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JURONG JUNIOR COLLEGE 2012 JC2 Preliminary Examination Name Class 11S PHYSICS 9646/03 Higher 2 10 Sept 2012 Longer Structured Questions 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST For Examiner’s Use Do not open this booklet until you are told to do so. 1 Write your name and class in the spaces provided at the top of this page. 2 Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use highlighters, glue or correction fluid. Section A Answer all questions. 3 4 5 6 Section B Answer any two questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. 7 8 Total (This question paper consists of 20 printed pages) JJC 2012 9646/JC2 Prelim Exam P3/2012 2 Data c = 3.00 108 m s1 o = 4 107 H m1 speed of light in free space, permeability of free space, permittivity of free space, elementary charge, the Planck constant, unified atomic mass constant, o = 8.85 1012 F m1 = (1/(36)) 109 F m1 e = 1.60 1019 C h = 6.63 1034 J s u = 1.66 1027 kg me = 9.11 1031 kg mp = 1.67 1027 kg R = 8.31 J K1 mol1 NA = 6.02 1023 mol1 k = 1.38 1023 J K1 G = 6.67 1011 N m2 kg2 g = 9.81 m s2 rest mass of electron, rest mass of proton, molar gas constant, the Avogadro constant, the Boltzmann constant, gravitational constant, acceleration of free fall, Formulae uniformly accelerated motion, s = ut + 1 2 at2 v2 = u2 + 2as W = p V p = gh work done on/by a gas, hydrostatic pressure, gravitational potential, = Gm r x = xo sin t v = vo cos t displacement of particle in s.h.m., velocity of particle in s.h.m., v = ( xo2 x 2 ) mean kinetic energy of a molecule of an ideal gas resistors in series, resistors in parallel, E = 3 2 kT R = R1 + R2 + . . . 1/R = 1/R1 + 1/R2 + . . . Q electric potential, V = alternating current / voltage, transmission coefficient, x = xo sin t T exp(2kd) 4 εo r where k = radioactive decay decay constant JJC 2012 82 m(U E ) h2 x = xo exp(-λt) 0.693 λ = t1/2 9646/JC2 Prelim Exam P3/2012 [Turn Over 3 Section A Answer all the questions in this Section. 1. Baldwin Street, in Dunedin, New Zealand, is considered the world's steepest residential street. Its distance is 350 m long and is inclined at 19.0o to the horizontal. The highest point of the street is 114 m higher than its lowest point, as shown in Fig. 1 below. The speed limit of a car travelling down the street is 50.0 km h-1. 350 m 114 m 19.0o Fig. 1 (a) A car of 1500 kg at the highest point of the street slides down from rest. Assume that the resistive forces are negligible, (i) Calculate the time taken for the car to reach the lowest point of the street. time = (ii) s [3] Determine whether the car will exceed its speed limit as it reaches the lowest point of the street. [2] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 4 (b) A boy standing at the highest point of the street throws a stone horizontally at a speed of 40 m s-1. It takes 2.81 s for the stone to hit the surface of the street. Assume negligible air resistance, (i) Calculate the vertical height of the stone above the lowest point of the street when it hits its surface. height = (ii) (a) [2] Determine the horizontal distance travelled by the stone as it hits the surface. distance = 2. m m [1] State the first law of thermodynamics, indicating the directions of all energy changes. [1] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 5 (b) Some gas, assumed to behave ideally, is contained within a cylinder which is surrounded by insulation to prevent loss of heat as shown in Fig. 2. piston gas Fig. 2 Initially the volume of gas is 2.9 x 10-4 m3, its pressure is 1.04 x 105 Pa and its temperature is 314 K. (i) The gas is then compressed to a volume of 2.9 x 10-5 m3 and its temperature rises to 790 K. Calculate the pressure of the gas after this compression. pressure = (ii) [2] The work done on the gas during the compression is 91 J. Determine the change in the internal energy of the gas during the compression. change in internal energy = (iii) Pa J [1] Explain why the temperature of the gas rises during the compression. [2] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 6 (c) An electric kettle, rated 240 V 6.0 A, contains some water. The kettle is switched on and the temperature of water is found to rise at the rate of 10.0 C per minute. The specific heat capacity of water is 4.2 103 J kg-1 K-1. (i) Calculate the mass of water in the kettle, assuming no heat loss to the surroundings. State another assumption made in your calculation. mass of water = kg [2] Assumption: [1] (ii) State and explain whether your answer to (c)(i) is greater or smaller than the actual mass of the water contained in the kettle. [1] 3. (a) A wooden cube of length L floats on water such that 30 % of its volume is below the surface of the water. If the density of water is 1000 kg m-3, what is the density of the wooden cube? density = JJC 2012 9646/JC2 Prelim Exam P3/2012 kg m-3 [2] [Turn Over 7 (b) The wooden