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GCE JAN 2007 : A2 1 Energy, Oscillations and Fields

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Centre Number 71 Candidate Number ADVANCED General Certificate of Education January 2007 Physics assessing Module 4: Energy, Oscillations and Fields A2Y11 Assessment Unit A2 1 [A2Y11] FRIDAY 12 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. For Examiner s use only 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA INFORMATION FOR CANDIDATES The total mark for this paper is 90. Quality of written communications will be assessed in question 2(a). Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Your attention is drawn to the Data and Formulae 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. A2Y1W7 2924 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 Some ballpoint pens have a spring in the barrel which is compressed when the user pushes the button at the end of the pen. Fig. 1.1 shows the way in which the compression force depends on compression for the spring inside such a pen. The spring has an original length of 20 mm. force/N 1.0 0.5 0.0 0 2 4 6 compression/mm 8 10 Fig. 1.1 (a) (i) Use Fig. 1.1 to determine the spring constant of the spring inside the pen. Spring constant = _____________ Nm 1 [1] (ii) The spring must be compressed to a length of 12 mm for the ballpoint tip to be extended. 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Show that the strain energy stored in the spring when it is compressed is 4.0 10 3 J. [2] A2Y1W7 2924 2 [Turn over (b) The pen is held vertically on the desk with the spring compressed to a length of 12 mm. It is then released and the pen, of mass 8.4 g, rises to a height of 40 mm above the desk. Examiner Only Marks Remark (i) Calculate the percentage efficiency of the energy conversion from strain potential energy to gravitational potential energy as the spring returns to its original length. Percentage efficiency = _____________ % [3] (ii) The time taken for the pen to rise to the height of 40 mm is 0.12 s. Calculate the power generated by the spring when it lifts the pen to this height. [1] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Power = _____________ mW A2Y1W7 2924 3 [Turn over (c) The mass of the spring is 0.24 g. The spring is made from a metal with a specific heat capacity of 450 J kg 1 K 1. Examiner Only Marks Remark (i) Define specific heat capacity. ______________________________________________________ ___________________________________________________ [1] (ii) Each time the spring is compressed and released, 10% of the strain energy stored in it is converted to heat energy in the spring. Calculate the number of times the spring must be compressed and released to cause the temperature of the spring to increase by 1K. Assume all the heat remains in the spring. [2] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Number of times = _____________ A2Y1W7 2924 4 [Turn over BLANK PAGE 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA (Questions continue overleaf) A2Y1W7 2924 5 [Turn over 2 In part (a) of this question you should answer in continuous prose, where appropriate. You will be assessed on the quality of your written communication. Examiner Only Marks Remark The apparatus shown in Fig. 2.1 can be used to investigate the relationship between temperature and volume of air. capillary tube heated water bath thermometer stirrer acid thread scale trapped air Fig. 2.1 A fixed mass of air is trapped between the lower, closed end of the capillary tube and the thread of concentrated sulphuric acid. The acid is free to move up and down the capillary tube as the volume of trapped air changes. (a) Describe how this apparatus would be used to investigate the relationship. __________________________________________________________ __________________________________________________________ 3- 26/10/06EA __________________________________________________________ __________________________________________________________ 2- 18/9/06BP __________________________________________________________ _______________________________________________________ [3] 1 - 4/9/06HF Quality of written communication A2Y1W7 2924 [1] 6 [Turn over (b) The capillary tube in Fig. 2.1 has an internal diameter of 0.60mm. During heating, the thread of concentrated sulphuric acid moves from a height of 20 mm to a height of 22 mm. The initial temperature of the air was 18 C. Calculate the new temperature of the air. Give your answer in C. Temperature = _____________ C Examiner Only Marks Remark [4] (c) The graph in Fig. 2.2, involving temperature and volume of air, was plotted from the results of a similar experiment. Label the axes and include appropriate units in each case. [2] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Fig. 2.2 A2Y1W7 2924 7 [Turn over 3 A pot on a potter s wheel completes 8.0 revolutions in 4.5 seconds. Examiner Only Marks Remark (a) (i) Calculate the angular velocity of the