00 AL/Structural Question/P.1 HONG KONG ADVANCED LEVEL EXAMINATION AL PHYSICS 2002 Structural Question 1. In December 1998, a serious car accident happened on the Lantau Link. The car sped up the concrete ramp and took off from the ramp. It then hit the top of a road sign of height 5 m above the road and 30 m away from the ramp as shown in Figure 1.1. Figure 1.1 (a) Sketch in Figure 1.1 the possible trajectories of the car in the air for a certain take-off speed. (b) Assume that the car hit the road sign at the highest point in its trajectory. Estimate (1) the take-off speed of the car; (2) the projection angle of the car; and (3) the time of flight before the car hit the road sign. (You might neglect the air resistance and the size of the car.) (c) Braking marks of 39 m long was found on the road in front of the ramp. Forensic measurements on the marks by the police indicated that the braking force was about 8000 N on the car of mass 1000 kg. Estimate the speed of the car just before applying the brakes. (d) A report on this accident appeared in a local newspaper in which the take-off speed of the car, u, is stated as Referring to the relation, the angle of elevation of the road sign from the ramp is taken as the angle of projection. Comment on the appropriateness of such an assumption. 2. Two identical pans, each of mass 150g, are connected by a light string which passes over a light pulley suspended from the ceiling. The pulley can rotate smoothly about a horizontal axis through its center. Two identical weights m1, and m2, each of mass 10 g, are placed on the pans as shown in Figure 2.1. (Neglect air resistance.) 00 AL/Structural Question/P.2 Figure 2.1 (a) In the space provided below, sketch and label all the forces acting on both m1 and the pan supporting it. Identify an action and reaction pair. (b) Write down all the possible state(s) of motion that the system can take. Initially the separation between the pans is 0.72 m. Now m2 is removed from the lower pan and the system accelerates from rest. (c) Show that the acceleration of m1 is given by a mg where m and M are m 2M the masses of the weight and the pan respectively. Calculate the tension in the string. (d) Find the speed of the pans when they are at the same level. (e) A light spring of force constant 4 Nm-1 is fixed vertically below the descending pan comes into contact with the plate when two pans are at the same level. The motion of the system becomes simple harmonic until it comes to rest momentarily. With the contact point taken as the origin, find the equilibrium position and the angular frequency of the motion. (Assume that the pan moves together with the plate once they are in contact and the string does not slack throughout.) 3. Figure 3.1 shows a circuit used for measuring the capacitance of a capacitor C. 00 AL/Structural Question/P.3 Figure 3.1 Lead Z is first connected to X, which is the positive terminal of the battery. After about one minute, lead Z is disconnected from the battery and is then connected to Y. The stop watch is stared when the current through the microammeter drops to 50μA. The variation of the current I with time t is recorded. t/s 0 2 5 9 17 22 26 34 I/ 10 6 A 50 40 30 20 10 6 4 2 (a) Explain why it is better to take readings of time for pre-selected current values (e.g. 50, 40, 30…) rather than trying to read current values at pre-selected times (e.g.0, 5, 10…)? (b) State two uncertainties associated with the experiment. (c) The experiment s repeated to measure the variation of current with time. Explain the advantage of doing so. (d) Deduce whether the e.m.f. of the battery used is 3 V, 4 V, 5 V or 6 V. (e) A graph of ln I against t is plotted. The slope of the graph is 9.4 10 2 s-1. 00 AL/Structural Question/P.4 (1) Write down the relation between I and t. Hence find the capacitance of C. (2) Explain why the capacitor is practically fully charged when lead Z has been connected to the positive terminal of the battery for one minute. (3) If another 100 kΩ resistor is connected in parallel with one in the circuit, state one possible change on the graph. ( No mathematical derivation is required.) 4. A metal cylinder of volume 0.5m3 contains some compressed gas at an initial pressure of 16 105 Pa . The gas is used to inflate identical non-elastic balloons, each to a volume of 1.2m3 at atmospheric pressure of 105 Pa. Assume that the balloons are inflated slowly so that the temperature of the gas does not change and the pressure in the balloons is always equal to the atmospheric pressure. (You may assume the equation of state for an ideal gas in the calculation.) (a) The density of the gas in the cylinder is 1.57kgm-3 at room temperature. Estimate the r.m.s. speed of the gas molecules. (b) Find the work done against atmospheric pressure in inflating one balloon. (c) (1) Calculate the decrease in gas pressure in the cylinder after inflating one balloon. 