cube is displaced vertically downwards by a small displacement A, such that 5% of its volume is further submerged in water before it is released from rest. (i) Calculate the magnitude of the initial acceleration of the wooden cube. acceleration = (ii) m s-2 [2] If there are no dissipative forces acting on the wooden cube, the subsequent motion of the wooden cube is simple harmonic. State the defining equation for simple harmonic motion. [1] (iii) The wooden cube takes 0.15 s to return to its equilibrium position the first time. Calculate the length L of the cube. length = JJC 2012 9646/JC2 Prelim Exam P3/2012 m [3] [Turn Over 8 4. (a) An evacuated tube contains two plane, parallel, metal electrodes, one of which is an emitter of electrons and the other a collector. When the emitter is illuminated with electromagnetic radiation of photon energy 2.0 eV of constant intensity, photoelectrons are emitted. The potential difference V between the collector and the emitter is adjusted, and the photocurrent I is measured. Fig. 4 shows the variation of I with V. I /10-8 A 1.0 - 0.5 - -1 0 1 2 V/V Fig. 4 (i) Suggest why the current is not at its maximum when V is equal to zero. [1] (ii) Calculate the maximum kinetic energy at which the electrons leave the emitter. kinetic energy = JJC 2012 9646/JC2 Prelim Exam P3/2012 J [2] [Turn Over 9 (iii) Deduce the work function of the material of the emitter. work function = (iv) eV [1] Explain why the current stays constant as V increases. [2] (b) JJC 2012 In Fig. 4, sketch the graph when the intensity is doubled using the same electromagnetic radiation photon energy. [2] 9646/JC2 Prelim Exam P3/2012 [Turn Over 10 5 (a) Use the band theory to account for the electrical properties of intrinsic semiconductors at room temperature. [3] (b) Fig. 5 shows a p-type semiconductor placed in contact with an n-type semiconductor. depletion region p n Fig. 5 Discuss how the p-n junction acts as a rectifier. [3] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 11 Section B Answer two questions from this Section. 6 (a) Explain what are meant by the moment of a force and the torque of a couple. Distinguish between the two terms. [3] (b) One type of weighing machine, known as a steelyard, is illustrated in Fig. 6. light rigid rod zero mark Fig. 6 The 12 N and 2.5 N sliding weights can be moved independently along the light rigid rod. With no load on the hook and the sliding weights at the zero mark on the rigid rod, the rod is horizontal. The hook is 4.8 cm from the pivot. (i) Explain why the light rigid rod can remain horizontal with no load on the hook. [1] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 12 (ii) Explain why the perpendicular distance from the hook to the pivot is deliberately kept shorter compared to the length of the rigid rod. [2] (iii) A sack of flour is suspended from the hook. In order to return the light rigid rod to the horizontal position, the 12 N sliding weight is moved 84 cm along the rod and the 2.5 N sliding weight is moved 72 cm. Calculate the mass of the sack of flour. mass = (iv) kg [3] Suggest why this steelyard would be less accurate when weighing objects with a weight of about 25 N. [1] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 13 (c) (i) By referring to work done being the product of force and the displacement in the direction of the force, derive the formula Ep = mgh for potential energy changes near the Earth’s surface. [3] (ii) A typical escalator at Jurong Point Shopping Mall rises at an angle of 30º to the horizontal. It lifts people through a vertical height of 15 m in 0.50 minute. Assuming all the users stand still while on the escalator, 60 users can get on at the bottom and get off at the top in 0.50 minute. The average mass of a user is 55 kg. 1. Determine the average power needed to lift the users when the escalator is fully laden. Assume that any kinetic energy transferred to the users by the escalator is negligible. average power = 2. W [2] The frictional force in the escalator system is 1.0 x 104 N when the escalator is fully laden. Calculate the power to overcome friction. power = JJC 2012 9646/JC2 Prelim Exam P3/2012 W [3] [Turn Over 14 3. When there are 60 users walking up the moving escalator, instead of standing still, at any point in time, explain whether more or less power is required by the motor to maintain the escalator at the same speed. [2] 7. (a) Define electric potential. [1] (b) Fig. 7.1 shows a square ABCD of length 2.0 cm. Three negative point charges of 1.2 C are fixed at B, C and D. A B D C Fig. 7.1 (i) JJC 2012 On Fig. 7.1, draw and label each of the forces acting on the charge at C due to the charges at B and D. [1] 9646/JC2 Prelim Exam P3/2012 [Turn Over 15 (ii) Determine the magnitude and direction of the resultant force acting on the charge at C due to the charges at B and D. magnitude = N direction = (iii) Determine the electric