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GCE MAY 2007 : A2 1 Energy, Oscillations and Fields

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Centre Number 71 Candidate Number ADVANCED General Certificate of Education 2007 Physics assessing Module 4: Energy, Oscillations and Fields A2Y11 Assessment Unit A2 1 [A2Y11] THURSDAY 31 MAY, MORNING 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 2(a). 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. A2Y1S7 3194 For Examiner s use only Question Number 1 2 3 4 5 6 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 six questions 1 (a) (i) State the principle of conservation of linear momentum. ______________________________________________________ ___________________________________________________ [1] (ii) State whether or not this principle always applies to interacting bodies. If your answer is no, give one example when it does not apply. ______________________________________________________ ___________________________________________________ [1] (b) An astronaut of mass 95.0 kg is on a space walk mission. Unfortunately his safety and supply lines become disconnected from the space vehicle. At this time he is stationary and 15.0 m away from the space vehicle. Immediately he throws the object he is holding in a direction directly away from the space vehicle. The object has a mass of 7.50 kg and he throws it with a velocity of 2.85 m s 1. (i) Explain in physical terms why the action taken by the astronaut was a sensible one. ______________________________________________________ ___________________________________________________ [1] (ii) Assume there are no further mishaps. Calculate the time taken by the astronaut to reach the space vehicle. Time = ___________ s A2Y1S7 3194 [3] 2 [Turn over (c) Later in the space flight a lunar landing craft of mass 17 500 kg moves in a circular orbit of radius 2.00 106 m around the moon. The gravitational field strength due the moon at this location is 1.23 N kg 1. Calculate the momentum of the lunar landing craft at this location and state its direction. Momentum = ___________ N s Remark [3] Direction _________________ Examiner Only Marks [1] (d) In 1680 Isaac Newton suggested that a carriage could be propelled forward at a constant speed by a jet of steam directed backwards. By considering the conservation of momentum discuss briefly the scientific validity of this suggestion. _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [3] A2Y1S7 3194 3 [Turn over 2 In part (a) you should answer in continuous prose, where appropriate. You will be assessed on the quality of your written communication. Examiner Only Marks Remark (a) (i) Describe an experiment to investigate how the volume of a gas varies with its temperature in degrees Celsius while its pressure remains constant. The experiment should commence about room temperature (20 C). Structure your answer using the headings provided. (1) Labelled sketch of the apparatus. [2] (2) Experimental procedure. __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ __________________________________________________ _______________________________________________ [3] (3) Suitable graph to display the readings. [1] A2Y1S7 3194 4 [Turn over (ii) Explain how the result obtained leads to the concept of the absolute zero of temperature. Examiner Only Marks Remark ______________________________________________________ ______________________________________________________ ______________________________________________________ ___________________________________________________ [2] Quality of written communication [2] (b) A molecule of nitrogen uses all its kinetic energy to reach a maximum height of 13.4 km in the earth s atmosphere. At ground level the gravitational potential energy of the nitrogen molecule is to be taken as zero. By considering the conservation of energy, calculate the temperature of the gas molecule at ground level to enable it to do this. The mass of a nitrogen molecule is 4.65 10 26 kg. Assume that the acceleration of free fall is constant over the height involved. Temperature = ___________ K A2Y1S7 3194 [3] 5 [Turn over 3 (a) A small spherical mass attached to one end of a light string is rotated with constant angular velocity in a horizontal plane as shown in Fig. 3.1. Explain briefly why it is impossible for the string to be horizontal as the mass rotates in a horizontal plane. Examiner Only Marks Remark horizontal string horizontal plane of rotation mass vertical axis of rotation Fig. 3.1 _________________________________________________________ _________________________________________________________ _________________________________________________________ ______________________________________________________ [2] (b) The plane of rotation of the mass is now changed from a horizontal plane to a vertical plane as shown in Fig. 3.2. The mass is again rotated at a constant angular velocity. The string is always