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GCE MAY 2008 : A2 1 Energy, Oscillations and Fields

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ERRATUM NOTICE General Certi cate of Education (Advanced Level) Physics, Assessment Unit A2-1, Module 4, Energy, Oscillations and Fields (A2Y11) Thursday 22 May, Afternoon Notice to Invigilator Before the start of the examination the following should be read to candidates. 1. Go to the Question Paper. (Pause) 2. Turn to page 7 of the Question Paper. (Pause) 3. Go to Fig. 2.1 at the bottom of the page. (Pause) 4. There is a small v at the top of the vertical axis beside the arrowhead. (Pause) 5. Change this small v to a capital V. (Pause) Repeat 1. Go to the Question Paper. (Pause) 2. Turn to page 7 of the Question Paper. (Pause) 3. Go to Fig. 2.1 at the bottom of the page. (Pause) 4. There is a small v at the top of the vertical axis beside the arrowhead. (Pause) 5. Change this small v to a capital V. (Pause) Please make this change in your question paper now. This is the end of the announcement. Centre Number 71 Candidate Number ADVANCED General Certificate of Education 2008 Physics assessing Module 4: Energy, Oscillations and Fields A2Y11 Assessment Unit A2 1 [A2Y11] THURSDAY 22 MAY, 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 six 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 question 4(b)(iii). 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 Formulae Sheet which is inside this question paper. You may use an electronic calculator. Question 6 contributes to the synoptic assessment requirement of the Specification. You are advised to spend about 55 minutes in answering questions 1 5, and about 35 minutes in answering question 6. 4700 For Examiner s use only Question Number 1 2 3 4 5 6 Total Marks Marks BLANK PAGE 4700 2 [Turn over If you need the values of physical constants to answer any questions in this paper, they may be found in the Data and Formulae Sheet. Examiner Only Marks Remark Answer all six questions 1 (a) (i) Define momentum. ______________________________________________________ ___________________________________________________ [1] (ii) Consider a system of two colliding particles. Use Newton s laws to derive the principle of conservation of linear momentum. ______________________________________________________ ______________________________________________________ ______________________________________________________ ______________________________________________________ ____________________________________________________ [4] 4700 3 [Turn over (b) In Fig. 1.1, A and B are two trolleys which can move on a frictionless track. Examiner Only Marks Remark v B A Fig. 1.1 The mass of trolley A is m and that of trolley B is 3m. Initially trolley A is moving with constant speed v directly towards B, which is stationary until the impact. At time t the trolleys collide. Fig. 1.2 is a graph of the velocity of trolley A before, during and after the collision. Velocities from left to right are taken as positive. velocity of A v 0 0 t 2t time v Fig. 1.2 (i) Describe in words the motion of trolley A after time t. ______________________________________________________ ______________________________________________________ ___________________________________________________ [2] 4700 4 [Turn over (ii) On Fig. 1.3 draw, to scale, a graph to show the velocity of trolley B before, during and after the collision. Any calculations may be made in the space below, but you will receive credit only for what appears on your graph. [2] Examiner Only Marks Remark velocity of B v 0 0 t 2t time v Fig. 1.3 4700 5 [Turn over (iii) Carry out a suitable calculation to see if kinetic energy is conserved during the collision. Hence classify the collision as elastic or inelastic. Record your conclusion by placing a tick in the relevant box. Show all calculations clearly. Examiner Only Marks Remark The collision is elastic (kinetic energy is conserved) The collision is inelastic (some or all of the kinetic energy is converted into other forms) [3] 4700 6 [Turn over 2 (a) An experiment on the behaviour of gases shows that the volume of a sample of gas is directly proportional to its temperature in kelvins. When such an experiment is carried out in a school or college laboratory, the temperature of the gas will be measured using a thermometer calibrated in degrees Celsius. Examiner Only Marks Remark (i) Draw a labelled sketch of the apparatus that could be used to investigate the way in which the volume V of a sample of gas depends on its Celsius temperature . [2] (ii) On Fig. 2.1, sketch a graph of the results that would be expected. Extrapolate the best straight line through the experimental points. Label the -axis with any significant numerical value. v 0 0 +100 / C Fig. 2.1 [2] 4700 7 [Turn over (b) The ideal gas equation is Examiner Only Marks Remark pV = nRT. In this equation, p and V are the pressure and volume respectively of a sample of ideal gas, n is the number of moles of gas in the sample, R is the molar gas constant and T is the temperature in kelvins. (i) The mole is the SI base unit of amount of substance. The definition of the mole refers to a number of particles. What is this number? _____________________________________________________ _____________________________________________________ _________ _ _ _______________________________________ [1] ___ (ii) One molecule of carbon dioxide contains one atom of carbon of mass 12 u and two atoms of oxygen, each of mass 16 u. (1) Calculate the mass, in u, of one molecule of carbon dioxide. Mass = __________ u [1] (2) Calculate the mass, in kg, of one mole of carbon dioxide. Mass = __________ kg 4700 [2] 8 [Turn over (3) Assume that carbon dioxide behaves as an ideal gas. Calculate the volume, in m3, of 1 mole of carbon dioxide at a temperature of 