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1 UNIVERSITY OF SWAZILAND (f FACULTY OF SCIENCE DEPARTMENT OF PHYSICS MAIN EXAMINATION TITLE OF PAPER: INTRODUCTORY PHYSICS II COURSE NUMBER: TIME ALLOWED: INSTRUCTIONS: P102 THREE HOURS ANSWER ANY FOUR OUT OF FIVE QUESTIONS EACH QUESTION CARRIES 25 MARKS MARKS FOR EACH SECTION ARE IN THE RIGHT HAND MARGIN GIVE CLEAR EXPLANATIONS AND USE CLEAR DIAGRAMS IN YOUR SOLUTIONS. MARKS WILL BE LOST WHERE IT IS NOT CLEAR HOW THE EQUATIONS USED WERE OBTAINED THIS PAPER HAS SEVEN PAGES INCLUDING THE COVER PAGE THE LAST PAGE CONTAINS INFORMATION THAT MAYBE USEFUL IN SOME QUESTIONS. IF IN DOUBT, RAISE YOUR HAND AND ASK DO NOT OPEN THE PAPER UNTIL PERMISSION HAS BEEN GRANTED BY THE CHIEF INVIGILATOR
2 QUESTION 1 (a) A wave is described by the following equation x =10.0 sin Grrt + 3;) m. 1. What is the amplitude ofthe wave? (1 mark) 11. What is the angular velocity ofthe wave? (1 mark) 111. Find the wavelength ofthe wave. iv. Find the frequency ofthe wave. (1 mark) Include correct units in your answers. (~ (b) An instrument produces isotropic sound at an average power P = 1.25 db. What is the sound level at a distance r = 15.0 m? (7 marks) (c) A light ray enters oil ofrefractive index 1.50 from air at an angle e. The light ray is refracted at an angle of25.00 in the oil. The oil floats on water of refractive index Upon reaching the oil-water interface, the light ray is refracted by an angle (J. Refer to Figure 1. Find the angles e and 9'. (6 marks) air oil water Figure 1. (d) An object is placed 8.00 cm in front ofa lens offocallengtbf= 14.0 cm. i. Find the image distance. 11. Determine the magnification From your results in (i) and (ii), state the nature ofthe image.. 2
3 ---~-- QUESTION2. Three point charges qt = 4.00 IlC and q2 =-8.00 IlC and q3 = 6.00 IlC are located at the comers of a triangle as shown in Figure 2. Point P is along the x-axis directly below q3. 1. Use a diagram to detennine the unit vectors Tl,3 and Tz,3 for the directions from ql iv. v. vi. Vll. V111. ix. to q3, and q2 to q3, respectively. (4 marks) Find the force on q3 due to ql in vector fonn. Find the force on q3 due to q2 in vector fonn. Find the total force vector on q3 due to the other two charges. Find the electric field vector at the location of q3 due to qt. Find the electric field vector at the location ofq3 due to q2. Find the total electric field vector at the position ofq3 due to the other two charges. Use the total electric field vector to obtain the force on q3 due to the other two charges. With what charge must q3 be replaced by to make the potential at point P to be ov? (5 marks) y %=6xI0-6C 100 em p x Figure 2. 3
4 QUESTION 3 (a) In the circuit shown in Figure 3 1 use Kirchoffs laws and a diagram to obtain any three equations that can enable you to determine the currents hi 12 and 13 given all the other quantities. (Do not solve/or the currents) (8 marks) b Figure 3. (b) Consider the network shown in Figure Find the effective resistance between points a and b (Rab). 11. Find the effective resistance between points b and c. (Rbc). iii. Find the effective resistance ofthe circuit Reff. IV. What is the total current through the network? v. What is the voltage drop Vab between junctions a an b? VI. Detennine the current through resistor R I (1 mark) (1 mark) R 1 = 100 R3 =100 c 24V Figure 4. (c) A galvanometer ofintemal resistance 60.0 Q requires a current of rna for full scale deflection, and is to be used as an ammeter. 1. Make a sketch that illustrates how the student can covert the -galvanometer into an ammeter. 11. Find the value ofthe resistor required to tum the galvanometer into a 250 rna ammeter.. 4
