PHY1015-2010-6-E-1 - UNIVERSITY EXAMINATIONS...

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Unformatted text preview: UNIVERSITY EXAMINATIONS UNIVERSITEITSEKSAMENS UNI§A 3;: PHY1 01 5 ( 489574) MayI'June 2010 ELEMENTARY MECHANICS (PHYSICS 101) Durahon 2 Hours 100 Marks EXAMINERS FIRST PROF ML LEKALA SECOND MR SJ MOLOI Use of a non-programmable pocket calculator is permissuale o This paper consxsts of two SBCthDS, SECTION A and SECTION B. 0 Answer SECTlON A (Multiple Chonce) on the examination mark reading sheet I Answer SECTION B (Written Solutlons) in the examination answer book. a The mark allocation for each question is indicated in brackets to the right. 0 This paper consists of eight (8) pages plus instructions for the completlon of mark reading sheet. a The information given at the end of SECTION B may be used Without proof. \ 2 PHY1015 May/ J une 2010 SECTION A (Multiple Choice) [Total marks: 10x3=30] 1 Con31der the followmg scenano for free-fall bodles Ball A 1s dropped from rest from a w1ndow At the same t1me, ball B IS thrown downward, and ball C IS thrown upward from the same w1ndow Wthl’l statement concermng the balls 18 necessarlly true 1f alr reelstance IS neglected? [3] 1 At some Instant after 1t 18 thrown, the acceleratIOn of ball C IS zero 2 All three balls strlke the ground at the same t1me. ) ) 3) All three balls have the same veloc1ty at any mstant 4) All three balls have the same acceleratlon at any mstant ) 5 All three balls reach the ground w1th the same veloc1ty 2 Startmg from rest, a part1cle confined to move along a stralght hne 1s accelerated at 4 rn/s2 How far Wlll the pmtlcle have travelled after 10 s? [3] 1) 20 m 2) 40 In 3) 100 m 4) 200 In 5) 400 m 3 Two objects of equal mass travelhng toward each other w1th equal speeds undergo a head on colhsmn Whlch one of the followmg statements concernlng the1r velomtles after COlllSlOIl lS always true? [3] 1) They w111 exchange velocitles 2) Then veloc1t1es Wlll be reduced 3) Then ve1001t1es Wlll be unchanged 4) Then veloc1t1es Wlll be zero ) 5 Thelr velocltles may be zero [TURN OVER] 3 PHY1015 May/June 2010 4. A pr0Jectlle lS fired at an angle of 60 0° above the horlzontal w1th an 1n1t1al speed of 30 0 m/s. What 15 the magnltude of the horizontal component of the prolectlle’s displacement at the end of 2 s7 [3] 1)10n1 2) 20m 3) 30m 4) 40m 5) 50m 5 A r1g1d body rotates about a fixed ax1s w1th a constant angular acceleratlon. Whrch one of the followmg statements IS true concernlng the tangentlal acceleratlon of any po1nt on the body? [3] 1 Its magnltude IS zero m/s2 2 It depends on the angular velocnty 4 5 It depends on the change 1n the angular veloc1ty ) J 3) It 18 equal to the centnpetal acceleratlon ) It IS constant 111 both magnltude and d1rect10n ) 6. ConSIder the four p01nt masses located as shown 1n the figure below What Is the a: coordlnate of the center of grav1ty for thls system? [3] [TURN OVER] 4 PHY1015 May/June 2010 7 A sunple pendulum cons15ts of a ball of mass m suspended from the ce111ng usmg a stung of length L The ball 15 (hsplaced from its equ1l1br1um p051t10n by an angle 0 What IS the magmtude of the restorlng force that moves the ball toward 1ts equ111br1um 1308113101] and produces a ample harmonlc 1110131011? [3] 1) km 2) mg 3) mg(cosl9) 4) mg(sm9) 5) mgL(s1n0) 8 Wh1ch one of the followmg statements concermng the buoyant force on an object submerged 1n a l1qu1d IS true? [3] 1 The buoyant force depends on the mass of the object 2 The buoyant force depends on the welght of the object 4 5 The buoyant force w111 Increase w1th the depth 1f the hqu1d 1s 1ncompress1ble ) ) 3) The