EXAMSfS':30 113/0~O~ 1-1 RLL 2.9 ,-Ctl=" OFFICE USE ONLY University of the Witwatersrand, Johannesburg Course or topic No(s) PHYS 180 Course or topic name(s) Paper number & title Examination! to be held during month(s) of (*delete as applicable) Year of Study (Arts & Science leave blank) Degrees/Diplomas for which this course is prescribed (BSc (Eng) should indicate which branch) Faculty/ies presenting Candidates Internal examiner(s) and telephone extension numbet(s) [ Physics IE JUNE 2002 [ First BSc Engineering (All Branches) , i. i, I I, [ Engineering ii Prof. A.G. Every 76823 Prof. T.E. Derry 76824 Mr. S. Srivastava 76827 1'1 t, Ii ",I External examiner(s) [ Prof. I. Rodrigues Prof. D. Joubert 76804 Non-programmable calculators may be used. 1'1 i' ! ! Ii Special materials required (graph/music/drawing paper, maps. Diagrams, tables, computer cards, etc) Time allowance Instructions to candidates (Examiners may wish to use this space to indicate, inter alia, the contribution made by this examilHttion or test towards the year mark, if appropriate) \. t rJ tl Ui I, I' l. I i, c~::se I PHYS180 I Hours 12 Hours I ~! 1.1 :\' Answer all Questions. All working must be shown is support of your answers. Total Marks = 100 After 2 hours your answer books will be collected and the practical test handed out. -, ~_.~'~~,' 6 Pages - Page I PHYSICS IE (PHYSI80) June Examination 2002 1. (a) Show, with the aid of a diagram, that when an image is produced of an object by a lens the lateral magnification is given by -v m---, u where u and v have their usual meaning. [5] (b) The optical system below consists of an object of height 2 mm placed 90 cm in front of a converging lens of focal length 1; = 30 cm. On the other side, at a distance of 75 cm is a pair of converging lenses in contact, each of focal length 20 cm. Find the position, nature and size of the final image formed. [8] h ,.. Z Jtr11\ ! i i ! <- CfOcm -I- ~ 1S"e-rM ~ II, , II i, :: 30 em -fa. ::::-fb :::. 2 0 cm 2. (a) The power P transmitted by a transverse wave traveling down a rope in tension is given by one of the following expressions: 1 - j..l 0) D2 2 m ' 1 0) 2D --j..l m 2 v 1 , - j..l V 0)2 D2 2 m , _ 2 1 2 j..l v2 0) D m where the symbols have their usual meaning. State which is the correct expression, and give reasons for your choice. [3] (b) A length I of rope of mass per unit length j..l hangs under its own weight --from a point of suspension. cont. - 6 Pages - Page 2 PHYSICS IE (PHYSI80) June Examination 2002 (i) Show that at a distance h below the point of suspension, the velocity for transverse waves in this rope is given by v (Y ou may assume that v =~ g(l- h). =~ F / j.l ). (ii) A wave of amplitude Do is launched from the suspension point and travels down the rope without any energy loss. Derive an expression for the amplitude Dh of the wave at a distance h from the point of suspension. At what distance will Dh = 2Do ? [8] c). A is a point source of sound of waves of frequency f, and B is a point reflector that reflects these waves in all directions with no change in phase. On moving along the line BCD, the first point at which there is destructive interference between the waves directly from A and those which go via B is at point C which is 8 m in front of B. Calculate the wavelength and frequency of these waves. Take velocity of sound = 340 m/s. B <f fj'M i;r c :D I (;m J [5] " 6 Pages - Page 3 PHYSICS lE (PHYSl80) June Examination 2002 3. (a) Draw the lowest three standing wave patterns for an air column oflength I, which is closed at one end and open at the other. Hence establish a general expression for the resonant frequencies. [5J (b) The first overtone of an air column of length I and with one end closed, beats at 3Hz with a tuning fork of frequency 256 Hz when the temperature of the air in the column is 273 K. By raising the temperature of the air, the beat frequency decreases. (i) Calculate the length of the air column. To what temperature must the air be raised for the two frequencies to be in resonance. (You may assume that the