potential at the centre of the square due to the three charges at B, C and D. electric potential = (iv) V [3] Determine the work done in bringing a positive charge of 1.2 C from 100 m away to the centre of the square. work done = JJC 2012 [3] 9646/JC2 Prelim Exam P3/2012 J [2] [Turn Over 16 (c) Define magnetic flux density. [1] (d) Fig. 7.2 shows the position of a wire in a magnetic field where the magnetic flux density B is 0.40 T, directed to the right. B wire with current out of plane of paper Fig. 7.2 The wire, which is of length 0.12 m, carries a current of 3.0 A out of the plane of the paper. (i) Draw a diagram to show the shape and direction of the magnetic field due to the current in the wire. [2] (ii) Calculate the force acting on the wire due to the magnetic field B. force = (iii) JJC 2012 N On Fig. 7.2, indicate the direction of the force acting on the wire. 9646/JC2 Prelim Exam P3/2012 [2] [1] [Turn Over 17 (e) Fig. 7.3 shows the arrangement of a mass spectrometer. An ion of mass m and charge +q is emitted with negligible speed from an ion source S. The ion is accelerated through a pair of parallel plates P1 and P2 of potential difference V. The ion then enters a region of uniform magnetic field of flux density B directed perpendicularly to the plane of the paper. In the field it moves in a semicircle, striking a photographic plate at a distance x from the entry slit. Region of magnetic field directed vertically to plane of paper r v q+ x P2 0V P1 +V photographic plate S Fig. 7.3 (i) Show that the ion enters the magnetic field with a velocity, v = 2qV m [1] (ii) The ion has a mass m = 9.3 × 1026 kg and a charge q = 3.2 × 1019 C. The magnetic flux density of the field B = 0.24 T. Determine the time taken for the ion to hit the photographic plate upon entry into the magnetic field. time taken = JJC 2012 9646/JC2 Prelim Exam P3/2012 s [3] [Turn Over 18 8 (a) In Fig. 8.1 (a), the nine dots show the equilibrium position of the particles when they are at rest in a medium. In Fig. 8.1 (b), the nine dots show the displacements of the particles from their equilibrium positions at an instant when a longitudinal wave passes through the medium. Taking displacement to the right as positive, using the scale shown, (i) deduce the displacement of particle 6 at the instant shown. displacement = (ii) cm [1] sketch the displacement-position graph of the particles in the wave at the instant shown. Fig 8.1 (a) 1 1 2 2 3 3 4 5 4 5 6 6 7 7 8 9 8 9 Fig 8.1 (b) displacement / cm position / cm [2] (b) A satellite passing the planet Saturn communicates with its controller on the Earth using a microwave transmitter with output power 23.0 W and wavelength 79700 µm. Saturn is 1.20 x 1012 m from Earth at the time when the communication takes place. Assume that the power transmitted by the satellite is radiated uniformly in all directions. (i) State whether the microwaves are longitudinal or transverse. [1] (ii) Calculate the time taken for the signal to travel from the satellite to the Earth. time = JJC 2012 9646/JC2 Prelim Exam P3/2012 s [2] [Turn Over 19 (iii) calculate the intensity of the microwave received on Earth. intensity = (iv) [2] calculate the power received on the Earth by an aerial dish of effective area 260 m2. power = (v) W m-2 W [2] The actual power received at the aerial dish is 1.3 x 10-15 W. Suggest why the actual power received is greater than that calculated in (b)(iv). [1] (c) The speed v of a progressive wave is given by the expression v f A stationary wave does not have a speed. With reference to the formation of a stationary wave, explain the significance of the product f for a stationary wave. [3] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over 20 (d) When a player blows into the piccolo as shown in Fig. 8.2 (a), the air within the piccolo vibrates. The piccolo produces sound in a column of air like a tube with both ends open. Fig 8.2 (a) Piccolo Fig 8.2 (b) shows the fundamental frequency of the stationary wave formed in the tube of a given length. The five black dots below the tube in Fig 8.2 (b) correspond to equilibrium positions of five air molecules. Fig 8.2 (b) (i) The displacement vector of the first air molecule is shown. Sketch on Fig 8.2 (b) the displacement vectors of the remaining air molecules. [2] (ii) Mark P on Fig 8.2 (b), the region(s) of maximum change in pressure. (iii) A stationary wave corresponding to the fundamental frequency of 262 Hz is obtained when the length of the tube is 0.655 m. For the same length of air column, determine the frequencies of the next two modes of vibration. (iv) 2nd mode frequency = Hz 3rd mode frequency = Hz [1] [2] The piccolo player can change the musical note by covering or uncovering the holes of the piccolo to change the length of the air column. Suggest another way in which the piccolo player can vary the pitch (frequency). [1] JJC 2012 9646/JC2 Prelim Exam P3/2012 [Turn Over