Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mass versus weight wikipedia , lookup
Nuclear physics wikipedia , lookup
Pioneer anomaly wikipedia , lookup
Gibbs free energy wikipedia , lookup
Negative mass wikipedia , lookup
Woodward effect wikipedia , lookup
Speed of gravity wikipedia , lookup
Weightlessness wikipedia , lookup
Work (physics) wikipedia , lookup
Schiehallion experiment wikipedia , lookup
1 CCC Hoh Fuk Tong College Mock Examination 2011-2012 Physics Paper I Secondary : 7 Time allowed : 3 hours Date : 7 / 2 / 2012 Marks : 108 ( 8:15 – 11:15 ) Name : ______________________________ Class : 7S Number : ______ 1. Answer ALL questions. 2. Write your answers in the spaces provided in the question paper. In calculations you should show all the main steps in your working. 3. Assume: velocity of light in air = 3 x 108 m s-1 acceleration due to gravity = 10 m s-2 electronic charge = 1.6 x 10-19 C Questions No. Marks 1 15 2 15 3 13 4 13 5 13 6 15 7 13 8 11 1. A spacecraft is launched with 31.3 MJ of kinetic energy per unit mass vertically upwards from the Earth surface. When the spacecraft is instantaneously at rest at the highest position, the rocket engine exerts an impulse of force parallel to the Earth’s surface below setting the spacecraft to move in a circular orbit round Earth. Given that: G M GM R = = = = gravitational constant mass of earth 4 x 1014 J kg-1 m-1 radius of earth = 6.4 x 106 m 2 a. What is the radius r of the circular orbit? ( 2 marks ) b. Find the gravitational force acting on an astronaut of mass 60 kg in the spacecraft. ( 2 marks ) c. The final mass m of the spacecraft ( with the astronaut ) when it is orbiting round the Earth is 5000kg. i. Find the orbiting speed v of the spacecraft ( with the astronaut ) in this circular orbit. ( 2 marks ) 3 ii. Find the sum of potential and kinetic energy (E0) of the orbiting spacecraft? ( 2 marks ) iii. The speed of the spacecraft in this orbit is increased to v’ such that it can leave the earth permanently. Find the minimum value of v’ . ( 2 marks ) iv. Owing to air resistance, the spacecraft loses mechanical energy at a rate of 1.4x106 J per complete orbital revolution. Adopt the reasonable approximation that the trajectory is a “circle of slowly diminishing radius” (1) Determine its height h above the Earth’s surface at the end of its 6000th orbital revolution. ( 2 marks ) 4 (2) What is the magnitude of the average retarding force F acting on the spacecraft? ( 3 marks ) 2. A light spring is fixed vertically to a trolley and a light platform is attached to its upper end. A small block of mass m is placed on this horizontal platform. When the system achieves static equilibrium, the spring is compressed by 0.08 m as shown in Figure 2.1 Figure 2.1 The block is released from the uncompressed position of the spring. The trolley is then given a push so that it moves together with the block at a uniform velocity on a smooth horizontal surface. Neglect air resistance and assume that there is no slipping between the block and the platform. (a) Find the period of the vertical oscillation of the block. ( 3 marks ) 5 (b) Figure 2.2 represents the stroboscopic photograph of the motion of the block. Figure 2.2 Use the result in (a) to find (i) the frequency of the stroboscope, ( 2 marks ) (ii) the speed of the trolley. ( 2 marks ) (iii) Suppose the mass of the block is halved and the force constant of the spring is doubled while its natural length remains unchanged. If the block is again released from the same position and the trolley is given the same uniform velocity as before, find the block’s period of 6 oscillation and draw the corresponding stroboscopic photograph in Figure 2.2. Use x to indicate the position of the block. ( 5 marks ) (c) The trolley is stopped suddenly when the block is just at its lowest position. The block slips on the platform and then moves off from it. Describe and explain the subsequent motion of the block as seen by a stationary observer on the ground. ( 3 marks ) 3. Longitudinal waves can be produced in a metallic slinky spring and the propagation speed of the waves is approximately given by where k = force constant of the slinky spring L = length of the slinky spring M = mass of the slinky spring Figure 3.1 7 A student conducts an experiment to verify this relationship. The spring is stretched to a length of 2.2 m as shown in Figure 3.2. A battery is connected across the spring and two search coils are placed at A and B which are at a fixed distance 1.0 m apart. The search coils are connected to the respective Y- inputs of a dual trace CRO. Figure 3.2 A sharp push is made at the left end of the slinky spring so that a compression pulse travels along the spring. When the compression pulse passes the search coil at A, the following trace is described on the screen of the CRO. (a) State the purpose of connecting the slinky spring to a battery. (b) Explain how the trace is formed. ( 1 mark ) ( 3 marks ) 8 (c) The time interval for the pulse to travel from A to B can be found from the corresponding traces registered by the search coils. The experiment is repeated with slinky spring stretched to different lengths and the corresponding time intervals found are tabulated below. (i) Complete the table by choosing a suitable physical quantity and plot a straight line graph to verify the given relationship. ( 4 marks ) Length of the slinky spring L / m 2.2 2.0 1.8 1.6 1.4 Time interval for 0.51 0.56 0.62 0.70 0.79 the pulse to travel from A to B t /s 9 (ii) Calculate the slope of the graph obtained. Hence, estimate a value for the force constant k when the mass of the spring is 0.3 kg. ( 3 marks ) (iii) Another student wants to verify whether the propagation speed of the waves is inversely proportional to the