273 K and a pressure of 1.01 105 Pa. Volume = __________ m3 Examiner Only Marks Remark [2] (4) A flexible container of carbon dioxide has a volume of 1.50 m3 at a temperature of 25 C and a pressure of 1.15 105 Pa. Calculate the mass of gas enclosed. Mass = __________ kg 4700 [4] 9 [Turn over 3 (a) A student is asked to draw a graph to show how the acceleration a of a particle moving with simple harmonic motion depends on the displacement x of the particle. The student s response is shown in Fig. 3.1. Examiner Only Marks Remark a 0 0 x Fig. 3.1 (i) The graph in Fig. 3.1 is a straight line through the origin. State one characteristic of simple harmonic motion which this correctly describes. _____________________________________________________ _____________________________________________________ [1] (ii) Two features of the student s graph in Fig. 3.1 do not give a correct description of simple harmonic motion. On Fig. 3.1, sketch a graph in which these features are corrected. [2] (iii) The defining equation for simple harmonic motion includes a quantity . State how this quantity can be obtained from your corrected graph in (a)(ii). _____________________________________________________ _____________________________________________________ _____________________________________________________ [2] 4700 10 [Turn over (b) A geologist carries out a gravity survey by finding the period of a simple pendulum at various places. At a particular site the pendulum, 37.50 cm long, has a period of 1.221 s. Examiner Only Marks Remark (i) Calculate the strength of the Earth s gravitational field at this site. Give your answer to an appropriate number of significant figures. Earth s gravitational field = __________ N kg 1 [3] (ii) There is an uncertainty of 0.001s in the measurement of the period of the pendulum, and a percentage uncertainty of 0.01% in the length of the pendulum. Calculate the percentage uncertainty in the value of the gravitational field in (b)(i). Percentage uncertainty = __________ % 4700 11 [3] [Turn over In part (b) of this question you should answer in continuous prose, where appropriate. You will be assessed on the quality of your written communication. 4 Examiner Only Marks Remark (a) The total energy E of a particle of mass m oscillating with amplitude A and frequency f is given by E = 2 2mx02 f 2 Equation 4.1 (i) Write down the SI base units of energy E. _______________________________________________________ [1] (ii) Write down the SI base units of the following quantities. Mass m _______________ Amplitude x0 _______________ Frequency f _______________ [1] (iii) Hence confirm that the units on the right-hand side of Equation 4.1 are equivalent to those on the left-hand side. [1] 4700 12 [Turn over (b) The way in which the displacement x of the bob of a damped pendulum varies with time t is shown in Fig. 4.1. Note that Fig. 4.1 shows that the frequency of the motion is constant. The mass of the bob is, of course, constant. Examiner Only Marks Remark x Displacement 0 t Fig. 4.1 (i) Make use of Equation 4.1 to deduce the way in which the total energy E of the pendulum depends on its amplitude x0. _______________________________________________________ [1] (ii) On Fig. 4.2 sketch a graph showing how the total energy E depends on time t. [1] E 0 t Fig. 4.2 4700 13 [Turn over (iii) Explain how the principle of conservation of energy applies to the way in which the total energy E of the pendulum bob varies with time t. Examiner Only Marks Remark _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ _____________________________________________________ [3] Quality of written communication 4700 [2] 14 [Turn over BLANK PAGE (Questions continue overleaf) 4700 15 [Turn over 5 A binary star system consists of two stars S1 and S2 of equal mass M. The stars orbit about a point O midway between them, as shown in Fig. 5.1. Examiner Only Marks Remark S2 S1 O d Fig. 5.1 The separation of the stars is d. The period of one orbit is T. (a) (i) Write down an expression for the gravitational force Fg between the two stars, in terms of d, M and the gravitational constant G. [1] (ii) Obtain an expression for the centripetal force Fc acting on one star, in terms of d, M and T. [3] (iii) Hence show that the mass M of one of the stars is given by the expression M= 2 2 d 3 GT 2 [2] 4700 16 [Turn over (b) Astronomical observations on a particular binary star system show that the stars are separated by 3.60 1011 m and the orbital period is 1.58 108 s. Calculate the mass of one of the stars. Mass = __________ kg 4700 Examiner Only Marks Remark [2] 17 [Turn over Data analysis question This question contributes to the synoptic assessment requirements of the Specification. In your answer, you will be expected to use the ideas and skills of physics in the particular situations described. You are advised to spend about 35 minutes in answering this question. 6 The scattering of electromagnetic radiation The classical wave theory of the scattering of light by atoms shows that electrons in the atom are driven into forced oscillations by the incident electromagnetic radiation. The oscillating electrons then re-radiate the energy in all directions without change of wavelength. For a given average spacing of scatterers, the intensity I of the scattered radiation depends on the wavelength of the incident and scattered light. The relationship between I and is I = A n Equation 6.1 where A and n are constants. This type of scattering is called Rayleigh scattering. Another sort of scattering, known as Compton scattering, is evidence for the photon aspect of electromagnetic radiation. It can be thought of as the elastic collision of a photon of energy E (wavelength ) with a stationary electron. The result of the interaction is that the electron moves off and the photon is scattered at an angle s with reduced energy Es (increased wavelength s), as illustrated in Fig. 6.1. target electron scattered electron incident photon s energy E Fig. 6.1 scattered photon energy Es In this type of scattering, the relationship between the energy loss E (= E Es) and the energy E of the incident photon is E E = s 2 (1 cos s ) E me c Equation 6.2 where c is the speed of electromagnetic radiation in free space and me is the rest mass of the electron. 