velocity of sound in air is given by T v = 331J 273 m/s, where T is the absolute temperature, and that the length of the-air column does not change. [7J (ii) 4. (a) A sound source of frequency 500 Hz is moving along the straight line between two stationary observers A and B at a speed of 60 rn/s. What is the difference in the frequencies heard by the two observers? You may assume the air to be stationary, and vsound 340 m/s. = [5J (b) An aircraft flying at Mach 1,5 in a horizontal direction passes directly above an observer at a height of 2000 m. How long will it be before the observer hears the shock wave from the aircraft, and what will the distance between the aircraft and observer be at that instant. Take vSOW1I I = 340 m/s. [6J ~ 6 Pages - Page 4 PHYSICS IE (PHYSI80) June Examination 2002 5. A storage tower of height h = 32 m supplies water to a house. A horizontal pipe at the base of the tower has a diameter d = 2 cm. To satisfy the needs of the home, the supply pipe is to be able to deliver water at a rate of 0,0025 m3 / s. If water were flowing at the maximum rate, what would the gauge pressure in the horizontal pipe be? Take g = 9,8 m.s-2. [5] 6. A thin film of water of thickness d = 80 ,umis sandwiched between two glass plates and forms a circular patch of radius 12 cm. The edge of the patch is approximately cylindrical in shape and of radius r = d / 2 (see diagram below). (i) Calculate the pressure difference across the curved surface of the liquid (ii) Hence calculate the force with which the two plates are being pulled together Surface tension of water . = 0.072 N/m.. r~~~ j/"./ .-" ./ ./ ///( v', e 11\1 't,hJOf" I ~ \ \. , \ \ Si d.e \ \ lOp ~ \?' \ ,(f" , \\\ \ '\ \1,ec.J [6] ./ 6 Pages - Page 5 PHYSICS IE (PHYSI80) June Examination 2002 7. (a) Water going over the Victoria Falls drops 130 ill. What is the increase in temperature of the water after it has struck the bottom of the Falls? Assume that 60% of the water's energy is converted into heat, and that no heat is lost to the surroundings. Take g = 10 m.s-2, Specific heat of water = 4.2 x 103J kg °C-1. [5] (b) A 0.2 kg glass contains 0.2 kg of a drink, all at 25°C. How many 0.02 kg ice cubes at 0°C must be added to bring the whole system to 10°C? Ignore heat exchanges with the surroundings. Specific heat of glass = 800 lkg -1.°C-1. Assume that the specific heat of the drink = 4,2.103 lkg-1.oC-1. Latent heat of fusion of ice =3.33xl05 lkg-1. [7] 8. (a) On a cool sunny day, a factory loses heat through its windows and gains heat through the ceiling; heat exchanges through the walls can be neglected. There are 16 windows each of 5 m2 area made of 10 mm thick glass, and the ceiling has an area of 800 m2 and is made of boards 25 mm thick. The temperature outside the factory is 10°C, but in the space above the ceiling it is 40°C. What is the equilibrium temperature inside the factory, if there are no internal sources of heat? Thermal conductivities: glass 1,1Wm-2 °C-1; board 0,15 Wm-2°C-I. J [8] (b) (i) The temperature of a 100 W lamp filament is 3000 K. Calculate the surface area of the filament, assuming it to radiate as a black body, and neglecting the temperature of the surroundings. [4] (ii) At what wavelength does the maximum in the radiation occur? [2] Stefan's Constant= 5.67xl0-8Wm-2K-4;Wien's Constant= 2.9xl0-3 m.K 6 Pages - Page 6 PHYSICS IE (PHYSI80) June Examination 2002 9. (a) A person inhales air at 1TC in which the partial pressure of oxygen is 21 kPa, and exhales the same volume at 32°C , the partial pressure of oxygen then being 14 kPa. If the volume inhaled in each breath is 3.5 x 10-4 m3, what mass of oxygen does he or she consume in each breath? Gas constant R = 8.31 x 103J kmor1 K-1 [6] Molar mass of oxygen = 32 kg kmor1 (b) How much heat is required to raise the temperature of 2.00 x 10-3kmol of helium gas from 300 K to 460 K if it is kept (i) at constant volume, (ii) at constant pressure? How much external work is done by the expansion in case (11. '7 ) " Gas constant R = 8.31xlO-3 J kmor1 K-1. [5] il )1 II ill