square root of the spring’s mass. He suggests using slinky springs of different masses stretched to the same length to repeat the experiment. Explain whether he can verify this relationship by plotting a suitable straight line graph. ( 2 marks ) 4. A rectangular slice, of width d = 2.0 mm and thickness t = 0.5 mm, carries a current I = 16 A in the direction as shown in Figure 4. A uniform magnetic field B = 0.1 T is applied in the direction shown. The Hall voltage is measured between X and Y. Given that there are 1.0 1029 charge carriers per cubic metre and each carries a charge of 1.6 1019 C. Figure 4 10 a. Determine the sign of the charge carriers in the slice. ( 1 mark ) b. Calculate the drift velocity of the charge carriers. ( 2 marks ) c. Calculate the electric force on each charge carrier. ( 2 marks ) d. i. Calculate the value of the electric field between X and Y. ( 2 marks ) ii. Hence, using the answer of (d)(i), determine the Hall voltage between X and Y. ( 2 marks ) 11 e. State one precaution in the process of measuring the Hall voltage. ( 1 mark ) f. Suggest any THREE modifications to the process of measurement so that the value of the Hall voltage can be increased. ( 3 marks ) 5. In Figure 5.1, a 47 µF capacitor, an inductor L and a 1 Ω resistor are connected with a cell of e.m.f. 3V and negligible internal resistance. The inductor L is of inductance 54 mH and resistance 0.5 Ω. Initially the capacitor is uncharged. Figure 5.1 (a) Find the current flowing in the 1 Ω resistor (i) when the switch S is just closed; (ii) a few minutes after the switch S is closed. Explain briefly. ( 4 marks ) 12 (b) (i) Calculate the maximum p.d. across the capacitor. (ii) Find the energy stored in the inductor at the steady state. (iii) ( 2 marks ) ( 2 marks ) If switch S is now opened, sketch the time variation of the p.d. Vc across the capacitor. ( 2 marks ) 13 (c) State how you would modify the circuit so as to demonstrate that a large induced e.m.f. is produced across the inductor when switch S is suddenly opened. Explain briefly. ( 3 marks ) 6. (a) A parallel-plate capacitor is formed by two square metal plates. The plates are kept apart by four small polythene spacers at the corners. The set-up shown in Figure 6.1 is used to investigate the relation between the capacitance C of the capacitor and the separation d of the plates when their area of overlap is kept constant. Figure 6.1 The frequency f of the reed switch is 400 Hz and the voltmeter reading V is 25 V. By varying the separation d of the plates, the corresponding 14 galvanometer readings I are obtained. A graph of I against 1/d is plotted below. (b) Write down an expression of C in terms of f, I and V. Use the graph to deduce a numerical relation between C (in F) and d (in m). ( 5 marks ) (b) A capacitor is formed by using the two square metal plate 6 mm separation. It has capacitance 92.2 x 10-12 F and is connected to a d.c. source as shown in Figure 6.3. Another 2 mm tick metal plate of the same area is inserted mid-way between the parallel plates of the capacitor as shown. The voltage of the d.c. source is maintained at 100 V. 15 Figure 6.3 (i) Calculate the increase in the following physical quantities. ( 6 marks ) (I) the capacitance of the capacitor (II) the charges on the capacitor plates connecting to the source (III) the energy stored in the capacitor 16 (ii) Calculate the work done by the d.c. source in moving the charges from the plate to another when inserting the 2 mm metal plate. Compare your result with that of (b)(i)(III) and account for the difference. ( 4 marks ) 7. A cylinder fitted with a movable piston contains 1.00 mole of a monatomic gas at a pressure of 1.00 x 105 Pa and a temperature of 200 K. The gas in first heated at constant pressure to 350 K. Take the gas constant. R = 8.31 mol-1 K-1. a. Find the volume of the gas i. before heating ii. after heating. b. Determine the change in internal energy of the gas. ( 3 marks ) ( 2 marks ) 17 c. Determine the heat input to the cylinder. ( 3 marks ) The gas is then compressed isothermally to its initial volume. Afterward, it is cooled at constant volume to its initial temperature. d. Sketch the changes happened to the gas on a p-V diagram, inserting all the initial and final pressure and volume values for all the processes described in this question. e. What does the area bounded by the curves represent? ( 3 marks ) ( 1 marks ) f. Mark on your curves in (d) the state of the gas when its density is highest. ( 1 mark ) 8. a. Xenon-139 has a half-life of 41 s and is produced at a constant rate during the fission of a particular sample of Uranium-235. No Xenon-139 escapes from the sample and it is found that eventually, the number of Xenon-139 nuclei present becomes constant. (Avogadro’s number = 6.02 1023 mol-1) 18 b. i. Define half-life. ( 1 mark ) ii. Suggest why the number of Xenon-139 nuclei in the sample becomes constant. ( 1 mark ) When the number of Xenon-139 nuclei has become constant, the activity of the Xenon-139 is 3.4 108 Bq. Calculate the mass of Xenon-139 present in the sample. ( 4 marks ) c. When Uranium-235 nuclei are fissioned by slow-moving neutrons, two possible reactions are: 235 reaction 1: +0n1 → 54Xe139 + 38Sr95 +2 0n1 + energy 92U 235 reaction 2: + 0n1 → 2 46Pd116 + n X + energy 92U 19 The binding energy per nucleon E for a number of nuclides is given in the following table. Nuclide E / MeV 95 38Sr 8.74 54 Xe139 235 92U (i) 8.39 7.60 State what is meant by the binding energy per nucleon of a nucleus. ( 1 mark ) (ii) Calculate the energy, in MeV, released in reaction 1. ( 2 marks ) (iii) The energy released in reaction 2 is 163 MeV. Suggest, with a reason, which one of the two reactions is more likely to occur. ( 2 marks ) *** END OF PAPER *** 20