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GCE JAN 2009 : A2 1 Energy, Oscillations and Fields

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1 2 Centre Number 3 71 4 Candidate Number 5 6 ADVANCED General Certificate of Education January 2009 7 8 9 Physics 10 assessing 12 Module 4: Energy, Oscillations and Fields 13 A2Y11 Assessment Unit A2 1 11 [A2Y11] 14 15 TUESDAY 13 JANUARY, AFTERNOON 16 17 18 TIME 19 1 hour 30 minutes. 20 21 INSTRUCTIONS TO CANDIDATES 22 Write your Centre Number and Candidate Number in the spaces provided at the top of this page. 23 Answer all six questions. 24 Write your answers in the spaces provided in this question paper. 25 26 INFORMATION FOR CANDIDATES The total mark for this paper is 90. 27 Quality of written communication will be assessed in question 1(b). 28 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question. 29 Your attention is drawn to the Data and Formula Sheet which is inside 30 this question paper. You may use an electronic calculator. 31 Question 6 contributes to the synoptic assessment requirement of the 32 Specification. You are advised to spend about 55 minutes in answering questions 1 5, 33 and about 35 minutes in answering question 6. 34 35 4707 For Examiner s use only Question Number 1 2 3 4 5 6 Total Marks Marks BLANK PAGE 4707 2 [Turn over 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 six questions 1 Your answer to part (b) of this question should be in continuous prose. You will be assessed on the quality of your written communication. Fig. 1.1 shows a cylindrical metal rod, clamped firmly at the left-hand end. F clamp area A L Fig. 1.1 The rod is of original length L and cross-sectional area A. The application of the longitudinal force F causes the rod to extend by x. The Young modulus E of the material of the rod is defined by the equation stress E = strain (a) Write down expressions for the stress and the strain in terms of the quantities defined above. stress: = ____________________ strain: = ____________________ 4707 [2] 3 [Turn over (b) Describe a school laboratory experiment to determine the Young modulus of a copper wire. Structure your answer under the following headings: labelled diagram of experimental arrangement, experimental procedure, processing of results. Examiner Only Marks Remark Diagram [2] Procedure __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ _______________________________________________________ [5] 4707 4 [Turn over Processing of results Examiner Only Marks Remark __________________________________________________________ __________________________________________________________ __________________________________________________________ __________________________________________________________ _______________________________________________________ [3] Quality of written communication 4707 [2] 5 [Turn over 2 The internal energy of a system is the sum of the random kinetic and potential energies of the constituents of the system. Examiner Only Marks Remark (a) A metal crystal has a lattice of positive ions, through which electrons can move at random. The ions in the lattice vibrate. Detail the contributions to the internal energy of the metal crystal. Kinetic: ___________________________________________________ __________________________________________________________ Potential: __________________________________________________ _______________________________________________________ [2] (b) Helium can be assumed to behave as an ideal gas. A sample of helium at 27 C contains 1.20 mol of atoms. (i) Calculate the internal energy of the helium sample. Internal energy = _____________ J 4707 6 [4] [Turn over (ii) A world-class sprinter of mass 80 kg can run 100 m in 9.8 s. Calculate the ratio: Examiner Only Marks Remark Internal energy of helium sample in (b)(i) average kinetic energy of sprinter Ratio = ______________________ 4707 [3] 7 [Turn over 3 (a) A particle rotates with uniform angular velocity in a circle of radius r. The particle has an instantaneous linear velocity v. Examiner Only Marks Remark (i) Define angular velocity. ________________________________ ___________________________________________________ [1] (ii) Write down the relation connecting v with . ___________________________________________________ [1] (b) A boy swings a ball attached to one end of a string in a horizontal circle at a constant angular velocity. The other end of the string is held in the boy s hand. (i) State the direction of the force on the ball to maintain this circular motion. ___________________________________________________ [1] (ii) How is this force on the ball provided? ___________________________________________________ [1] (iii) What is the direction of the force on the boy s hand? ___________________________________________________ [1] 4707 8 [Turn over (iv) The string attached to the ball breaks. Air resistance is negligible. Examiner Only Marks Remark 1. Describe exactly the motion of the ball at the instant the string breaks. ____________________________________________________ __________________________________________________ _______________________________________________ [1] 2. What is the only force that now acts on the ball? ____________________________________________________ Describe the effect of this force. __________________________________________________ Describe also the subsequent path taken by the ball. __________________________________________________ _______________________________________________ [3] 4707 9 [Turn over BLANK PAGE 4707 10 [Turn over 4 (a) One of the equations which describes simple harmonic motion is Examiner Only Marks Remark a = 2x State what the following symbols in the equation stand for: x: ________________________________________________________ a: ________________________________________________________ : _____________________________________________________ [3] (b) A loaded helical