taut. P vertical plane of rotation mass string S Q R Fig. 3.2 A2Y1S7 3194 6 [Turn over Point P is the highest point in the vertical plane of revolution and Q, R and S are points at 90 degree intervals around one revolution. On Fig. 3.3 sketch a graph to show how the tension in the string varies as the spherical mass makes one revolution from P past the points Q, R and S. P Q R S 180 270 360 Remark P 90 Tension Examiner Only Marks 0 Angular position/ Fig. 3.3 [3] (c) A mass of 135 g, attached to one end of a light string, is rotated in a vertical circular orbit of radius 320 mm at a constant angular velocity of 8.50 rad s 1. Calculate the minimum tension in the string. Minimum tension = ___________ N A2Y1S7 3194 7 [3] [Turn over 4 (a) A mass executes simple harmonic motion along the horizontal direction. Displacement x of the mass is measured from the central position O, where displacement to the right of O is positive and displacement to the left of O is negative. The amplitude of the motion is x0. Fig. 4.1 shows the situation. O x0 Examiner Only Marks Remark +x0 x Left +x Right Fig. 4.1 (i) At particular points in the motion of the mass, Table 4.1 indicates the force with its direction, the displacement x, and the velocity as the mass executes simple harmonic motion. Complete the blank cells in Table 4.1. Table 4.1 Displacement x Velocity Force (if any) and its direction Maximum Maximum to the right [2] (ii) Fig. 4.2 shows how the velocity of the mass varies with time t. On the axes provided in Fig. 4.2 draw a graph to show how the displacement x of the mass varies with t. Velocity + t 0 Displacement + t 0 Fig. 4.2 [2] A2Y1S7 3194 8 [Turn over (iii) The amplitude of the motion is 50.0 mm and the maximum velocity is 0.35 m s 1. Calculate the frequency of the motion. Frequency = ___________ Hz Examiner Only Marks Remark [3] (b) (i) Damping often occurs in oscillating systems. Explain the meaning of the term damping. ______________________________________________________ ___________________________________________________ [1] (ii) A system consists of a mass suspended from one end of a vertical helical spring. The system has light damping. The mass is displaced to a point P and released. Commencing at P on Fig. 4.3 draw a graph to show how the displacement of the mass varies with time t. [1] Displacement P t 0 Displacement Q t 0 Fig. 4.3 (iii) The system is now subjected to heavy damping. The mass is displaced to a point Q and released. Commencing at Q on Fig. 4.3 draw a graph to show how the displacement varies with time t. [1] (iv) Suggest how the heavy damping in (b)(iii) may be achieved. ______________________________________________________ ___________________________________________________ [1] A2Y1S7 3194 9 [Turn over 5 (a) State the purpose of the constant 0 (the permittivity of a vacuum) in the law for the force between two point charges. Examiner Only Marks Remark _________________________________________________________ _________________________________________________________ ______________________________________________________ [1] (b) A point charge of +2.0 C is subjected simultaneously to two electric fields E1 and E2 as indicated in Fig. 5.1. E1 is a vertical field of magnitude of 6.0 V m 1 and E2 is a horizontal field of magnitude 4.5 V m 1. E1 Horizontal 2.0 C E2 Fig. 5.1 Calculate the resultant force on the point charge and find its direction relative to the horizontal. Resultant force = ___________N Direction of the force ______________________ A2Y1S7 [4] [1] 3194 10 [Turn over (c) Three point charges are on a straight line. The magnitude of the charges and their separations are shown on Fig. 5.2. Examiner Only Marks Remark The two outer charges are both positive but the sign and the magnitude of the charge X are unknown. 4.0 m 6.0 m X +25.0 C +2.0 C Fig. 5.2 The resultant force on the +2.0 C charge is 3.0 10 3 N to the right. Find the sign and the magnitude of the charge X. For simplification of calculations you may assume 1 = 9.0 109 F m 1. 4 0 Sign of X = ___________ Magnitude of charge X = ___________ C A2Y1S7 [1] [3] 3194 11 [Turn over 6 Data analysis question Examiner Only Marks Remark This question contributes to the synoptic assessment requirement of the specification. 