96/AL/Structural Question/P.1
HONG KONG ADVANCED LEVEL EXAMINATION
AL PHYSICS
1996 Structural Question
1.In a game of table tennis, the ball is struck when it is at C, which is 0.40 m vertically above the edge A of the table. Immediately after it is struck, the ball moves with a horizontal velocity v. It then just passes the net, hits the table at D and reaches the highest point E as shown in Figure 1.1. The table is 2.70 m long and the net is 0.15 m high.
(a)Neglecting the effects of air resistance, calculate
(i)the value of v,(2 marks)
(ii)the speed of the ball just before it hits the table.(2 marks)
(iii)If point E is at 0.25 m above the table, draw the graph of vertical velocity, vy, of the ball against time from C to E. Take downwards as positive. (tC, tD and tE on the time axis are the times when the ball is at C, D and E respectively.) (3 marks)
(b)The effects of air resistance are now taken into account. Figure 1.2 shows the top view of the flight of the ball struck with a spin.
(i)Indicate on Figure 1.2 the spinning direction of the ball and the directions of the forces acting on the ball besides its weight. (2 marks)
(ii)Explain why the ball flies along a curved path instead of a straight one.
(2 marks)
2.
In Figure 2.1, a 1.4 m long rigid rod of negligible mass is suspended form the ceiling by two 0.8 m long vertical wires attached to its ends A and B. The wire attached to the end A is an aluminium wire of diameter 1.2 10-3 m; and that attached to the other end B is a brass wire of diameter 0.8 10-3 m. Initially, the rod is precisely horizontal. The young modulus and breaking stress of aluminium and brass are as follows (Assume that the change in cross-sectional area of the wires under stress is negligible.):
Material / Young modulus/Pa / Breaking stress/Paaluminium / 6.9 1010 / 2.2 108
brass / 9.1 1010 / 4.7 108
(a)A 10-kg mass is hung from the midpoint, C, of the rod. Assume that the elastic limits of both wires are not exceeded.
(i)Calculate the extensions of the two wires.(4 marks)
(ii)Find the angle that the rod makes with the horizontal.(2 marks)
(iii)In what direction should the 10-kg mass be shifted so that the two wires have equal extension? State which wire is in a greater tension. (1 mark)
(b)The 10-kg mass is replaced with another mass hung at a distance, d, from end A. For a certain optimum value of d, the rod can support the maximum amount of mass without breaking either wire. (The angle between the rod and the horizontal is very small and therefore can be neglected.)
Calculate
(i)the maximum mass the rod can support,(3 marks)
(ii)the optimum value of d.(2 marks)
3.(a)A police car and a lorry are moving with the same speed, u, towards each other. The siren on the police car emits sound waves of frequency 1 000 Hz and the velocity of sound in air is 330 ms-1.
(i)With the aid of a diagram, derive the expressions for the wavelength, ’, and the frequency, f’, of the sound waves heard by the driver of the lorry. (4 marks)
(ii)When the police car passes the lorry, the frequency of the sound waves heard by the driver of the lorry suddenly drops by 200 Hz. Calculate the speed of the police car. (3 marks)
(b)State and explain one pieced of evidence which suggests that the universe is expanding. (3 marks)
4.One mole of helium gas undergoes a cycle ABCA in which its pressure, P, and volume, V, are indicated in the P-V diagram in Figure 4.1.
Given : Universal gas constant = 8.31 Jmol-1K-1
Avogadro constant = 6.02 1023 mol-1
Assume that helium gas behaves as an ideal gas.
(a)(i)Find the temperature of the gas at state A.(2 marks)
(ii)The average separation between helium atoms can be taken as the cube root of the average volume of space occupied by each atom. Estimate a value for this average separation at state A. (2 marks)
(b)In an ideal gas, there are no intermolecular forces between molecules except during collisions. Is this ideal gas assumption justified for the helium gas? Explain briefly. (2 marks)
(c)(i)Find the work done by the gas in going from (1) A to B, (2) B to C and (3) C to A. (3 marks)
(ii)Find the internal energy of the gas at state A.(2 marks)
(iii)Calculate the heat absorbed by the gas in going through the cycle ABCA.
