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GCE JAN 2010 : A2 1 Energy, Oscillations and Fields

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Centre Number 71 Candidate Number ADVANCED General Certificate of Education January 2010 Physics assessing Module 4: Energy, Oscillations and Fields A2Y11 Assessment Unit A2 1 [A2Y11] MONDAY 18 JANUARY, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number in the spaces provided at the top of this page. Answer all seven questions. Write your answers in the spaces provided in this question paper. INFORMATION FOR CANDIDATES The total mark for this paper is 90. Quality of written communication will be assessed in questions 2(a) and 4(c). Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question. Your attention is drawn to the Data and Formula Sheet which is inside this question paper. You may use an electronic calculator. Question 7 contributes to the synoptic assessment requirement of the Specification. You are advised to spend about 55 minutes in answering questions 1 6, and about 35 minutes in answering question 7. 5515 For Examiner s use only Question Number 1 2 3 4 5 6 7 Total Marks Marks If you need the values of physical constants to answer any questions in this paper, they may be found on the Data and Formulae Sheet. Examiner Only Marks Remark Answer all seven questions 1 A wire of cross sectional area A and length L is clamped at one end and is stretched by a force F applied at the other. This force causes an extension x. (a) Write down expressions for: (i) the stress acting on the wire, = ________________ (ii) the strain in the wire. = ________________ 5515 [2] 2 [Turn over (b) A copper wire of length 2.70 m and diameter 1.50 mm is clamped at one end as shown in the experimental arrangement in Fig. 1.1. It is stretched by the application of a load of 468 N. clamped end wire Examiner Only Marks Remark pulley load Fig. 1.1 Given that the Young modulus of copper is 128 GPa. (i) Calculate the extension of the copper wire when the load is applied. Extension = ________________ mm [3] (ii) Calculate the strain energy per unit volume stored in the wire when it is extended. Strain energy per unit volume = _____________ kJ m 3 5515 3 [2] [Turn over 2 (a) Describe an experiment to verify Equation 2.1 for a real gas of fixed mass held at constant pressure. V = a constant T Examiner Only Marks Remark Equation 2.1 where V = gas volume and T = temperature in kelvin. In your description you should include (i) a labelled diagram of the apparatus, (ii) how a series of results are taken, (iii) how the relationship is verified. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _______________________________________________________ [5] Quality of written communication 5515 [1] 4 [Turn over (b) A container of volume 4.3 10 2 m3 holds 3.1 10 2 kg of an ideal gas at a pressure of 0.43 105 Pa and a temperature of 17 C. Examiner Only Marks Remark (i) Calculate the number of gas molecules in the container. Number of molecules = ____________ [3] (ii) Calculate the root mean square speed of these molecules. r.m.s. speed = ____________ m s 1 5515 [3] 5 [Turn over 3 Fig. 3.1 shows a cross-section of the Earth. Examiner Only Marks Remark A B Fig. 3.1 (a) Describe and explain how the angular velocity and linear velocity of a person on the surface of the Earth changes as he travels along the Earth s surface from the point A on Fig. 3.1 to the point B at the equator. Angular velocity _________________________________________________________ _________________________________________________________ _______________________________________________________ [2] Linear velocity _________________________________________________________ _________________________________________________________ _______________________________________________________ [2] 5515 6 [Turn over (b) The radius of the Earth is 6.4 106 m. Calculate the centripetal acceleration of an object placed at the equator. Acceleration = ___________ m s 2 5515 Examiner Only Marks Remark [3] 7 [Turn over 4 (a) State the characteristics of the acceleration of a body moving in simple harmonic motion. Examiner Only Marks Remark _________________________________________________________ _________________________________________________________ _________________________________________________________ _______________________________________________________ [2] (b) An object oscillates in simple harmonic motion with amplitude 0.023 m and maximum acceleration 2.75 m s 2. Calculate the periodic time of the oscillation from these data. T = __________ s 5515 [4] 8 [Turn over (c) An object is executing simple harmonic motion. From time t = 0 to time t = t1 the oscillations are not damped. From time t = t1 to time t = t2 the oscillations are lightly damped. Examiner Only Marks Remark Write an account of the variation with time of the amplitude of the object from time t = 0 to time t = t2. