# Monday 11 June 2012 Afternoon

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2 2 Answer all the questions. Section A 1 Fig. 1.1 shows an ideal transformer. primary coil 200 turns secondary coil 400 turns laminated iron core Fig. 1.1 A 50 Hz alternating p.d. of 12 V is applied to the primary coil. (a) Choose the correct statement from the sentences below: A B C D The p.d. across the secondary coil is 24 V, frequency 100 Hz. The p.d. across the secondary coil is 6.0 V, frequency 50 Hz. The p.d. across the secondary coil is 24 V, frequency 50 Hz. The p.d. across the secondary coil is 6.0 V, frequency 100 Hz. The correct statement is... [1] (b) The current in the primary coil is 1.8 A. Calculate the current in the secondary coil. current =... A [1]

3 2 Here is a list of particles. 3 electron neutron photon positron (a) Which particle is composed of quarks?... [1] (b) Which particle has the highest rest energy?... [1] 3 The electric field strength at a distance r from a point charge Q is given by where k is a constant. Show that the units of k are N m 2 C 2. E = kq r 2 [1] Turn over

4 4 Fig. 4.1 shows a sketch graph of average binding energy per nucleon against nucleon number. 4 0 nucleon number A B C D binding energy / nucleon Fig. 4.1 (a) The Sun releases energy through nuclear fusion. State in which region, A, B, C or D on the graph, nuclei may release energy through fusion. region... [1] (b) The Sun releases energy at a rate of W. Calculate the mass lost by the Sun in one second. c = m s 1 mass lost in one second =... kg

5 5 Fig. 5.1 shows a point X near an isolated proton m proton X Fig. 5.1 The field strength at X, m from the centre of the proton, is 58 N C 1. (a) Calculate the potential at X. k = N m 2 C 2 charge on a proton = C A second proton moves to a position as shown in Fig potential =... J C m m proton X proton Fig. 5.2 (b) State the field strength at X for the situation in Fig [1] (c) State how the potential at X in Fig. 5.2 compares with your answer to (a). [1] Turn over

6 6 The centripetal force F on a charge q moving at right angles to a magnetic field is given by 6 F = q v B where v is the speed of the particle in the field. Combine this equation with that for centripetal force F = m v 2 / r to show that a singly-charged ion of momentum kg m s 1 travelling at right angles to a magnetic field of strength 0.70 T will move in a circular path of radius about 0.2 m. e = C 7 In April 1986 the Chernobyl nuclear reactor released radioactive caesium-137 into the atmosphere. Caesium-137 has a half-life of 30.1 years. Show that, in June 2012, approximately 26 years after the release, less than 60% of the caesium-137 remains. [3]

7 8 Fig. 8.1 shows the direction of a current I in a wire at right angles to a field of flux density B. 7 I B Fig. 8.1 Calculate the force on a 15 cm length of wire in a field of flux density 400 mt when the wire carries a current of 0.23 A. force =... N [Section A Total: 19] Turn over

8 8 Section B 9 This question is about the behaviour of electrons when passing near nuclei. When an electron passes near a nucleus it is deflected as shown in Fig nucleus path of electron Fig. 9.1 (a) Explain why the electron follows a path of the shape shown. You may add arrows to Fig. 9.1 indicating magnitude and direction of forces on the electron. In your answer you should make clear how the force on the electron varies along its path. (b) At high energies the momentum p of a particle is given by [3] p E c where E is the energy of the particle and c is the speed of light. (i) Show that E c has the units of momentum.

9 (ii) 9 Show that an electron accelerated to a high energy of J (425 MeV) will have a de Broglie wavelength of about m. h = J s c = m s 1 (c) Fig. 9.2 shows how the number of 425 MeV electrons scattered by carbon nuclei varies with the scattering angle. The graph shows a clear diffraction minimum. The nuclei diffract high energy electrons like dust particles diffract light. accelerator detector number scattered / (arbitrary units) angle / degree Fig. 9.2 The angle of the first diffraction minimum in such a pattern is given by the equation sin θ = 1.2 λ b where b is the diameter of the diffracting object and λ is the wavelength of the electrons. Use data from the graph to estimate the diameter of the carbon nuclei in the sample. diameter =... m [3] [Total: 10] Turn over

10 10 10 This question is about using accelerated protons in medicine. The protons are accelerated to kinetic energies of 220 MeV. The rest energy of a proton is 940 MeV. (a) (i) State what is meant by the term rest energy. [1] (ii) Show that the relativistic factor γ for these accelerated protons is about 1.2. [1] (iii) Show that these protons are travelling at about 0.6 c. (b) In a medical procedure a cluster of cells of total mass kg is irradiated with 220 MeV protons. Show that it will take at least 10 5 protons to deliver an effective dose equivalent of 125 msv to the cluster of cells. e = C quality factor of protons = 10 [3]

11 11 (c) The effect of a proton beam on tissue can be modelled by passing the proton beam through water. Energy is transferred from each proton when it ionises particles along its path. Fig shows how the energy of a proton beam varies along the path of the beam through water. energy of proton beam penetration depth / cm Fig (i) Use information from the graph to estimate the depth at which the beam ionises the greatest number of particles per cm. Explain how you reached your answer. depth =... cm [3] (ii) Explain why the graph shows that your answer to (b) must be a minimum value. [Total: 12] Turn over

12 11 This question is about using an electric field to deflect falling particles of material m 1.9 m 0 V + 48 kv Fig Fig shows two vertical metal plates connected to a 48 kv supply. (a) (i) Draw five lines to represent the electric field between the plates in Fig (ii) Add the 24 kv equipotential to the diagram. Label the line. [1] (b) Use data from the diagram to show that field strength between the plates is about 0.2 MV m 1. [1]