(2 marks)
5.In Figure 5.1, an a.c. signal generator of constant r.m.s. output voltage is connected in series with a resistor, R, of resistance 110 , a capacitor, C, of capacitance 4.7 F and an ammeter, A. Both the signal generator and the ammeter have negligible impedance. Y1 and Y2 are connected to the two Y-inputs of a dual trace CRO while E is connected to its common earth connection. Figure 5.2 shows the stable trace pattern, y2, of the voltage across R and C shown on the CRO screen. The voltage gain and time base for y2 are 2.5 Vcm-1 and 2.5 ms cm-1 respectively.
(a)(i)What are the peak voltage and the frequency of the applied a.c. signal?
(2 marks)
(ii)Draw a phasor diagram to show the relationship between the applied a.c. voltage, the voltage across the capacitor and the voltage across the resistor. (2 marks)
(iii)Find the phase angle between the applied a.c. voltage and the voltage across the resistor. (2 marks)
(iv)What is the peak voltage across the resistor?(2 marks)
(v)Sketch on Figure 5.2 the trace pattern of the voltage across R, using the same time base setting of y2 but with a voltage gain of 1 Vcm-1. (2 marks)
(b)A variable inductor, L, is added to the circuit in Figure 5.1 to form an RLC series circuit. When the inductance of L is gradually increased, the reading of the ammeter A increases to a maximum and then decreases.
(i)Explain why the ammeter reading attains a maximum.(2 marks)
(ii)Find the value of the inductance of L corresponding to the maximum ammeter reading. (2 marks)
6.
A heavy uniform flywheel is mounted vertically at its centre on a horizontal cylindrical axle of radius 0.02 m and of negligible mass. the flywheel is free to rotate about the axle in a vertical plane as shown in Figure 6.1. A 3-kg weight is hanging from a light inextensible string wound round the axle. The system is then released from rest. Assume that the frictional force acting on the axle is negligible and there is no slipping between the string and the axle.
(a)(i)Would the tension in the string increase, decrease or remain unchanged when the system is released? Explain briefly. (2 marks)
(ii)If T is the tension in the string, I is the moment of inertia of the flywheel about the axle, a and are the linear and angular accelerations of the weight and the flywheel respectively, write down the relation between a and as well as the equations of motion of the weight and the flywheel.
(3 marks)
(b)To measure the angle turned through by the flywheel in a certain time interval, a paper disc coated uniformly with fine powder is first attached to the flywheel. A vibration generator with a pointer moving up and down would leave a trace on the paper disc by scratching away the powder when the flywheel starts to rotate (as shown in Figure 6.2). Overlapping of the trace is avoided as the vibration generator is gradually raised by a gear system (not shown). The frequency of the vibration generator is 100 Hz.
The angular displacements, , for every 10 periods of vibration are recorded as follows:
1st10 periods / 2nd
10 periods / 3rd
10 periods / 4th
10 periods / 5th
10 periods / 6th
10 periods
/rad / 0.31 / 0.37 / 0.41 / 0.46 / 0.51 / 0.55
/rads-1
(i)Complete the table for the average angular speed for each time interval of 10 periods. (1 marks)
(ii)Plot a graph of angular speed against time.(3 marks)
(iii)Use the graph to find the angular acceleration of the flywheel. Hence calculate its moment of inertia about the axle by using the results in (a)(ii). (4 marks)
(c)Briefly explain why a flywheel is often found in the engine of a motor vehicle.
(2 marks)
7.(a)
A coil and a retort stand are arranged as shown in Figure 7.1. The coil is connected to a d.c. supply by a switch S. When the switch is closed, the aluminium ring placed on top of the coil jumps up momentarily and falls back afterwards.
(i)Briefly explain the phenomenon.(3 marks)
(ii)What would be observed if the d.c. supply is replaced by an a.c. one? Suggest a practical use of this experimental result. (2 marks)
(iii)The heat capacity of the ring is 7.8 JK-1 and its temperature rises from 25 °C to 40 °C during the first 50 s when the a.c. supply is on. Find the average rate of increase in internal energy of the ring. (2 marks)
(b)
A centre-zero galvanometer A (full-scale deflection of 100 A) is connected in series with a resistor, R, and a 1.5 V cell as shown in Figure 7.2. The pointer of A deflects to the left.
