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Q1 Three cylinders of the same height are filled with liquid. Cylinder A is filled with liquid mercury (pmercury = 13600 kg/m?3). Cylinders B and C are filled with water (pwater = 1000 kg/m?3). Rank the force exerted by the liquid at the bottom of each container from largest to smallest. 23 A U-tube with one sealed arm and another arm open to the atmosphere is filled with water (density 1000 kg/m?) so hat the left arm is fully filled and water in the right arm is at the same level as the top of the left arm (see plcture) Each ide is of cylindrical shape, with cross-sectional area 100 cm? (left) and 500 cm? (right). = 50 U \ cylinder of volume 0.002 m? and density 500 kg/m? is then placed in the right arm. Assume that the water does not ipill. With the cylinder floating in the right arm, what is the change in pressure at the point P below the top of the =\3. Lg,. iealed arm (i.e. at the point marked with a white cross)? A. Fa=Fg=Fc ’ p ] - " P B. Fa=Fe>Fc @ Increases by 196 Pa P ‘ ! \ 0 AV Men £ Lxpugh p 7777 [ v C. Fc>Fa=Fg B C B. Increases by 304 Pa s 2V B A - = - | Ty D. Fc>Fa>Fs FA=ry r =2r, © v C. Increases by 980 Pa R R Decreases by 980 Pa aﬂ“ oV ¢ Vu,.u,f = V‘d"‘” The pressure at P does not change 4 & bP % e”fi 0-?&& N (000 Lé )(fi!m XO«()(O 00Lm )‘ Patm 0N @FA>FC>FB F: w - h"g % e‘\/‘:g z Q‘ Akfife"nrpthg E.' Frct Guln - '3"€“rL Fo ot Qurg = Q' o~ Q"" Q-V') “f ew s s vaiiela & ‘ + 24 The figure below shows a hyd of same cross-sectional areas. A mass of 100 kg is tput nd a mass of 70 kg on the other A force is being applied at the input arm. The hydraulic lift is illed with water and the system is in equilibrium. Is the shown configuration of the hydraulic lift possible? ) d uuuuuu F Q2 Inthe U-tube sown, there are two different liquids of different densities that do not mix. Both sides of the U-tube 100 kgfi- ‘000 N are open to the air. The dashed lines show points which are at the same height as each other. p 4‘90 '\) 70 kg | Rank the pressures at points 1 to 5, from greatest to smallest. / 1;L\ A, A A// 2 2 5 1 A. P3>P3s>P;>P1=Ps B. P3>Ps>Ps>Py>Py P ?( - P{ * Pahn 3 e)‘ ?‘1 L4 P\){ 0 6N C. P3>Py=Ps4>P1=Ps A. Yes _E. \l_’%:-’-t ?.5"‘ 4 3%; A N { D) Py=Pu>Py>Py=Ps b~ Pue 6 Mok r-ssal.b_ It is not possible to answer this question without knowing the values for A; and A; RG’P" G D. Itis not possible to answer this question without knowing the magnitude F of the applied force E. P3=P3>P1=Ps=P; Q7 Gas flows from left to right through the pipe from points a to b to c. The pipe’s interior is hidden. A manometer (device for measuring p a liquid and is connected directly to the three points along the gas pipe. The liquid levels in the manometer 5|t lowest at point ¢ and highest at point b. 3 Q9 One end of a garden hose of constant diameter is connected to a tap. The absolute pressure at the bottom of the hose is 3 atmospheric pressure (3Pam). What is the maximum height you can take the other end of the hose such that the pressure at the open end of the hose is 1.1Pam. [1 Pam = 1.01 x 10° Pa]. Choose the value that is closest to the answer. The density of water is 1000 kg/m>. At which point does the gas pipe have the smallest inner diameter? A. Pointa . 