4700 18 [Turn over (a) Rayleigh scattering Examiner Only Marks Remark Table 6.1 gives the intensity I obtained for various values of the incident and scattered wavelength for a particular scattering system. Table 6.1 /nm I/arbitrary units 100 9.80 103 300 1.23 102 500 1.60 101 1000 1.00 1500 1.98 10 1 2000 6.25 10 2 (i) In Table 6.1 the values of intensity I have been quoted in arbitrary units. Which of the following would be appropriate SI units for intensity? Indicate your choice by placing a tick (or ticks) in the appropriate box (or boxes). [2] Nms 1 W m 2 W s 1 kgs 3 kg m 1 s 2 m2 s 2 (ii) Two students are discussing significant figures. Student A says that the intensity value of 1.00 in Table 6.1 is to one significant figure. Student B says that the value is to three significant figures. Which student is correct, and why? _____________________________________________________ _____________________________________________________ ____________________________________________________ [2] 4700 19 [Turn over The order of magnitude of a quantity is the nearest power of ten to the value of the quantity. For example, in Table 6.1 the order of magnitude of 9.80 103 is 104. Examiner Only Marks Remark (iii) How many orders of magnitude do the intensity data in Table 6.1 span? Four orders of magnitude Five orders of magnitude Six orders of magnitude Seven orders of magnitude [1] (iv) It is required to use the data of Table 6.1 in a logarithmic plot to determine the value of the constant n in Equation 6.1. The logarithmic form of Equation 6.1 is log I = log A n log Equation 6.3 In Equation 6.3 the symbol log is used for the logarithm to the base 10. (1) The vertical (y) axis of your logarithmic plot is to be labelled log (I/arbitrary units) . Compare Equation 6.3 with the standard linear equation y = mx + c Hence state how you will label the horizontal (x) axis of the graph. _______________________________________________ [1] (2) State how the value of n can be obtained from the proposed logarithmic plot. __________________________________________________ _______________________________________________ [2] (3) Insert suitable headings in the blank columns of Table 6.1. Complete the columns, quoting the data to two decimal places. [5] (4) On Fig. 6.2, plot the linear logarithmic graph from which the value of n can be obtained. Label the axes, insert suitable scales, and plot your values from Table 6.1. Draw the best straight line through the points. [5] 4700 20 [Turn over Fig. 6.2 Examiner Only Marks Remark (5) Use your graph to find the value of n. State its unit. If n does not have units, state no units . n= ___________________ Unit of n: ___________________ 4700 21 [4] [Turn over (v) Rayleigh scattering by impurity ions in the silica-based optical fibres used in communications is an important part of the loss of signal strength. The lasers used in communications often operate at a wavelength of about 1.65 m, although laboratory demonstrations of optical fibres always use sources of visible light. Suggest why a move from the visible to a longer wavelength is sensible for the communications application. Support your answer by a relevant calculation. Take the average visible wavelength as 550 nm. Examiner Only Marks Remark _____________________________________________________ _____________________________________________________ _____________________________________________________ ____________________________________________________ [3] (b) Compton scattering (i) Equation 6.2 may be rewritten as = s = B(1 cos s) Equation 6.4 where and s are the wavelengths of the incident and scattered radiation respectively, s is the scattering angle, and B is a constant. Use the relation between photon energy and photon wavelength to show that h B= mec where h is the Planck constant. [3] 4700 22 [Turn over BLANK PAGE Questions continue overleaf 4700 23 [Turn over (ii) In an experiment, a researcher uses photons of a suitable energy and measures values of at corresponding scattering angles s. To test the Compton equation in the form of Equation 6.4, he draws a graph of against (1 cos s). This is shown in Fig. 6.3. 5.0 /10 12 m 4.0 3.0 2.0 1.0 0 0 0.5 1.0 Fig. 6.3 4700 24 1.5 (1 cos s ) 2.0 [Turn over The researcher concludes that his results support Equation 6.4, both from the shape of the graph and the numerical value of its gradient. Explain why he comes to this conclusion. Examiner Only Marks _____________________________________________________ _____________________________________________________ _____________________________________________________ __________________________________________________ [4] (iii) The relative decrease in the scattered photon energy in Compton scattering is too small to measure unless the incident photon energy is comparable with the energy equivalent to the rest mass of the electron. Use the mass energy equivalence relation to calculate the energy equivalent to the electron rest mass me (9.11 10 31 kg). Give your answer in MeV. Energy = ____________ MeV [3] THIS IS THE END OF THE QUESTION PAPER 4700 25 Remark 529-034-1 [Turn over 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 4700.02 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 4700.02 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 May 2008 Assessment Unit A2 1, Module 4: Energy, Oscillations and Fields
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