buoyant force IS 1ndependent 0f the den51ty of the 11qu1d ) The buoyant force depends on the volume of the hqu1d J 9 A ball 18 klcked at an angle of 45° What IS the ratlo 0f the ball’s maxnnum he1ght to Its range? [3] 1) 10 2) 0 75 3) 067 4) 0.50 5) 0.25 10. An 80 kg man balances the boy on the beam as shown 1n the d1agram Ignormg the welght of the beam, what IS the apprOXImate mass of the boy? [3] boy man 50kg fucrum W4m——>+I-Im—I~ [TURN OVER] 5 PHY1015 May/ June 2010 SECTION B (Written Solutions) [Total marks = 70] l G1ve a br1ef definltlon (1n words) of each of the folloWIng (a) Stress (2) (b) Impulse (2) (c) Conservatlve force (2) ((1) Center of gravity (2) E 2 Object A of mass 30 kg rests on object B of mass 60 kg, and is attached w1th a horlzontal rope AC to the wall, as shown 1n the figure below. A force P Incllned at 15° to the honzontal is applied on object B The coefiic1ent of statlc fr1ct10n between A and B IS 0.25, and between B and the floor IS 0 4 Assume the system 18 1n equ1librium, and calculate the magnitude of (a) the force P, and (4) (b) the tensmn 1n the rope AC (4) 3 Con51der an object of mass m sl1d1ng down an Inchne angled at 9 to the honzontal. The coefliment of kinetIC fI‘lCtIOIl between the object and the surface of the 1nchne IS the. (a) Draw a schematlc d1agTam to Illustrate the S1tuat10n, showmg all the forces actmg on the object, half-way along the 1nc11ne (2) (b) Is the mechanical energy conserved or not dunng the shdmg" Explain. (2) (c) Show that the acceleratlon of the object as 1t shdes down the 1nehne is given by a = g(sm 9 — pk cos 0), where g 15 the grav1tat10nal acceleratlon. (6) [10} [TURN OVER] 6 PHY1015 May/ June 2010 4 State the followmg clearly (a) The Archlmedes’ prlnciple (2) (b) The pr1n01p1e of conservatlon of mechanlcal energy. (2) (c) The pr1nc1ple of conservatlon of angular momentum (2) (d) The Work-Energy theorem (2) [3] . The figure below shows a 9.0 kg box of oranges shdmg from rest dewn a fr1ct1onless 1nchne from a he1ght of 5 0 m A constant frlctlonal force, mtroduced at pomt A, brmgs the block to rest at pOmt B, 19 m to the r1ght of pomt A. What IS the speed of the block Just before 1t reaches pomt A? [10] 5.0 In J.“ A B I" “19 m ————-—>| A car’s fan rotatmg WIth an 1n1tial angular velomty of 1000 rev/mm IS sw1tched OH. The angular velotnty decreases to 200 rev/Hun 1n 2 s Assummg the angular acceleratlon is constant, how many revolutlons does the blade of this fan undergo durmg thlS txme? {8] [TURN OVER] 7 PHY1015 May/June 2010 7. The drawmg shows a top Vlew of a frlctionless horlzontal surface where two springs With objects of mass m1 and m2 attached to them. Each spring has a spring constant of 120 N/m The objects are pulled to the right and then released from the peeltions shown How much tune passes before the objects are Side by side for the first time atx=0mifm1=30kgandm2=27kg7 [8] Posatlon of unstramed spnng (x 2 0 I11) 8. COIlSldeI‘ the figure below, which shows a crate of welght 4420 N being lifted. The two cables are wrapped around their respective pulleys, of radn 0 600 m and 0 200 m. The pulleys are fastened together to form a “dual” pulley and turn as a smgle umt about the center axle, relative to Wthh the combined moment of inertla IS 50 0 kg-m2. A tensmn of magnitude 2150 N 1s maintained 1n the cable attached to the motor (a) Draw the free—body dlag‘rams for the (1) pulley, and (11) crate (2) (b) Flnd the angular acceleration of the dual pulley, and (4) (0) Calculate the tensmn in the cable connected to the crate. (4) [10] [TURN OVER] 8 PHY1015 May/June 2010 USEFUL INFORMATION ov=vo+at, ow=w0+at, = £000 + vfi) :1: = vat + éat2, 6 = wot + %Gt2, v2 = '03 + 2am; (1)2 = Lug + 20¢, o F = 0%, :1“ = usFN, fk = kaN, W = (Fcosfi)s; 'f=71«; = w=%¢; w=21rf; 2 2 .T=2'U£3 Fc=mf1L1 ac=v?; vT=Tw; 0T=F€, aT-T—T'Oi, ZT=Ia, I=Zmr2; _, ‘ . _ AL z AV = _ . Impulse - FAt, F _ Y A, AP B F km, Zsz, .xcg= : col-2:701 P2=P1 KErot=%-Iw2 © UNISA 2010 Sr: unwersuty of south alnca UNIVERSITY OF SOUTH AFRICA U N I EXAMINATION MARK READING SHEET UNIVERSITEIT VAN SUlD-AFRIKA EKSAMEN-MERKLEESBLAD PART 1 (GENERAL/ALGEMEEN) DEEL T INITIALS AND SURNAME VOOHLEI'TERS EN VAN av - _.— . STUDV UNIT 3 g PSV'IOD X STUDIE EENHEID bv FSYTW X m PAPER NUMBER DATE OF EXAMINATION DATUM VAN EKSAMEN EXAMINATION CENTRE (E G PRHORIA) VRAES‘I’ELNOMMER EKSAMENSENTRUM (BV PRETORIA) STUbEMT HUMMER LINIEKEV -. STEL NH 1 U‘ [01 [D] [D] m [11:11 For use by examination InVIgIIator {2] r21 r21 [:1 Vrr gebrmk deur eksamenopsaener E J [5: . IMPORTANT BELANGHIK 1 [J55 ONLY AN HB PENCIL TD COM “LETE THIS SHEET 1 GEBRUIK bLEGb N HB PDTLOOD OM HIERDIE BLAD TE VOLTOOI ’1 MARK LIKETHIE: F2! 2 MEFIK ASVOLG F2! 3 CHECK THAT YOUR INITIALS AND SLRNAME HA5 BEEN MLLEJ IN COHRECIL‘I 3 KONIH‘ULEER DAI U VOOHLHTERE) EN VAN HtG INGEVUL IS 4 ENTER YOUR STUDENT NUMBER FROM LEFT T0 RIGHT ’5 \«UL U STU DENTENOMMER VAN LINKS NA REGS IN 5 CHECK THAI YOLR STUDENT NUMBER HAS BEEN FILLED IN CORRECTLY 5 KONTROLEER DAT U DEE KDRREKTE STUDENTENOMMEH VFRSTfiI-K HFT 5 CHECK THAT THE UNIQUE NUMBER HAS BEEN FILLED IN COHRECTLY 6 KONTROLEEH DAT DIE UNIEKE NOMMER REG INGEVUL I5 7 CHECK THAT ONLY ONE ANSWER PER QUESTION HAS BEEN MARKED 7 MAAI‘: SEKER DAT NET EEIN ALTERNATIEF PER VRAAG GEMERK IS 3 30 NOT FOLD 3 MOENIE VOU ME PART 2 {ANSWERS/ANTWOORDE) DEEL 2 bNiSA PIES? MARK READING SHEET INSTRUCTIONS Your mark reading sheet Is marked by computer and should therefore be filled In thoroughly and correctly USE ONLY AN HB PENCIL TO COMPLETE YOUR MARK READING SHEET PLEASE DO NOT FOLD OR DAMAGE YOUR MARK READING SHEET Consult the Illuswatlon of a mark readmg sheet on the reverse ofthIs page and follow the InStl‘UCthl’lS step by step when workmg on your sheet lnstructton numbers 0 to @ refer to spaces on your mark readmg sheet which you should fill In as follows 0 WrIte your paper code In these eIght squares, for Instance Hall“!!- The paper nI'mber pertalns only to first-level courses con51st1ng of two papers WRITE for the first paper and for the second If only one paper, then leave blank FIll In your InItIals and surname WI 11'] the date of the examtnatlon FIIl In the name of the examinatlon centre @000 WRITE the dIgIts of your student number HORIZONTALLY (from left to fight) Begin by fillIng In the first dIgIt of your student number In the first square on the left. then fill In the other dIgIts, each one In a separate square ln each vertlcal column mark the dlglt that corresponds to the dlglt In your student number as follows [-1 WRITE your unlque paper number HORIZONTALLY NB Your umque paper number appears at the top of your examlnatlon paper and con51sts only of dIgIts (e g 403326) 9 In each vertlcal column mark the dlgIt that corresponds to the dlgIt number In your uanue paper Q number as follows [—] ® QuestIon numbers I to I40 Indicate correspondlng question numbers In your examInatIon paper The five spaces w1th dIgIts l to 5 next to each question number Indtcate an alternatlve answer to each questlon The spaces of Much the number correspond to the answer you have chosen for each question and should be marked as follows H . 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PHY1015-2010-6-E-1 - UNIVERSITY EXAMINATIONS...

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