2 . - A. 10m for o N‘J’h st U2 0 mls = Y, 1.1P, @ @ Point b B. 15m P - ! CJL\ C. Pointc @ 20m h: P('Vz - @ - 11) th +Y c? Pa " Pb —_ —_— n D. Impossible to tell without knowing the liquid’s density. Vee Vg < U, D. 37m Cj Q:‘s [;:D(fi') l 9 A A A, E. 55m Q8 Water (density 1000 kg/m?) is flowing through a horizontal pipe. At some point along the pipe is a blockage that reduces the cross-sectional area of the pipe to only 50% of its original size. What must be the pressure difference (wider minus the narrower section) of the pipe so that the water flows in the narrow section with a speed of 1 m/s? Choose the value that is closest to the answer. 1 A 0 0 _1 05 , ' ‘ (D\ = Pz. e g B. m/4rad 375 Pa ) 2 o T . | Q10 For the shown displacement versus time graph of a simple harmonic oscillator, described by the equation x(t) = (1.0 m) cos (7t + @), what is value of the phase constant ¢? A. C, C @ n/2 rad \Jw‘” 1500 Pa —s Vp =lmls IN) b D. mrad b /P‘ | D. 4500 Pa fi A - A\ E. 3m/2rad B E. 9000 P - a vt s Gelqnt 0 Kue o-S Vs () &% o - . =Y, =05V X({'sO\ - ) = COSqo U Y < O-YMm 2 f-he Sellar-0s)) ae Q5 One kilogram of iron (density 7.8 g/cm?) and one kilogram of aluminum (density 2.7 g/cm?) are dropped into a pool of water where they both sink to the bottom, completely immersed. Which has the larger buoyant force acting on it? A. Theiron. F C. The magnitude of the buoyant force on both is the same. R Vg Ruslh e e = she is standing on her back legs. \ La > \/l. . “fi dF? (g’m " (@t Qe So Fgm b4 F; wa. The aluminum. VA\ = o Neither has a buoyant force because they sunk. E. There’s not enough information to tell. - teh P1/p = hz/h ?a"" i ‘ - ¢ Pfp, = M2fy +2Pum » I h. 0. Pifpy = Mfy, = 2Puem E. None of the above P~ Py Q6 A rock is hanging in air from a string. The tension on the string is measured to be 30 N. A beaker of water (density of - 36N 1000 kg/m?3) is then raised up so that the rock is fully submerged in water but does not touch the bottom. The tension on py‘w e 3L" ,W %L the string is now measured to be 20 N. What is the density of the rock? .L| @ . T ',7>0N ,\/‘ 2 LN ’ A. 1500 kg/m? n B. 2000 kg/m3 0 ‘L @ el ittty 1 ide (left) and 500 cm (right). = SOV K(0™ m® 230N i ik ber st C. 2500 kg/m?3 l/ W i @ 3000 kg/m3 A. Increases by 196 Pa M‘,\ e > P,-\ eufi‘l\ P ) é Increases by 304 Pa e b\; _Al E. 3500 kg/m3 m r Increases by 392 Pa Ru- Fo= €9 Voy = Qo "0Y T I ' e(‘ ' 0P~ Qg 05V . conn‘%)(fix.{_yos )(n._'w-’)‘ Aun <004 3()~ lo (v (LN =y ll,) ‘9/’\} = (N = Qou‘) IUU\)\“J".) Pr - er Q3 A jack-in-the-box can be thought of as a head (of mass 200 g) sitti rtical spring. You compress the spring by 10 cm. To hold it in place you need to apply a force of 10 N. When you remove your hand the head begins to oscillate. What is the period of oscillations of the head? A. 0.06s I S N the mass is at x = 0 cm, and the amplitude of oscillations is 2 cm. B. 0125 Ew o \ 0285 o el e W B ™ Q13 What is the velocity of the block in the lower picture (at t = 1'5)? e - D. 0.86s N - w = Yeep _ o \oo.N[w S @ 0cm/s E 2% vy S-\ow - B. —1cm/s W\ = 2.00 %—\mwfi = O ’lDVX = »N C. -2cm/s P i \f_"_‘f_ﬂr . {Bmo 5 = 22-36 ~ad[g - A w 020 W% D. +lcm/s E. +2cm/s = q{% e \ B39 8 Q14 What can be said about the accelerations of the block in the two pictures? A. The acceleration at t = 0s is zero and positive att=1s < ) . . . i Omi i i i jod T. If the | h of the stri B.) The acceleration at t =0 s is zero and negative at t = 1 s Q4 A simple pendulum