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. Charging a capacitor Introduction Fig. 6.1 shows a capacitor of capacitance C in series with a resistor of resistance R and a switch S connected to a battery of e.m.f. V0 (10.0 V). V C R S V0 Fig. 6.1 Inititally the capacitor is uncharged. Switch S is now closed. Table 6.1 indicates the voltage V across the capacitor C at the time t after switch closure. Table 6.1 V/V 0.00 1.66 3.65 5.97 7.44 8.97 9.74 t/s 0.00 2.00 5.00 10.00 15.00 25.00 40.00 (a) State the number of significant figures to which the voltage readings are stated. Voltage readings to _______________ significant figures A2Y1S7 3194 12 [1] [Turn over (b) (i) On Fig. 6.2 you are to draw a graph to show how the voltage V across C varies with time t. Label the axes with suitable scales, plot the points and draw an appropriate smooth curve through the points. [4] Examiner Only Marks Remark Fig. 6.2 A2Y1S7 3194 13 [Turn over (ii) Describe in detail the shape of graph you have drawn in Fig. 6.2. Examiner Only Marks Remark ______________________________________________________ ______________________________________________________ ______________________________________________________ ___________________________________________________ [2] (iii) The time constant for the charging of the capacitor, which is the same as for discharge, may be estimated from your graph on Fig. 6.2 by following the procedure described in steps 1, 2 and 3 below. 1. From the 10.0 V point on the voltage axis draw a horizontal line parallel to the time axis. 2. At the point on your graph where the gradient is maximum draw a tangent to the curve which extends to intersect the horizontal line drawn in 1. 3. At the intersection point of these two lines read the corresponding value on the time axis. This is an estimate of the time constant. Execute this procedure and state the result you obtain for the time constant. Time constant = ___________ s A2Y1S7 3194 [4] 14 [Turn over (c) The equation which defines the variation of V with time t as the capacitor is charged is given by Equation 6.1. V = V0(1 e t/CR) Examiner Only Marks Remark Equation 6.1 where V0, the battery e.m.f., is 10.0 V. By rearranging Equation 6.1 and taking natural logarithms of both sides, this equation may be rewritten as Equation 6.2. V t ln 1 = 10 CR ( ) Equation 6.2 This equation corresponds to the standard form of the equation of a straight line through the origin (y = mx). (i) Using Equation 6.2, you are to plot a linear graph to determine the time constant of the charging circuit in Fig. 6.1. State the quantities you intend to plot on your graph. Vertical axis ___________ Horizontal axis ___________ A2Y1S7 3194 [1] 15 [Turn over (ii) To plot this graph you will need to calculate values of a quantity (or quantities) using data previously given but repeated in Table 6.2. Blank columns are provided in Table 6.2 to aid you to do this. Insert suitable headings with units if necessary to enable any quantities required for the vertical or horizontal axis to be obtained. (You do not necessarily have to use all the columns in the table.) [5] Examiner Only Marks Remark Table 6.2 t/s V/V 0.00 0.00 2.00 1.66 5.00 3.65 10.00 5.97 15.00 7.44 25.00 8.97 40.00 9.74 (iii) Label the axes of the graph on Fig. 6.3 and choose suitable scales. Plot the points and draw the best straight line through them. [5] (iv) Use your graph to find the value of the time constant. Show and explain your work clearly. Time constant = ___________ s A2Y1S7 3194 [4] 16 [Turn over Fig. 6.3 A2Y1S7 3194 17 [Turn over (d) Two methods have been used to determine the time constant, one in part (b) and the other in part (c). Examiner Only Marks Remark For each of these methods state and explain clearly one advantage and one disadvantage of each method. Method (b) Advantage ________________________________________________ _________________________________________________________ Disadvantage ______________________________________________ _________________________________________________________ Method (c) Advantage ________________________________________________ _________________________________________________________ Disadvantage ______________________________________________ ______________________________________________________ [3] (e) (i) Using information from the work of previous sections, answer the following. Determine the time taken after closure of the switch for the capacitor to be charged to 50% of the maximum charge. Explain clearly how you obtain your result. Time for 50% charge = ___________ s A2Y1S7 3194 18 [3] [Turn over (ii) The resistor in Fig. 6.1 has a resistance of 220 k . Making use of the voltage across the capacitor 13.0 s after closure of the switch, determine the charging current in the circuit at 13.0 s. Current = ___________ mA Examiner Only Marks Remark [3] THIS IS THE END OF THE QUESTION PAPER A2Y1S7 3194 19 [Turn over S 1/07 7-165-1 [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 A2Y1S7 3914.02 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= 0NI l 0I 2 a Alternating currents A.c. generator E = E0 sin t = BAN sin t Particles and photons Two-slit interference = ay/d Diffraction grating d sin = n Lens formula 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 Potential divider 3194.02 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 A2Y1S7 = 3 kT 2 = h /p Particle Physics Nuclear radius 1 r = r0 A3 hf hf0

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Additional Info : Gce Physics May 2007 Assessment Unit A2 1, Module 4: Energy, Oscillations and Fields
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