5 QUESTION 4 a) A 8.00 J.LF capacitor is charged with a 12 V battery through a resistor R. 1. What is the total charge in the capacitor after one time constant? 11. Find the total energy stored in the capacitor after one time constant Suppose the capacitor is then discharged through the resistor R. Find the energy remaining in the capacitor after one time constant. b) A horizontal rod carrying a current 1== 2.00 A along its length I == 50.0 cm is placed in a magnetic field ofmagnitude B == 3.60 T in to the page. The direction vectors (unit vectors) are as shown in Figure 5 on the right. The magnetic force pulls the rod upward, while the gravitational force pulls the rod downward. 1. Find the direction ofthe current in the rod. (4 marks) 11. What is the force due to the magnetic field on the rod? lll. Find the mass ofthe rod. Ie t J ~r I Figure 5. c) Particles ofcharge q and mass m are accelerated from rest through a potential difference ~V. 1. Find an expression for the velocity v ofthe charged particles in terms ofm, q and ~V 11. The accelerated particles are then subjected to a magnetic field B perpendicular to their direction ofmotion. Find an expression for the radius ofcurvature ofthe particles in the magnetic field in terms ofb, m, q and ~V. (7 marks) 5
6 QlTESTION5 a) An independent power producer generates 20 MW of electricity at a peak voltage of9.50 kv. Detennine the nns voltage and current for the system. (5 marks) b) A step-down transfonner is used for recharging a battery. The turns ratio ofprimary to secondary in the transfonner is 24.4:1 and is used with a 220 V (nns) household service. The transfonner draws a current of 50 ma nns from the house outlet. (i) What is the voltage supplied to the battery? (ii) What is the current supplied to the battery? (iii)how much does it cost to charge the battery each time, if it takes 12 hours per charge, assuming that electricity costs 88 cents per kilowatt-hour c) An inductor (/ = 500 mh), a capacitor (C = 3.48 j.1f) and a resistor (R = 470 Q) are connected 0 a 50.0 Hz power source with a peak voltage of450 V. (i) Find the impedance ofthe network. (5 marks) (ii) Determine the peak current Imax. (iii)find the phase angle and state with justification whether the current lags or leads the voltage. (4 marks) (iv)what is the power consumed by the network? 6
7 DATA SHEET General data Air refractive index Avogadro's number NA = X mor Boltzmann's constant kb = 1.38 X10-23 JIK Density of mercury = 1.36 x 10 4 kglm 3 Gas constantr =8.314 J/(mol.K) Gravitational acceleration g =9.80 mls 2 Standard atmospheric pressure = x 105 Pa Speed oflight in vacuum c = x 10 8 mls Speed of sound in air Us =343 mls Stefan-Boltzmann constant 0= 5.67 x 10-8 W/(m2.K4) Threshold of hearing 10 = W/m 2 Universal gravitational constant G == 6.67 X N. m 2 /kg 2 1 calorie = 1 c J 1 food calorie = 1 Calorie = 1 C 10 3 calories == x 10 3 J Water data c(water) = 4186 J/(kg.K) c(ice) 2090 J/(kg.K) c(steam) =2079 J/(kg.K) Lrt)ce) =3.33xl0 5 J/kg Lv(water) = 2.260xl0 6 J/kg p (water) 1000 kg/m = 3 refractive index nw == Electricitv and nuclear data Alpha particle mass = x kg Charge of an electron = -1.6 x C Charge of a proton = +1.6 X10-19 C Coulomb's constant ke == x 10 9 Nm2/C 2 Deuteron mass = x kg Electron mass, me = x kg Neutron mass mn = x kg Proton mass, mp = x kg 1 atomic mass unit = 1 amu = 1 u = 1.66 x kg EO =8.85 Xl0 12 C 2 (N.m 2 ) 1 Ci = 3.7 x decays/s IBq = 1 decay/s 7
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