00 AL/Structural Question/P.5 (2) Find the number of balloons that can be inflated before the gas pressure in the cylinder drops below 10 105 Pa . (d) Briefly explain whether there is heat transfer between the cylinder and the surroundings when the balloons are inflated in the way described in this question. 5. Figure 5.1 shows an ionization chamber that can be used to estimate the activity of a sample of uranium-238. The sample is placed inside a metal can held at a negative potential. Electrons produced inside the metal can migrate to the sample while positive ions migrate to the wall of the can. The sample is connected to the ground via a 109Ω resistor. The potential difference across the 109Ω resistor is measured by an op-amp circuit. Figure 5.1 (a) Name the op-amp circuit used in Figure 5.1. (b) Figure 5.2 shows the variation of the voltmeter reading with potential difference across the metal can and the sample. Figure 5.2 Explain the variation of the voltmeter reading. (c) In the sample, uranium-238 decays into thorium-234 by emitting an α-particle. This nuclear reaction can be represented as: 00 AL/Structural Question/P.6 238 92 4 U234 90Th 2 He Given: Mass of one nuclide of U-238 = 238.0508 u Mass of one nuclide of Th-234 = 234.0436 u Mass of one nuclide of He-4 = 4.0026 u 1 u (atomic mass unit)= 1.660 1027 kg which corresponds to 934 MeV (1) Calculate the energy, in MeV, released in this nuclear reaction. (2) From the information provided in Figure 5.2, calculate the number of air particles being ionized per second inside the metal can. Assume that each ionized air particle carries one electronic charge. (electronic charge = 1.6 10 19 C ) (3) If the energy required to produce an ion-electron pair is 30eV, estimate the activity, in disintegrations per second, of the U-238 sample. State the assumption(s) in your calculation. (4) Is this experiment method suitable for estimating the activity of a sample emitting β-particle? Give TWO reasons to support your answer. 00- IB 6. (a) Two conductors, a metal rod and a hollow cylindrical conductor, are arranged coaxially. Figure 6.1 shows their cross-section. The inner and outer conductors are charged with +Q and –Q respectively, which is distributed uniformly on their surfaces. Draw the resulting electric field lines. Figure 6.1 (b) Figure 6.2 shows a coaxial cable. The cable consists of an inner conductor, an insulating layer, an outer conductor and a protective layer. 00 AL/Structural Question/P.7 Figure 6.2 (1) The cable can be represented as conductors AB and A’B’ in a circuit diagram. The cable can be treated as a capacitor when the inner and outer conductors are taken as the positive and negative plates. To measure its capacitance per unit length C0, the cable is connected in series with an a.c. source and a 10 k Ω resistor as shown in Figure 6.3. The frequency of the source is 100kHz. The r.m.s. voltage across the resistor is found to be 1.80 V when that of the source is 2.00 V. Figure 6.3 (I) Find the r.m.s. voltage across the inner and outer conductors of the cable, that is the voltage across AA’. (II) If the cable is 3.0 m long, find its capacitance per unit length, C0. (2) The cable can also be treated as an inductor (single loop) when the inner and outer conductors are connected (i.e. B is connected to B’). (I) The separation between the inner and outer conductors is so small that it is negligible when compared with the distance from the cable when it is treated as an inductor carrying a current? (II) It is known that the inductance per unit length of the cable, L0, is of the order 10-7 H m-1. With the 10kΩ resistor replaced by a 2 Ω one, the circuit in Figure 6.3 can now be used to measure L0. There are two frequencies, 100kHz and 1 MHz, that can be chosen for the measurement. Which one is a better choice? Explain briefly. 7. (a) You are a member of a project group. Your group has planned a project to investigate the magnetic field pattern around two parallel wires carrying currents in opposite directions. The project would include measuring and comparing the field strength at different points around the two wires. 