13 13 (c) A grain of mass kg enters the region between the plates, falling at constant (terminal) vertical velocity of 0.8 m s 1. The grain carries an electric charge of C. (i) State why the data above suggests that the vertical force due to air drag is about N. g = 9.8 N kg 1 [1] (ii) The horizontal force on the grain is much smaller. Show that the horizontal force is about N. [1] (iii) Show that the horizontal distance moved by the grain as it falls through the 1.9 m plates is of the order of 0.1 m. Any horizontal drag forces can be ignored. (d) Suggest and explain how the horizontal distance would change if the separation of the plates was doubled but all other factors remain constant. [3] [3] [Total: 12] Turn over

14 12 This question is about magnetic circuits. 14 The permeance Λ of a magnetic circuit is given by the equation Λ = Φ N I where: Φ is the magnetic flux in the circuit N is the number of turns of the coil I is the current in the coil A magnetic circuit is illustrated in Fig cross-sectional area = m 2 data: I = 31 ma N = 150 turns Φ = Wb length of magnetic circuit, L = 270 mm Fig (a) Calculate the permeance of the circuit in Fig permeance =... unit... (b) The permeance of a magnetic circuit is also given by the equation Λ = μa L where μ is the permeability of the iron in the core, A the cross-sectional area of the core and L the length of the magnetic circuit. Use data from Fig and your answer to (a) to calculate the permeability of the iron in the core. permeability of iron in the core =... Wb A 1 m 1

15 15 (c) A crack develops across the core, making an air-gap running across its entire cross-section as shown in Fig part of core crack across core Fig (i) State how the permeability of air compares to that of iron. [1] (ii) Explain why the flux through the core is reduced when the core develops a crack. You may find it useful to refer to an equation given earlier in the question. (d) A student believes that the equation Λ = μa/l shows that the permeability of the iron in the core has also reduced. Discuss whether you agree with the student or not. [Total: 9] [Section B Total: 43] Turn over

16 16 Section C These questions are based on the Advance Notice. 13 Explain how brittle fracture occurs in rocks under stress, starting at the cracks in the rock (lines 6 7 in the article). You may use diagrams in your answer. [Total: 2] 14 Use the data given in Fig. 2 in the article to show that (a) a surface wave L would take less than four hours to travel once around the circumference of the Earth radius of Earth = 6400 km (b) the P and S waves have the same wavelength. [1] [Total: 3]

17 17 15 Explain how a combination of transverse and longitudinal waves can result in vibrations in all three spatial directions (lines 9 10 in the article). You may find drawing a diagram useful in your answer. [3] [Total: 3] 16 A P wave travelling at 6.0 km s 1 meets a boundary between two rock types at an angle of incidence of 30 and passes through it at an angle of refraction of 21. Use the information given about wave refraction in Box 1 in the article to calculate the speed of the wave in the second type of rock. speed =... m s 1 [3] [Total: 3] Turn over

18 18 17 (a) Explain why it is important that the natural frequency of the seismometer is deliberately not equal to that of the vibrations caused by earthquakes. (b) Show that the effective length L of the pendulum in a Milne seismometer (Figs. 3 and 4 in the article) needs to be about 100 m in order for it to have a frequency less than that of the lowest frequency waves (L waves, see Fig. 2 in the article). natural frequency of a simple pendulum, f = 1 2π g L where g = 9.8 m s 2 (c) Hence calculate the angle α at which the boom needs to be tilted, if it has a length of 1.0 m. α =... degrees [Total: 6]

19 19 18 Like many seismometers, the Milne design incorporates a large mass which remains essentially motionless when the ground beneath it vibrates. Lines in the article list the factors involved in ensuring that this occurs. (a) Explain how the combination of a large mass and a small force ensures that the mass remains essentially motionless. (b) Suppose you could have a pendulum of length 100 m. Explain why the accelerating force on the mass would be very small for a displacement of a few millimetres. [Total: 4] Turn over

20 19 Earthquake magnitude can be measured using the Richter Scale (lines in the article). 20 (a) Calculate how many times greater the shaking amplitude of a magnitude 6.0 earthquake is than one of magnitude 4.0. Explain how you reached your value. answer... (b) Using the relationship given in line 56 in the article, calculate how many times greater the energy released by a magnitude 6.0 earthquake is than one of magnitude 4.0. answer... [Total: 4]

21 21 20 The relative movement of the mass and base (Fig. 4 in the article) is detected using a magnet attached to the mass and a coil attached to the base. (a) Explain how this movement can produce an emf. (b) Here are some data for a particular magnet and coil arrangement used to detect vibrations in a seismometer (lines in the article). The coil is square and its area is completely contained within the area of the uniform magnetic field at right angles to the plane of the coil. strength of magnetic field = 0.15 T cross sectional area of coil = 4.0 cm 2 number of coil turns = 200 (i) Show that the flux through the coil is greater than Wb. (ii) Hence calculate the flux linkage through the coil. flux linkage =... Wb turns [1] Turn over

22 22 (iii) During an earthquake, the ground shakes. This causes the coil to move a distance of 3 mm out of the magnetic field at an average speed of m s 1. The flux linkage reduces to half its original value as the coil moves partially out of the magnetic field. Calculate the magnitude of the emf induced in the coil as a result of this motion. induced emf =... V [4] [Total: 9] 21 The seismometer is damped to reduce unwanted vibration. One method of damping is mentioned in lines in the article, using an aluminium plate moving in a magnetic field. With particular reference to induced voltage and energy transfers, describe how this arrangement produces the damping required. You should make each step of your argument clear. END OF QUESTION PAPER [4] [Total: 4] [Section C Total: 38]

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