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Unformatted text preview: DEPARTMENT DF PHYSICS
PHYS 105 FIFIST MIDTEHM EXAM mg M[NUTE5 Nov. 2D. 1999 (D MIDDLE EAST TECHNICAL UNNEHSIT‘I’ TIME: TDTALEHADE I956 Fill in this art with I I] not 1with i ncil: LnsT NAME FInsT NAME. srun. ND. sroNnTuuF. seer. IUHADES.‘ * There are 4 elassical type problems. ~fou must solve all of them. Calculator not permitted.
 Do not ask proctors any question about the problems. Read. understand and solve.
* The shape of the solution of each problem must be shown clearly in the space provided. Numerical answers must be given with correct 5] units and 5! unit symbols must be used only.
Write your answers in boxes provided. otherwise your answer will not be considered. PROBLEM (1} {as points} A hotair balloon is ascending {rising} vertically at the constant rate of 10 ms and is 24:] rn above
the ground when a key is dropped from the balloon at time r: G. Take the direction of motion along
the vertical 3; axis. 1rvith the positive direction ot‘y upward. [g = 10' misﬁt ta]: Find the maximum height H from the ground reached by the key. 4 3
. 
Extvirilth in “her. gramrid; 15* M heap: i
i 1!:
.J;=+¢..1i5  ii = + atom ‘ ' “’1'
{frynear 5
L5 = J 
a ‘L __ I
LT a a; +1.9 {:1 :1.)
SI :4ﬁSF‘Eﬂ L) GTEHrd : iGJ'E—Gﬂ 'i' qgﬂa  his = assa
21' a J Phys 1135 First Midtcn’n Page 1 Nov. 11]. 1999 {b} Find time I at which the key hits 111: ground.
hhHuL 49 Mjwudﬂd 3 )5? WEEfl Lr‘:+mmh. a ,L *’
gzlE'H‘ﬂm '5! ﬁa+Uj+lai
a: a: m +w+ w
3 :3 EtL—Iut—l‘+ﬂ=ﬂ
t. ._.
__E 4:. —2t  “+3 ‘ ‘3
t t His—“hm
1 L"
J A :4i?
.r t __ g .2.
{:3} ﬁnd th: position J: of lhe key WW 5 s after being released from the hallnnn.
t=55 1L +LFJt,+1—ﬁ11_1
:. E ‘31 JD a 2' l
3 ' 3:3.“13+EL01ﬁ}—5f5}
: 3+: + 5:: — :19
:1E5 M
{d} In unitvecth notation. ﬁnd the vclﬂcity v1.3; at the. Ray {H} mm} 5 s after
being mlemd fmm the: balloon. km} A
—H H “"
t=53 d Una—UKG+LEE—VLG*LEE
{3 : rad1
j 7* =3 fa :JF5u:+ﬂtd——abr=t‘£"3t
Um : ,9 am?)
_h A : L'H} M'll‘: Phys 105 Firsn Midlcnn Page 2 NM. 23. I??? PRGBLEM {I} {25 points) Two blocks. in] = 3.0 kg on the inclined plane (6 =
37"} and m; = 5.0 kg on the horizontal plane are
connected by a light cord over a frictionless pulley. A
force F = 5!] N is acting on m: in a direetion making
53" Iliritli the horizontal as shown. The coefﬁeients of
the static and the kinetic frictions for both blocks and
surfaces are as = 0.3 and is“ = {12. The system is
initially at rest. {1:115 37"” = Sin 53* = 118, sin 37'" = :05
53" = 115, g =1ﬂI misl} {a} li‘the system is released from rest, how does it behave? Explain brieﬂy giving argument to
support your answer. gait dogs net I Asses«E “iivi M 93ele lend/ugh meme Lu ‘qu pupillee dame LilMia le‘lCiFi ﬁqi'Cii
.3: 519ng is + . ‘Lﬁ = Fmﬁg‘: Eatstalﬂﬁ'hl H w
EH ‘Me swim Iii — mess: 1F“ = migmss' 1iner : Ii rﬁgi i s
: lg +{iihlmlgmsss"; + [GiHr‘ﬂgg— Fe
:13 + iiiEllen‘s + iﬂiilEe—ilo}
: [‘ﬁ 4' Tr'll‘l'B 3 RigEH Wire. '2 F... ‘7 2. F. “hue sugsiew 5W1” +0 Wﬁ w Tﬁiﬂﬂdﬁew
{Iii Flnd lhe acceleration o of the blocks.