00 AL/Structural Question/P.8 (1) A steady d.c. current is passed through the wires. Sketch in the space below the magnetic field pattern around the two wires. (2) With reference to Figure 7.2, if the current flowing through both wires is 5 A and the separation between them is 0.05m, predict the magnitude of the magnetic field strength due to these two wires at point X, which is 0.02 m from wire Q. (The diameters of the wire are negligible.) Given: permeability of free space = 4 107 Hm 1 Figure 7.2 (3) Name the apparatus that you would use to measure the magnetic field in this experiment. (b) Your group then submits the plan to the teacher. However, the teacher disagrees with the use of d.c. in this experiment and he points out that the measuring apparatus available in the school laboratory is not sensitive enough to measure 00 AL/Structural Question/P.9 even the earth’s magnetic field, which is about 50μT. He further suggests that since the plan is to compare the magnetic field strength at different positions, absolute measurement of field strength is not necessary. (1) Suggest TWO reasons why the teacher disagrees with the use of d.c. in this experiment. (2) Your group then decides to investigate the magnetic field pattern around two parallel current-carrying wires by using a modified experiment. The set-up is shown in Figure 7.3. With the time base of the CRO switched off, a vertical trace is observed no the screen of the CRO. Figure 7.3 (I) Explain what is represented by the length of the trace observed on the CRO and state TWO advantages of this modified experiment. (II) State TWO necessary precautions carrying out the experiment. 8. (a) Figure 8.1 illustrates a thought experiment. A metal bar XY of length l is pulled through a uniform magnetic field B with a velocity v. The direction of the velocity is perpendicular to the bar and they are both perpendicular to the magnetic field. Figure 8.1 (1) Draw on Figure 8.1 all the forces acting on the positive charge +Q in the bar. Label the forces. 00 AL/Structural Question/P.10 (2) Describe the movement of the charges in the bar and show that the e.m.f. induced across the ends XY is given by ε=B/v. (b) In 1996 astronauts on the space shuttle Columbia performed an experiment to test an idea for generating electricity in the upper ionosphere. In the ionosphere, the ultraviolet radiation from the Sun or other radiations causes the air particles to undergo ionization, and they tend to remain ionized as the chance of recombination is small. Once in orbit, Columbia released a satellite attached to it by a 20km long conducting cable. With the satellite vertically above the shuttle, the two moved together around the earth above the equator. Given: Magnetic field strength in the orbital region = 30 10 6 T Orbital position of the shuttle = 6.8 106 m from the center of the earth Mean radius of the earth = 6.4 106 m Figure 8.2 (1) Calculate the orbital speed of the shuttle at the orbital position. (2) Estimate the e.m.f. induced across the cable. State the assumption(s) that you have made in the calculation. (3) The experiment was in fact successful and a steady was detected in the cable. Indicate the direction of the current in the cable and explain why a current can be sustained. 9. A diffraction grating is used to study the hydrogen spectrum from a discharge tube. The first-order diffraction angles of some of the various discrete lines are tabulated below. First-order 23.19 16.96 15.09 14.25 12.64 00 AL/Structural Question/P.11 diffraction angle θ/° Wavelength 656.3 486.1 434.0 410.2 364.6 λ/nm (a) Plot a suitable graph to find the grating spacing, in lines per mm, of the diffraction grating. (b) (1) Which line corresponds to blue light? (2) One of the lines cannot be seen by naked eyes. Name the region in the electromagnetic spectrum to which this line belongs. (c) What activity within an atom gives rise to these emission lines? What is the physical significance of the spectrum consisting of discrete lines? (d) In fact, the wavelengths of the emission lines satisfy the formula of the Balmer series: (364.6nm ) n2 , where n = 3,4,5… n2 4 (1) Show that the formula can be transformed into h K ( 1 1 ) , where ν n2 4 represents the frequencies of the emission lines, h is the Planck constant and K is a constant. (2) Find K in units of eV. State the physical significance of the sign and the magnitude of the term K in the formula of h . n2 (Planck constant = 6.626 1034 Js ; electronic charge = 1.6 10 19 C ) 10. Figure 10.1 shows an operational amplifier circuit. Figure 10.1 (a) (1) What is meant by negative feedback in an operational amplifier circuit? State TWO effects of using negative feedback. (2) What will be the effect on the above circuit if Rf increases? (3) Find Vout when Vin equals (I) 10mV (II) 2 V (4) The graph below represents the variation of the input voltage Vin with time. 00 AL/Structural Question/P.12 Sketch the corresponding variation of the output voltage Vout. (b) (1) The circuit in Figure 10.1 can be used to amplify the signals of the order of 10mV from an electronic stethoscope monitoring heart beats. An earphone requiring a peak voltage of at least 0.5V to operate is connected to the output of the circuit. What should be the minimum resistance value of the feedback resistor Rf? (2) Although a step-up transformer can give a larger output voltage from a small input voltage, it cannot serve the same purpose as the amplifier circuit in Figure 10.1. Explain briefly.