(i)Give the order of magnitude of R for protecting A from overload.(1 mark)
(ii)The galvanometer is now connected to a coil as shown in Figure 7.3. A student moves a bar magnet with uniform speed towards the coil and the pointer of A deflects to the right.
(I)Indicate on Figure 7.3 the direction of the induced current in the coil and the poles of the magnet. (2 marks)
(II)Where does the electrical energy in the circuit come from?(1 mark)
(III)Suggest THREE ways to increase the deflection of A.(2 marks)
8.
Figure 8.1 shows a simple current balance. A flat solenoid is connected to a horizontal rectangular copper loop ABCD, such that the same current can pass through them as shown. The loop is pivoted on the axis XY which is mid-way between AB and CD, with CD inside the solenoid and perpendicular to the axis of the solenoid. When a current, I, flows through the solenoid and the loop, a rider of mass 10-4 kg has to be placed on AB to restore equilibrium. The length, l, and the number of turns, N, of the solenoid are 50 cm and 600 respectively. The length of CD is 20 cm.
(Permeability of free space 0 = 4 10-7 Hm-1)
(a)Indicate on Figure 8.1 the direction of the magnetic field inside the solenoid.
(1 mark)
(b)(i)If the magnetic field strength inside the solenoid can be calculated by the formula , find, in terms of I, the force acting on arm CD. (2 marks)
(ii)Hence deduce the value of I.(2 marks)
(c)State and explain one precaution of the experiment.(2 marks)
(d)Is this current balance useful for measuring a.c. as well? Explain briefly.
(2 marks)
(e)The solenoid is not infinitely long. What effects does this have on the value of I obtained in (b)? Explain briefly. (2 marks)
9.In a photoelectric experiment, a thin metal plate of dimension (8.0 10-3) (8.0 10-3) m2 is illuminated with a parallel beam of ultraviolet light of wavelength 230 nm. The work function of the metal is 2.21 eV.
Given: Planck constant = 6.63 10-34 Js
Charge of an electron = 1.60 10-19 C
(a)What is meant by the work function of a metal?(1 mark)
(b)Explain why photoelectrons are emitted with different speeds though the energy of each incident photon is fixed. (1 mark)
(c)(i)Calculate the maximum kinetic energy of the photoelectrons emitted.
(2 marks)
(ii)Find the stopping potential.(1 mark)
(d)The intensity of the ultraviolet light used is 3 Wm-2 and it falls normally on one side of the metal plate. Find, in the absence of the stopping potential, the number of photoelectrons emitted per second. Assume that every incident photon can successfully release a photoelectron. (3 marks)
(e)State the change in (i) the stopping potential and (ii) the number of photoelectrons emitted per second, if another source of ultraviolet light with the same intensity, but having a shorter wavelength, is used. Explain briefly. (4 marks)
10.A thyratron tube filled with xenon gas at low pressure is used for measuring the excitation potential of xenon. Figure 10.1 shows the circuit used.
In the experiment, electrons emitted from the hot cathode, C, are accelerated by the variable potential difference between cathode C and the perforated grid, G. Collisions occur between the electrons and the xenon atoms. The potential of anode A is made slightly negative with respect to grid G by using a cell E. Electrons with enough energy to reach A constitute a current, which is detected by the light beam galvanometer. The voltage of the d.c. supply is varied and a graph of the galvanometer reading, I, plotted against the voltmeter reading, V, is shown below:
(a)Explain why a heater is required to heat up cathode C.(2 marks)
(b)(i)State the condition for a collision between an electron and a xenon atom to be inelastic. (1 mark)
(ii)Deduce from Figure 10.2 the first excitation potential of xenon.(1 mark)
(c)Explain why the potential of anode A is made slightly negative with respect to grid G. (2 marks)
(d)Describe the energy change of an electron when, after emitting from the hot cathode C, it accelerates towards the grid G and undergoes an inelastic collision with a xenon atom, and finally reaches anode A. (3 marks)
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