spring is often used as an example of a system which undergoes simple harmonic motion. The period T of this system is given by m T = 2 k where m is the suspended mass and k is the spring constant (the constant of proportionality in Hooke s law equation as applied to the spring). (i) State the SI base units of the spring constant. ____________________________________________________ [1] (ii) Hence show that the SI base unit of the left-hand side of the equation for the period is consistent with the SI base units of the right-hand side. ______________________________________________________ ______________________________________________________ ____________________________________________________ [1] 4707 11 [Turn over (c) A baby bouncer is a light harness, into which a baby can be placed, suspended by a vertical spring (Fig. 4.1). Examiner Only Marks Remark spring harness floor Fig. 4.1 The length of the vertical spring is adjusted so that, when the baby is in the harness and the spring is fully extended under his or her weight, the baby s feet are a few centimetres above the floor. An adult starts vertical oscillations by pulling the baby in the harness downwards and releasing the baby. The baby can amuse him or herself, and take exercise, by kicking the floor to continue the oscillations. The oscillations die away quickly, and to keep them going the baby has to keep kicking on the floor at just the right moment. The arrangement can be modelled using the equation for the loaded helical spring. Here m is the mass of the baby and harness and k is the spring constant of the vertical spring. (i) The spring constant is 130 SI units and the mass of the baby is 7.50 kg. Show that the period of vertical oscillations is about 1.5 s. [2] 4707 12 [Turn over (ii) State the name that is given to oscillations that die away quickly. Examiner Only Marks Remark ______________________________________________________ Describe how a loaded helical spring system in a school laboratory could be made to show oscillations that die away quickly. State how your modification achieves the effect. ______________________________________________________ ______________________________________________________ ____________________________________________________ [3] (iii) State the name that is given to oscillations such as those that are kept going by the baby kicking on the floor. ____________________________________________________ [1] (iv) The baby finds that by kicking on the floor at a certain frequency the amplitude of the bounces can be made to increase to a maximum. State the name that is given to this effect. ______________________________________________________ Using the data given in (c)(i), find the frequency that is most effective in producing it. Frequency = _________ Hz [2] (v) The baby s cousin, of mass 6.00 kg, comes on a visit, and is placed in the bouncer. Calculate the frequency at which this child must kick the floor to produce the largest amplitude of oscillation. Frequency = _________ Hz 4707 [2] 13 [Turn over 5 The planets move round the Sun in approximately circular orbits. Examiner Only Marks Remark (a) State the force that causes a planet to move in this way. _______________________________________________________ [1] (b) For a planet in a circular orbit, it can be shown that 4 2r3 T 2 = GMs Equation 5.1 where T is the period of the orbital motion and r is the radius of the orbit. The quantity G is the gravitational constant and Ms is the mass of the Sun. r3 Table 5.1 gives data for T, r and for some of the planets. T2 Table 5.1 r3 2 T Planet T/Earth years (yr) r/106 km Mercury 0.241 57.9 3.34 Venus 0.615 108.9 3.33 Earth 1.000 150.9 3.38 Mars 1.880 228.9 3.35 11.900 778.9 3.33 Jupiter 1024 km3 yr 2 (i) Find the arithmetic mean of the figures in the right-hand column of Table 5.1. Mean value = ____________________ km3 yr 2 4707 14 [1] [Turn over (ii) Calculate the conversion factor which should be used to multiply a value in km3 yr 2 to turn it into a value in m3 s 2. (1 yr = 3.16 107 s.) Multiplying factor = ____________________ Examiner Only Marks Remark [1] (iii) Use your answers to (b)(i) and (ii) to express the arithmetic mean of the figures in the right-hand column of Table 5.1 in m3 s 2. Mean value = ____________________ m3 s 2 [1] (iv) Use Equation 5.1 and your mean value from (b)(iii) to calculate a value for the mass of the Sun. Give your answer to an appropriate number of significant figures. Mass of Sun = _____________ kg 4707 [4] 15 [Turn over 6 Data analysis question Examiner Only Marks Remark 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. Black-body radiation A perfect black body is a body that absorbs all electromagnetic radiation, of any wavelength, that falls on it. Such a body is also a perfect emitter; that is, at any wavelength, it is a more efficient emitter of radiation than any other body. Radiation emitted from such a body is called black-body radiation. Theory gives the following relations for black-body radiation: For a perfect black body of surface area A at kelvin temperature T, the total power P of radiation emitted is given by the Stefan law P = AT 4 Equation 6.1 where is a constant called the Stefan Boltzmann constant, which is equal to 5.67 10 8 W m 2 K 4. The spectrum of black-body radiation is a smooth curve with a maximum at a wavelength that depends on the temperature of the emitter. Fig. 6.1 is a sketch graph of the way in which the power P of radiation at a particular wavelength depends on that wavelength, for two emitter temperatures T (1400 K and 1600 K). 4707 16 [Turn over Note that the maximum in the spectrum shifts to shorter wavelengths as the temperature of the emitter increases. Examiner Only Marks Remark P emitter temperature 1600 K 1400 K 0 0 Fig. 6.1 The relation between the wavelength m of the maximum in the spectrum and the emitter temperature T is given by the Wien law mT = B Equation 6.2 where B is a constant. 