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _______________________________________________________ [3] Quality of written communication 5515 [1] 9 [Turn over 5 (a) (i) What is meant by a field of force? Examiner Only Marks Remark _____________________________________________________ ___________________________________________________ [1] (ii) State one similarity and one difference between electric and gravitational fields: Similarity: _____________________________________________________ ___________________________________________________ [1] Difference: _____________________________________________________ ___________________________________________________ [1] (b) A sphere of mass 2.30 g has an electric charge of +3.40 C. It is dropped in a vacuum between two metal plates as shown in Fig. 5.1. The plates are separated by 9.0 cm, and a potential difference of 160 V is applied between them. Sphere Vacuum + Fig. 5.1 5515 10 [Turn over (i) Calculate the magnitude of the gravitational force acting on the sphere. Gravitational force = ________ N Examiner Only Marks Remark [1] (ii) Calculate the magnitude of the electrical force acting on the sphere. Electrical force = ________ N [2] (iii) Describe the path of the sphere between the metal plates under the action of both forces. _____________________________________________________ ___________________________________________________ [1] 5515 11 [Turn over 6 (a) State, in words, Newton s law of gravitation. Examiner Only Marks Remark _________________________________________________________ _________________________________________________________ _______________________________________________________ [3] (b) Using Newton s law of gravitation, show that the period T of revolution of a satellite is related to the radius r of the orbit by Equation 6.1 4 2 T 2 = r3 GM Equation 6.1 where M is the mass of the planet that is being orbited. [3] 5515 12 [Turn over (c) In this part of the question, use the following data: Examiner Only Marks Remark Radius of Earth = 6.37 106 m Mass of Earth = 5.98 1024 kg (i) A satellite orbits the Earth in a geostationary orbit. What is meant by a geostationary orbit? _____________________________________________________ ___________________________________________________ [1] (ii) Calculate the height of the satellite above the Earth s surface. Height = _________ m [3] (iii) Calculate the linear velocity of the geostationary satellite. Linear velocity = _________ m s 1 5515 13 [2] [Turn over 7 Data analysis question Examiner Only Marks Remark In your answer, you will be expected to bring together and apply principles and contexts from different areas of physics, and to use the skills of physics, in the particular situation described. You are advised to spend about 35 minutes in answering this question. Sedimentation equilibrium Introduction When a large number of identical particles are suspended in a liquid, they tend to settle in the way illustrated in Fig. 7.1. There are many particles at the bottom of the liquid column, but progressively fewer as one goes up from the bottom. h Fig. 7.1 According to theory, the equilibrium number density n of particles at a height h above the bottom of the liquid column is given by Equation 7.1 n = n0 mg h e kT Equation 7.1 where n0 is a constant, m is the mass of a particle, g is the acceleration of free fall, k is the Boltzmann constant, T is the temperature in kelvin and allows for the difference in density of the liquid and the material of the particles. is given by Equation 7.2 =1 l p Equation 7.2 where l is the liquid density and p is the particle material density. 5515 14 [Turn over About a century ago, Jean Perrin carried out experiments based on this theory. He used particles of a yellow pigment called gamboges, suspended in water. By counting the particles at different heights h in the water column, he obtained values of n which could then be fitted to his theory. From his results he was able to deduce a value for the Boltzmann constant k of 1.38 10 23 J K 1. Examiner Only Marks Remark (a) (i) What name is given to the mathematical function represented by Equation 7.1? ___________________________________________________ [1] (ii) Name another physical phenomenon which is governed by the mathematical function in Equation 7.1, but which uses different variables. ___________________________________________________ [1] (iii) On Fig. 7.2, sketch the variation of n with h represented by Equation 7.1. n 0 0 h [2] Fig. 7.2 5515 15 [Turn over 1 (b) (i) Show that the height at which n has a value equal to n0 is given 2 by Equation 7.3. kT h= loge 2 mg Examiner Only Marks Remark Equation 7.3 [3] (ii) Show that the base unit on the right hand side of Equation 7.3 is the metre, the same as that on the left hand side. [3] When an object is immersed in a liquid, it is