of length 10.0 m is executing SHM with a small amplitude and period T. If the length of the string is reduced by a factor of two, the period of oscillations will become C. The accelerationsatt=0s and att=1s are both zero A 20T - F D. The acceleration at t = 0 s positive and positive att=1s 6 s = 2V % E. The accelerationatt=0s is negative and negativeatt=1s i 1 L \: a B ATOTT 2 i e \ =T Vi =2\ X = Q15 If the period of this SHM is 4 s, in which direction is the block in the upper picture moving? E. 05T 4. 2 \\ L =2 2T & e G- (’7— \\\ % = % % A. Itis moving to the left - A m J2 @ It is moving to the right C. Itis not moving at this moment (velocity = 0) D. Not enough information to answer this question. Q5 A block of wood of mass 0.10 kg and density less than that of water is floating in water, only partially submerged. A mass of 0.05 kg is placed on top of the block. The block with mass on top is still floating. The magnitude of the buoyant -~ (1 force exerted by the water on block is: A. 049N B. 098N 0.10kg @ 147N D. 196N N, E. Cannot be determined from the given information b by = e M'f) = (0.1Sk (18 (Ols 5)( sks) =1 N Q6 A cube with sides of 1 cm and density p = 600 kg/m? is suspended from the ceiling. A guarter of its volume is immersed into water with density py = 1000 kg/m>. What is the magnitude of the tension in the rope? 3.4x10° N B. 24x10° N C. 59x10°N D. 0 E. 1.6x10° N 3\/0 ( g 9 z‘s'f‘—’) = (7.4) (0.2lr) (‘009 0% (W‘:) £ Q11 The acceleration of a mass-spring oscillator as a function of time, is shown in the graph. Which of the following statements is correct with respect to the displacement and velocity of the mass at timet =4 s? a(k) < - W% (k) 34 a (m/s"2) ) A. The displacement is positive and velocity is negative. ® The displacement and velocity are both negative. C. The displacement and velocity are both positive. @ The displacement is negative and the velocity is positive. Q12 The position, x, vs time, t, graph for a mass on a spring is given. Which of the velocity, v, vs time, t, graphs below correspond to the given ) position-time graph? A v (A) v () £ 5 £.5 " © ® NN i} c (© el / / D. (D) v (€) v (D) oy E. None of these velocity-time graphs. / \ i \ t / Y x \\ AW Nl - | ol M, Q“M:( fav\‘ = 'd«.‘\ 33 he Q5 The graphs below represent a snapshot graph (position plot) of a wave at time t=1 s and a history graph (time plot) of a point in the presence of this wave, located at x=1 m. Which of the following equations correctly describes the wave equation for the wave represented by these graphs? = ? & \ N= 2om B 04 gl 4= o 02— - - — a 0 ; ; ' \ V= Kos 2 4 5 6 1 8 -021—/ t(s) ; -0.4 \/ \ A. D(x,t) = (0.5 m)sin(mx — mt) B. D(x,t) = (0.5 m)sin(mx + mt) Ve./D(x, t) = (0.5 m)sin(mx + g t+ g) D. D(x,t) = (0.5 m)sin(mx +t) E. D(x,t) = (0.5 m)sin(mx — 2t +7) EX\ ™ (X, %) Lo.gmys\\;(’;}—x:‘\. = (s-5w) sxv:('\Yx—_-\_‘%‘t—\-C\)\, So Mo awswer v eifet €, D on B Caow DL, 1) ‘6""“\" we see W DO, = —-0'5m D (\,0) = (0:5w) sw (T~ ‘\7\4 —o'5wm = 6\»&(1(*-62\'-‘-—-\ & = et Puk Sw L?’l‘-_;_\ wet 4 1‘;—_. = DUty = (0:5m) Sw (—Wx;?ik;-\“i) ¥ VW At £=\ Frew D(LGE) we 3 Wt \>on¥u,\e. & dstl w . ‘I\“\ ?ﬂwfi‘ébb““ we_ Seé. ‘“"a‘ Voo W@ Wy wese Yewads \efr. awswet v Con & Seo “0\;\-—:« \L,k (—-\' e velo