wheel. Angular velocity = _____________ rad s 1 [2] (ii) Calculate the difference between the linear velocity of a point on the wheel 5.0 cm from the centre and one at 15 cm from the centre. Difference in linear velocity = _____________ m s 1 [2] (b) (i) A lump of clay is placed on the potter s wheel a distance r from the centre of the wheel. On Fig. 3.1, sketch a graph showing how the centripetal acceleration of the clay changes as r increases from zero. Centripetal acceleration 0 3- 26/10/06EA 0 r [1] Fig. 3.1 1 - 4/9/06HF 2- 18/9/06BP (ii) At what value of r is the centripetal acceleration 19 m s 2? r = _____________ cm A2Y1W7 2924 [2] 8 [Turn over (c) A lump of clay of mass 0.20 kg is placed 10 cm from the centre of the wheel and the speed of the wheel is increased gradually from rest. The maximum frictional force between the clay and the wheel is 4.2 N. Calculate the angular velocity of the wheel just as the clay starts to slip. Remark [2] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Angular velocity = _____________ rad s 1 Examiner Only Marks A2Y1W7 2924 9 [Turn over 4 (a) Define simple harmonic motion. Examiner Only Marks Remark _________________________________________________________ _________________________________________________________ _______________________________________________________ [2] (b) (i) A sodium ion vibrates in a sodium chloride lattice made up of positively charged sodium and negatively charged chlorine ions. Name the force that provides the acceleration to cause the sodium ion to vibrate with simple harmonic motion. ___________________________________________________ [1] (ii) In a simplified model of the lattice vibrations, the sodium ion may be supposed to be attached to the rest of the lattice by a spring of spring constant 110 N m 1. A sodium ion has a mass of 3.82 10 26 kg. The rest of the lattice does not move during the vibrations of the sodium ion. Calculate the natural frequency of oscillation of the sodium ion in this model. Natural frequency = _____________ Hz [3] (iii) Suppose that the sodium chloride lattice absorbs microwave radiation of frequency 8.54 1012 Hz. State and explain whether or not the sodium ion will undergo resonance. 3- 26/10/06EA ______________________________________________________ ______________________________________________________ 1 - 4/9/06HF 2- 18/9/06BP ___________________________________________________ [2] A2Y1W7 2924 10 [Turn over 5 (a) Communications satellites are usually placed in geostationary orbits. The radius of such an orbit has a definite value. Examiner Only Marks Remark (i) State two other features of a geostationary orbit. 1. ____________________________________________________ 2. _________________________________________________ [2] (ii) The mass of the Earth is 6.0 1024 kg. Calculate the radius of a geostationary orbit. Radius = _____________ m [4] 2- 18/9/06BP 3- 26/10/06EA (b) A daily influx of meteorites and meteor dust is well known to scientists, but the total mass added daily to the Earth s surface is difficult to estimate. Some scientists estimate that 7.9 107 kg is added per year. Calculate how many years it would take for the gravitational field strength at the surface of the Earth to increase by 0.1%. Assume that the increase in mass continues at a steady rate and that the radius of the Earth is unaltered. [Radius of Earth = 6.38 106 m; gravitational field strength at Earth s surface = 9.81 N kg 1.] [4] 1 - 4/9/06HF Time = _____________ years A2Y1W7 2924 11 [Turn over 6 1 q1q (a) Use Coulomb s law for the force between point charges, F = 2 2 , 4 0 r to express the unit of 0 in terms of the SI base units m, kg, s and A. Examiner Only Marks Remark [2] (b) Two point charges of magnitude 3 C and 6 C are placed 30 mm apart in a vacuum. (i) Calculate the magnitude of the force between them. Force = _____________ N [2] (ii) When they are free to move the charges accelerate towards each other. State what sign each charge could have. Sign on 3 C charge = __________ [1] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Sign on 6 C charge = __________ A2Y1W7 2924 12 [Turn over (c) There are a number of differences between Examiner Only Marks Remark 1. the electric field produced between two parallel plates with a potential difference across them and 2. the field around a point charge. Describe the difference between the electric field strengths in each case. Use diagrams to help to explain your answer. _________________________________________________________ _________________________________________________________ _________________________________________________________ 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA _______________________________________________________ [3] A2Y1W7 2924 13 [Turn over 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. 