subjected to a second force. This force, called upthrust, acts upwards and has a magnitude equal to the weight of liquid displaced by the object. Thus, the effective weight of an object is the resultant of the weight and upthrust forces acting on the object. (c) (i) If the density of the liquid that the particles are suspended in is reduced, state how the effective weight of the particles will change. [1] (ii) Predict and explain how using a liquid of lower density would affect the distribution of particles throughout the liquid. [1] (iii) Explain your prediction using Equation 7.1 and Equation 7.2. [2] 5515 16 [Turn over (d) In Table 7.1 are recorded the data for a sedimentation equilibrium experiment that used water as the liquid. The information directly below is relevant to this question. Examiner Only Marks Remark Density of water at 290 K = 0.999 103 kg m 3 Density of material of particle = 1.003 103 kg m 3 Temperature of water = 290 K Boltzmann constant, k = 1.38 10 23 J K 1 Acceleration of free fall, g = 9.81 m s 2 Table 7.1 h/mm n/mm 3 0.200 1160 0.400 632.7 0.600 347.2 0.800 188 1.000 103.5 1.200 loge (n/mm 3) 56 (i) Two of the values in the column headed n/mm 3 have been expressed to a different number of significant figures than the rest of the column. Write down the two values and state to how many significant figures they have been expressed. _____________________________________________________ ___________________________________________________ [2] (ii) Use Equation 7.1 to explain why a graph plotted of loge (n/mm 3) against h/mm will be a straight line and that it will not go through the origin. _____________________________________________________ _____________________________________________________ _____________________________________________________ ___________________________________________________ [3] 5515 17 [Turn over (iii) Obtain values of loge (n/mm 3) and insert these values into the appropriate column of Table 7.1. [2] Examiner Only Marks Remark (iv) Plot a graph of loge (n/mm 3) against h/mm on the graph grid of Fig. 7.3. [5] (v) Obtain the gradient of your graph in Fig. 7.3. Give the unit for the gradient. Gradient = ____________ Unit = ____________ [3] (vi) Use a suitable form of Equation 7.1, your answer to (v) and relevant data given, to calculate a value for the mass m of a particle. Show clearly how you obtain this value. Mass of particle = _________ kg [4] (vii) Calculate a value for n0. n0 = __________ 5515 [2] 18 [Turn over Fig. 7.3 5515 19 [Turn over 1312-026-1 GCE Physics (Advanced Subsidiary and Advanced) Data and Formulae Sheet Values of constants speed of light in a vacuum c = 3.00 108 m s 1 permeability of a vacuum 0 = 4 10 7 H m 1 permittivity of a vacuum 0 = 8.85 10 12 F m 1 1 = 8.99 109 F 1 m 4 0 ( ) elementary charge e = 1.60 10 19 C the Planck constant h = 6.63 10 34 J s unified atomic mass unit 1 u = 1.66 10 27 kg mass of electron me = 9.11 10 31 kg mass of proton mp = 1.67 10 27 kg molar gas constant R = 8.31 J K 1 mol 1 the Avogadro constant NA = 6.02 1023 mol 1 the Boltzmann constant k = 1.38 10 23 J K 1 gravitational constant G = 6.67 10 11 N m2 kg 2 acceleration of free fall on the Earth s surface g = 9.81 m s 2 electron volt 1 eV = 1.60 10 19 J A2Y11INS 5515.02 USEFUL FORMULAE The following equations may be useful in answering some of the questions in the examination: Thermal physics Mechanics Momentum-impulse relation mv mu = Ft for a constant force Average kinetic energy of a molecule 1 m<c2> 2 Power P = Fv Kinetic theory pV = 1 Nm <c2> 3 Conservation of energy 1 mv 2 2 1 mu 2 = Fs 2 for a constant force Simple harmonic motion Displacement x = x0 cos t or x = x0 sin t Velocity v = x 0 2 x 2 Simple pendulum T = 2 l / g Loaded helical spring T = 2 m / k Medical physics Sound intensity level/dB = 10 lg10(I/I0) Sound intensity difference/dB = 10 lg10(I2/I1) Resolving power sin = / D Waves Capacitors Capacitors in parallel 11 1 1 = + + C C1 C 2 C 3 C = C1 + C2 + C3 Time constant = RC Capacitors in series Electromagnetism Magnetic flux density due to current in (i)i long straight (i)i solenoid B= (ii) long straight (i)i conductor B= = ay/d Diffraction grating 0I 2 a A.c. generator E = E0 sin t = BAN sin t Stress and Strain Hooke s law F = kx Strain energy E = <F > x (= 1 Fx = 1 kx 2 2 2 if Hooke s law is obeyed) Electricity Vout = R1Vin/(R1 + R2) A = N A = A0e t t1 = 0.693/ 2 Photoelectric effect 1 mv2 = max 2 de Broglie equation 1/u + 1/v = 1/ f Radioactive decay Half life Light 5515.02 l Alternating currents d sin = n Potential divider 0NI Particles and photons Two-slit interference Lens formula = 3 kT 2 = h /p Particle Physics Nuclear radius 1 r = r0 A3 hf hf0

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Additional Info : Gce Physics January 2010 Assessment Unit A2 1, Module 4: Energy, Oscillations and Fields
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