Q1 Consider the displacement versus time graph of a damped harmonic oscillator shown below. If the mass attached t the spring is 1.0 kg, what is the damping constant of this oscillator to two significant figures? 0.6 LS8 A o\ [ 1 ' Yo t(s) i -0.4 ( v -0.6- | Q11 On a standing wave pattern the distance between two consecutive nodes is 0.25 m. If the wave speed on the string is measured to be 200 m/s, what is the frequency of the standing wave? A. 50 Hz B. 340 Hz C. 100 Hz D. 680 Hz \/EAOO Hz Q9 A mass () is hanging on the end of a string of length L . When you pluck the string, you observe that the pulse moves along the string at 20 m/s. You replace the mass with one that is 3 times heavier (3 7). This stretches the string by 20% (1.2 L ) What is the new wave speed? - B oo R ‘ \,\ ’5_ = Q20 \i;- l ,):.—:.OQ-SYV\ = X’-—'- o.S5owm A. 72m;s I“'\ P‘ 2 B. 60m/s e % ¢ - N -~ 260 ws C. 35m/s s o i—a“g P Tt \] = g’ P 0. 90 W VBASm/s t)-,_ HL G w\_‘w E. 32m/s w 1\/ Q12 Rank the frequencies of the three standing waves depicted below, assuming that they all are under the same tension and the strings have the same linear mass densities. The vertical dotted line is to aid in comparing the SRRV - /zm \/A/O10kg/s Ay = A = w=\-0 kg B. 0.20 kg/s »‘ (0\ = P\ »” o 6 i \ov C. 0.22kg/s e wavelengths. D. 0.40 kg/s : Aldys (o0:8w) & B R Faom groln A= o-3ew A fa<fo=fe o \O = Ten Bo vk B. fc<fo=fa AUz (0Sw) < = O° \5 b( ’ C. fa<fo<fc B 3 ” :%‘0.6 P fo=fe<fa i NN (0-6) = o\ \ﬂ“ls E. Not enough information ~ i mlig) WE S Q2 At t=10s, the energy of the oscillations shown in Q1 is A. zero 2 \D_,Y. WA \/B./at36%ofitsinitialvalue c &) = < o) & i . ~\oXx O- C. at 60% of its initial value - \o’x__\b s (Al ™ - D. at 78% of its initial value EL\D\ =z Bl & = © (o) E. the same as its initial value N e ()= s & R o1 . &=l € (o) >\o\ < >\\o"’>\Q T v v string with linear mass density 2, w fb string the same? A M/2 fe B. M/2 , c M 7' D. V2M Y In the presen: between two is given by: r 'b‘“‘%ul) 0 Na l g—_l % _i s @T@ . 20w 229 = s Q10 A string with linear mass density p is held at tension by a hanging weight with mass M. If this string is replaced by a hat replacement mass would keep the wave speed on the horizontal part of the Ay | E }A.-—; 3_?;, Yok W wss:M, ™ ,__iMl% —;J% ap r ce of a wave of wavelength A the phase difference points of the medium, that are a distance Ax apart J » Sowme g,“’au‘o\-(-\'\‘ " 5 S, ? - Z S;_ 5 = D =C & A phase difference = (27”) Ax‘ Q13 A standing wave is oscillating on a string at 700 Hz, as shown in the figure. What is the speed of the travelling waves Q6 The wave equations of three different waves (A, B and C) are given below: ~&— A 2 - Dy (x, t) = (1.0 m) sin(5x + 3t) that produce this standing wave? D, (x,t) = (2.0 m) sin(3x + 5t + ) A. 340m/s B. 210m D3(x,t) = (1.5 m) sin(10x + 11t) i C. 410 m/s Rank the wave speeds of these three waves, from highest to lowest D7 280 m/s A. D1>D,>D R N ""/$ E. 140 m/s VB/Dz >D3>Dy > C. D,>D1>Ds3 9\ Q/\( = /g D. D3>D;>D; P, w/w = 5)3 \ PP P> D\ E. D;<D;>D; B w/% = “/\o Q7 For the wave D5(x,t) = (1.5 m) sin(10x + 11¢t), what is the transverse speed of a particle located atx=1matt=1s? S; - “\oo k2 ' \ = hoewm =0 Lo w 1@@@ g N 60 cm oo W2 x o- ko w = 1%0‘“[3, Q14 A pipe has two consecutive resonances at frequencies 900 Hz and 1500 Hz. There are no other resonances between these two. What is the fundamental frequency of the pipe and is it open at both ends or open at one and A. 0.82m/s ) (\ \\t) closed at the other end? B 3 > = \.Sw)sﬂ\h oX¥% \/B' 1.3 m/s $? Wk = :’b (x"t\ L \)/300 Hz open-closed C.