] Mass of H = 1.007 28 u Mass of He = 4.001 51 u Mass of e = 0.000 55 u Mass of νe = 0.000 00 u (iii) The Sun can be assumed to have come to the end of its life when it has lost 0.7 % of its mass to radiated energy. Estimate the lifetime of the Sun in years. Take the mass of the Sun to be 2.0 × 1030 kg and assume it to have a constant power output of 3.8 × 1026 W. [2] H + + He 41 1 2 0 –1e 4 2 2νe 1 1 4 2 0 –1 (A420U30-1) Turn over. 41 © WJEC CBAC Ltd. 41 Examiner only (b) The power output, P, from a photovoltaic (PV) cell of surface area, A, can be calculated using the equation: P = μAIcosθ where μ is the conversion efficiency of the cell, I is the intensity of solar radiation and θ is the angle between the normal and the incident sunlight. 20° 60° PV cell θ Diagram not to scale A factory decides to install rooftop PV cells at an angle of 20° to the horizontal. At midday when the Sun’s elevation is 60° the solar radiation incident upon the surface of the Earth has an intensity of 600 W m–2. An individual PV cell has a conversion efficiency of 20 % and is found to produce a power output of 150 W. (i) Show that the area of the PV cell is approximately 1.3 m2. [2] (ii) The factory roof covers an area of 3.6 × 104 m2 and the factory owner plans for the installation to produce a mean power output of 4.0 MW. It is suggested that the company should install 27 500 of these PV cells. Discuss whether or not you believe this to be suitable. [3] (A420U30-1) 42 © WJEC CBAC Ltd. 42 (c) (i) Describe what is meant by the enrichment of uranium and explain why it is necessary. [2] (ii) Gaseous diffusion was one of the original methods used to enrich uranium fuel. Uranium hexafluoride gas composing of 235UF6 and 238UF6 moves from a region of high pressure to a region of low pressure through a porous membrane. The lighter and faster 235UF6 molecules diffuse through the membrane at a greater rate. The first stage of the enrichment process is shown below. Porous membrane During this stage, the mixture is enriched by a factor that can be calculated using: Use the equation and data below to show that the uranium hexafluoride gas would need to complete more than 450 stages if it is to increase the concentration of uranium-235 from 0.7% to 5%. [3] Molar mass of 235UF6 = 349 g mol–1 Molar mass of 238UF6 = 352 g mol–1 (iii) State an alternative method for the enrichment of uranium. [1] Further enrichment Gas enriched in 235UF6 Gas depleted of 235UF6 235UF6 238UF6 Gas mixture of 235UF6 and 238UF6 Examiner only enrichment factor = molar mass of 238UF6 molar mass of 235UF6 43 (A420U30-1) © WJEC CBAC Ltd. 43 (d) A method of reducing CO2 emissions involves the use of fuel cells to power cars. The basic layout for a proton exchange membrane fuel cell is shown in the diagram below. Electric current Unused gases out Electrolyte Anode Cathode Air in Fuel in Excess fuel out H2O H2 O2 (i) Describe the purpose of the electrolyte and state the waste product from the reaction. [2] (ii) In order for the fuel cell to be considered to have no CO2 emissions, the sourcing of the hydrogen fuel must be considered. Two possible sources are: • Electrolysis of water – where electrical energy is used to split water molecules to create hydrogen and oxygen; • Reforming fossil fuels – where steam at high temperature is reacted with a fossil fuel to separate the hydrogen from the carbon in a hydrocarbon. Discuss their likely impact on CO2 emissions. [2] END OF PAPER Examiner only 20 Turn over. e– e– e– e– H+ H+ (A420U30-1) 44 © WJEC CBAC Ltd. 44 Question number Additional page, if required. Write the question number(s) in the left-hand margin. Examiner only