ErMG'tarbibu: 1F=Mﬂ —:I ‘51: We; M sealslieu “ﬁnalistj we .ittw‘i Lei1; LEMMA ﬁrm. ,_,,'_,.I W
Letleulam.
, ii: = s + iiisires} +ﬂ2i5u’r—‘iﬁl Bil—F :1 lila _:F_ WildML = [3+ E.s +1: iii3N J “Hus” 8* Ans; is: E]. Eﬁmﬂl {ch Find the distance d travelled by ml in 21] s after the system being released. 'I.._,.'' IL
Us=3 I=Ka+bﬂi+i~91L—ha:'liﬂi
t ; 9:055Wl5i {legroeelﬂij: slam l’hgs “15 ﬁrst Mid1cn‘n Page 3 Nos. ill I??? PROBLEM {3] {25 paints} A man is riding en a ﬂatear travelling with a constant speed of IE mi's. He wishes to threw a hall
thmllgh at 51311011”! hﬂﬁP [ﬁxed en the ground] 51} m above the height of his hand in such a
manner that the hall 1wiii he meving heriiszintalljrr as it passes threugh the hnep. He throws the hall
with a speed OH 1345 ntfs with respect to himself. [g = 10' W52}
{a} What must be The venical component of the initial veieeity ef the bail? Variimi Hw+bﬁljut reﬂex—Hug 49 ‘i‘m. ﬁrms in ii
9‘44 FE'QHHIEL +0 Mf1ﬂ+ﬁﬂf will [TE M ngt HtsLe. fw ‘fw. hell I); :
QT = #3:."iﬂﬂii'riz'
"He “‘5'
s ‘5’”
Uh'fL ‘ Jail + “I (Tye)
J : [121:FEC3ir5) Ans; my: ‘fﬂ' “f5. Eh} Haw many Secends after he threw: the hall 1r'Itiil it pass through the heap? \IJEPH Lei! mam .' £1:ng +0.,t
o 2 te—tet
t = '1 3 Phys 1435 First Midwn‘n Page 4 NEW. 2}, 1999 {e} 1Illt'rite the initial velgeilx 93.; of the hall {B} relative to the ground {G} in terms of the unit
vectors?
_.._'.I —5
h“ t lcdcaw
Wag. : We: "i" ﬁfe:6 C If EEG11239159 LJ‘ : LEE 1 + E53
:; [Haiti "4“: LL LJ A II T" Jr A U, J
“ILEEC; '— U‘Etjxl + Jamit: E1  r “t _ " I24?
Ueeig  that: “SHE " Vet; ' éL +161} +
A “I 2 +1 A
$12.; = “health 4" mi 5 {at DJ An$.:93.5 ={lEC 'l'lajﬁmllﬁ PROBLEM {4} [25 paints} Twe mama m. = 4 ltg and :11; = 5 ltg are attached
by a rape ever a frietienless pulley, as shown.
Mass m1 retetes with the pulley in the 1: plane
while mass m: staying at rest on the axis of
tﬂtallﬂn.Tht len 1h 91“ the rope from the pulley 1e
mass m. is L 243,131. Neglect the mass 01' the
pulleyI and rape. {g = lﬁTnfsTj“ I'M {3} Find the tensiﬂn T'm the rape. K5) Fare Mmem. m1”. ZF=O
Tagazo
T: 53 H Phys. E95 Firsl Midlerm Page 5 New. 29. I999 {hj Find angle 9. {ms 3‘?“ = sin. 53” = 0,3, sin 3?“ = mg 53¢ : {L451 sin 300 = mg me 2 351.305 3am: =
sin ﬁt)“ a ﬁt; sin 45* = ms 45” a ﬁg] Ermaga ml: ZFT=O ﬂ Tamﬁ=m,g_ ' :nﬁE—rB—g J " LIT  .'. B: 5?: [a] What is v, thc speed uf mass #1.“? EN mam ml: EFL: MID. . l '
Tmem‘T? ——:u LFL: LEE—fig— . q. (ggyfaEECZ‘JfﬂE} £335.; _ 3,
r  Ur : __—————'—"__"__F _ t: _'
Li
I : 3 “I5 Ans.:v= 3Mf’5
lid} What is N, the number of rotations of mass MI] in It] 5? {Take .1 = 3} Period T = 1W ; Ln“) = H *5 Phys m5 F'Lm Midterm Page t3 Nov. 2!}. 1999 ...
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