%9.0m/s \\{7) - ] " 300 Hz open - open " 5 )(\) cos (Nox~ D. 14m/s Np (% vt) (%) 600 Hz open - closed E. 17m/s ’:\\QL)(:\)‘\'-’\B" _q.0% Mk D. 900Hz open -open E. None of the above options spert = (ol | Q8 Consider the history graph (time plot) and snapshot graph (position plot) of a wave. The snapshot graph was taken at t = 0. The wave is travelling to the left. Which location marked on the snapshot graph can plausibly produce the history graph? gm-\-\ =\ 500 \2 AC = Geo w2 = § T (> % dher-don Wou W \orwonio oste A Yk Y wob Ba e AD= ooz = 25 @Peu—dfikg\ Qoo k2 ¢ Goolk, \2oolk2, o\gm— clese™ S\ = Deo W2 Wignex Natweawis £ Qoo (Bl S3) Q15 A hollow tube is open at one end and closed at the other end. It is observed that standing sound waves in this tu - \/:/} : 2 /\ /\ /\ /\ T A C/\t & } the speed of sound in air to be 340 m/s. C c i ; I I \ l E " / \ / / \/085m ED_Z = : \ \ \ \ A —]/\\/ \/ B A . None of these \ \ \ \/ , BE'\/ C. 34m -2 1 : o = i D. 42m =2 0 t%s) 4 6 - " im) % 6 E. 85m Az3wm Tz 25 5 For the shown snapshot and history plots determine the wave equation i.e. D(x,t). — o T Z Aw )\:\N T=Ls A=0:5m T ] . AT I X 2 \ DNt | = (05) M \/(m) \/ w(ax g5t = B4l G ) v D(0,1) X=0 T=4s Plalesn) N /N s (WX -’%_—(:) '[\/‘ 3 (\\/ P " y\ejax—wl $\o\>¢ A harmonic wave is passing through a medium and the history graph of] a point located at x = 2 is shown. Determine the equation for D(x,t) for can be produced at 300 Hz and 500 Hz and none between these two frequencies. What is the length of this tube? Tak P R— 20X = ’2":\ x\a \00\‘\}-' N - L §¢ A = 3o “$s = I x\oo &2 L= 0:95M S\w (T-”\Y-h'\' \‘/ this wave and draw the snapshot graph of the wave 1=1s 15 x=2m A=0-Sm \l-’—f‘-—‘; o6 )\"7—"“ T=25§ D(2,1) (m) 04] /\v 40m/s/\ )\_— & w 0.2 )\—Q S M Sim (lx-'fi, ‘('4)) ° I D(Xt\=(o6m Dl | = (o'5™) | : >(210)= (o-S\v\\slfi(g’"' “7) = (-o-5wm) 2 (] {—Q\—--—\ s (30 \‘: For the shown time and position plots determine the wave equation 18 DXG1): . \ D(x,1 A=lm T=1\5 \ /I\ /\ / VEEVERVE v 'D(x\'l\ = (p.8m) sm (T x 2w &B =0, t=1 D(1,1) Y=\ '])(O,$z: lO‘GM> = e (a+ 8\ =05 M \/ b o & \/"\e‘“\r\-\-\vc S\Dk-‘ “Uwn (,7«“*4’)‘( ari (@ d) ()= =T D(X\’\' \= = E IR ] (D'Sm)SlJ\(E\;X <k a -WB (D*SM)SI\; (—\'{-(X’}{'yo (o-Em)é\k("%x\ Siw (‘nx—-..t & A?S DX ioy=(0:-6w) S\n(‘\T)L+ &) & 'D(o~5,o') =0 6w) s (1;-\'«))-; obm \ si (T4 p)=+) &=0 e Ax Phase difference (rad) 0 0 M4 /2 N2 T 3N4 31/2 The mass attacl " - X(t) (m) [N\ SN/ (=] — o€ At\=h e ™7 oY= A= A(\\: p I = a’M:\' LE_;'-O'v\S >3 \ — Y\ — 8 The snapshot graph at t=0 of a wave is shown. Determine the equation for D(x,t) for this wave and draw the history graph of a point located at ‘/D(X\-t )= (o~ bw) SM('\V\L’%\—:&) o.er D(x.0) SAvVAIvAR-S oo Ww(o-1%) b :«1\««\\&!03‘3} \WA b= o-5% K’(;/g 2 — b E() = E)=EG)e — B PR ) E(Z\ :‘-ECOXE/ ..2_x0~‘5@ /\.p E(2) < R S = (%) ~ O?;_é_;\ Smahdt T0 Mok Question 11 1 pts Consider the hlstory and snapshot graphs of a wave shown below. The snapshot graph g to the left. Nhich rked on th hot h plausibly produce the history v graph? q v=0.5m/s / . /\ 3 2 X g 0 : 7 t(s) o D (meters) -0.6 \» A —~— D (Q;b) I\ P - Sht) (o o) sx (2= 24 (0-6wyam (-—E‘t) S\fi(—@ \= - am®d ocC OA C(oemysm | ) - R

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