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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 nonprogrammable 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 freefall 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——>+IIm—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, halfway 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 WorkEnergy 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 kgm2.
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€, aTT—T'Oi, ZT=Ia, I=Zmr2;
_, ‘ . _ AL z AV = _
. Impulse  FAt, F _ Y A, AP B F km,
Zsz,
.xcg= : col2:701 P2=P1 KErot=%Iw2 © UNISA 2010 Sr: unwersuty
of south alnca UNIVERSITY OF SOUTH AFRICA U N I EXAMINATION MARK READING SHEET UNIVERSITEIT VAN SUlDAFRIKA
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