4707 17 [Turn over (a) Analysis of data on the Stefan law Examiner Only Marks Remark A practical approximation to a black body is a small, enclosed, electrically-heated furnace pierced with a small hole. The hole acts as the black body. The total power P radiated from a small hole in such a furnace is given by P = AT 4 Equation 6.3 where , T and A are defined as in Equation 6.1 and is a constant called the emissivity of the furnace. It is a measure of how efficiently the radiation from the hole in the furnace approaches that from a perfect black body. A researcher decides to use data from an experiment with such a furnace to test whether the power of 4 in Equation 6.3 is correct for his furnace and to determine the emissivity of the furnace. He first re-writes Equation 6.3 in the logarithmic form lg P = lg( A) + 4 lg T Equation 6.4 (the notation lg P means the logarithm to the base 10 of the numerical value of P ) and then compares Equation 6.4 with the standard linear equation y = mx + c, with the idea of obtaining a linear graph from which the value of m can be deduced. He plots the values of lg T from his experiment on the horizontal axis and those of lg P on the vertical axis. The plotted points are shown on Fig. 6.2. (i) The researcher writes down the temperature T corresponding to the extreme right-hand point on Fig. 6.2 as 2501 K. 1. To how many significant figures is this value recorded? 0 1 2 3 4 2. To how many decimal places is this value recorded? 0 1 2 3 4 In each case, state your answer by inserting a tick ( ) in the appropriate box. [2] 4707 18 [Turn over Examiner Only 0.6 lg(P/W) Marks Remark 0.4 0.2 0 0.2 0.4 0.6 0.8 1.0 3.0 3.1 3.2 3.3 3.4 3.5 lg(T/K) Fig. 6.2 (ii) By recording this temperature as 2501 K, the researcher is indicating that he is confident that the value of T lies between certain limits. State these limits. Lower limit = _________ K 4707 Upper limit = _________ K [2] 19 [Turn over Examiner Only (iii) The symbol T represents a quantity that has both magnitude and unit. Marks Remark The researcher has correctly labelled the horizontal axis as lg( T /K ). Explain why it would be wrong to label it as lg T. ______________________________________________________ ______________________________________________________ ____________________________________________________ [2] (iv) State how the power 4 to which T is raised in Equation 6.3 can be checked from Fig. 6.2. ______________________________________________________ ______________________________________________________ ____________________________________________________ [2] (v) On Fig. 6.2, draw the best straight line through the plotted points. [1] (vi) Use the line you have drawn in (a)(v) to carry out the procedure you have described in (a)(iv). State your value of the power to which T is raised. Power = ________________ [3] (vii)You will have found in drawing your best straight line in (a)(v) that the researcher s points do not lie on a perfect straight line. By drawing a line on Fig. 6.2 which you think represents the steepest example of a good straight line through the points, obtain an estimate of the uncertainty in the value of the power you obtained in (a)(vi). Range of values of power = value from (a)(vi) ___________ [4] 4707 20 [Turn over (viii) By reference to Equations 6.1 and 6.3, deduce the maximum possible value of the emissivity . Explain why this is the maximum possible value. Examiner Only Marks Remark Maximum value = _____________ Explanation: ______________________________________________________ ___________________________________________________ [2] (ix) Choose a value of lg T in the range of values on Fig. 6.2 and read off the corresponding value of lg P from your best straight line. Substitute these values in Equation 6.4 and obtain a value of for the researcher s oven. The area A of the hole in the furnace from which the radiation is emitted is 1.5 mm2. (Reminders: Equation 6.4 is lg P = lg( A) + 4 lg T. The value of is 5.67 10 8 W m 2 K 4.) Chosen value of lg T = ____________________ Corresponding value of lg P = ____________________ Emissivity = ____________________ 4707 21 [4] [Turn over (b) Analysis of data on the Wien law Examiner Only Marks Remark The researcher analyses the spectrum of radiation from the emitter at various temperatures to determine the constant B in the Wien law mT = B. The researcher measures the wavelength m at which the maximum in the spectrum occurs for a number of emitter temperatures T and tabulates the results in Table 6.2. Table 6.2 T/K m/ m 1200 2.42 1400 2.07 1600 1.81 2000 1.45 2300 1.24 You are to plot a straight-line graph on Fig. 6.5, using values obtained from these data, to determine the value of B. In this part of the question, do not use a logarithmic graph. (i) State the quantities you will plot on the graph. Horizontal axis: ____________________ Vertical axis: ____________________ [1] (ii) State how the constant B will be determined from your graph. ______________________________________________________ ____________________________________________________ [1] (iii) Head the blank column of Table 6.2 appropriately, calculate the values required, and enter them in the table. [2] (iv) Label the axes of the graph grid of Fig. 6.5 and choose suitable scales. Plot the points and draw the best fit straight line through them. [5] 4707 22 [Turn over Fig. 6.5 (v) Use the graph to find the value of B and enter its value below. State an appropriate unit. Examiner Only Marks Remark Numerical value of B = ____________________ Unit: ____________________ 4707 [4] 23 [Turn over 935-076-1 24 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 4707.02 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 4707.02 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 2009 Assessment Unit A2 1, Module 4: Energy, Oscillations and Fields
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