7 Aerodynamic Drag The aerodynamic drag force experienced by motorcycles is an important factor when considering their design. The factors affecting the amount of drag on a motorcycle can be investigated by carrying out experiments in the controlled environment of a wind tunnel. Wind tunnel experiments have shown that the aerodynamic drag force FD on an object depends on a number of variables, according to Equation 7.1. ACD FD = v n 2 Equation 7.1 where CD is the drag coefficient, A is the frontal area of the object, is the density of the fluid in the wind tunnel, v is the speed of the fluid relative to the object, n is a constant. The frontal area of an object is the surface area that faces directly into the fluid flow. The drag coefficient is a number that describes a characteristic amount of aerodynamic drag around the object. (a) Explain why it is an advantage to design motorcycles with low drag coefficients. _________________________________________________________ _________________________________________________________ 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA _______________________________________________________ [2] A2Y1W7 2924 14 [Turn over (b) In one wind tunnel experiment, the variation in drag force with speed was investigated. A scale drawing of the motorcycle being tested is shown in Fig. 7.1. The actual frontal area of the motorcycle shown is 0.57m2. Estimate the scale of the drawing in Fig. 7.1. Examiner Only Marks Remark Fig. 7.1 1 cm on drawing = _________ cm in real space [3] (c) The results of the wind tunnel experiment are shown in Table 7.1. Table 7.1 FD/N 10 17.0 15 38.50 20 68.3 25 106 30 154 35 3- 26/10/06EA v/m s 1 209 2- 18/9/06BP (i) One of the values in the column headed FD has been quoted to an inconsistent number of significant figures. How should this value have been recorded? [1] 1 - 4/9/06HF _____________ N A2Y1W7 2924 15 [Turn over (ii) It is possible to obtain a value for n by plotting a logarithmic graph. Taking logarithms to the base 10 of each side of Equation 7.1 leads to Equation 7.2: ACD log10 FD = log10 + n log10 v 2 ( ) Examiner Only Marks Remark Equation 7.2 (1) Compare Equation 7.2 with the standard linear equation y = mx + c State what should be plotted on the y- and x-axes of the proposed logarithmic graph. y-axis: _____________ x-axis: _____________ [2] (2) State how the value of n can be obtained from the proposed logarithmic plot. ________________________________________________ [1] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA (3) Insert suitable headings in the blank columns of Table 7.1. Complete the columns, quoting the data to three significant figures. [4] A2Y1W7 2924 16 [Turn over (iii) On Fig. 7.2, plot a suitable linear graph from which the value of n can be obtained. Label the axes, insert suitable scales, and plot your values from Table 7.1. Draw the best straight line through the points. Fig. 7.2 Examiner Only Marks Remark [5] (iv) Use your graph to confirm that n is numerically equal to 2 and state its unit. If n does not have units, state no units . 3- 26/10/06EA Your value of n = _____________ [4] 1 - 4/9/06HF 2- 18/9/06BP units of n: _____________ A2Y1W7 2924 17 [Turn over (v) The density of the air in the wind tunnel is 1.225 kg m 3. Work out a value for CD, and state the units of CD. If CD does not have units, state no units . Examiner Only Marks Remark CD = _____________ units of CD: _____________ [4] (d) (i) Knowing a value for n, it is possible to plot a different, nonlogarithmic, linear graph of the results obtained in Table 7.1 to obtain a value for CD. State the axes to be used for this graph. y-axis ________________ x-axis ________________ [2] (ii) Explain how CD would be obtained from this graph. ______________________________________________________ ______________________________________________________ ___________________________________________________ [2] (e) Table 7.2 shows the variation in the density of air with temperature. Table 7.2 1.341 273 1.293 283 1.247 293 1.204 1 - 4/9/06HF 2- 18/9/06BP Density/kg m 3 263 3- 26/10/06EA Temperature/K A2Y1W7 2924 18 [Turn over (i) By calculation from values in Table 7.2, show that the density of air is inversely proportional to the absolute temperature of the air. Examiner Only Marks Remark [2] (ii) The density of air in (c)(v) was taken to be 1.225 kg m 3. At what temperature was the air? Temperature of air = _____________ K [1] (iii) The temperature of the air in the wind tunnel is reduced from 293 K to 273 K. Calculate the change in drag force that would be experienced by the motorcycle when the steady speed of the air moving past it is 28 m s 1. [2] 1 - 4/9/06HF 2- 18/9/06BP 3- 26/10/06EA Change in drag force = _____________ N A2Y1W7 2924 19 [Turn over 3- 26/10/06EA 2- 18/9/06BP 1 - 4/9/06HF S 9/06 2100 9-006-1 20 [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 A2Y1W7 2924.02 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 A2Y1W7 2924.02 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 2007 Assessment Unit A2 1, Module 4: Energy, Oscillations and Fields
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