Final Exam 8-9

Final Exam 8-9 - Physics 1 Final Exam (AM) 3!20i2009 Name;...

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Unformatted text preview: Physics 1 Final Exam (AM) 3!20i2009 Name; K E Ll) , start 1. (This problem is worth 40 points.) A small object of mass m is released from rest at the top of a frictionless, stationary, semicircular ramp of radius of curvature R. The object then slides down the ramp. (3) At the instant the object has moved an angle 9 down the ramp as shown, what is the speed of the object? Your anSWer should involve no quantifies other than m, R, 0, and g. (It may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answer. “QC”; «3: R ’.._-~ «3: K‘RSMQ Emblem cmsexvai-tm: k.+u,= Kg: 02 0+ M52 : q—{MV2+M8_(E-Esm a) v1: 232mm 8) ‘V=4/2323ma (b) At the instant the object has moved an angle Bdown the ramp as shown, what is the tangential acceleration of the object? Your answer should involve no quantifies other m, R, 0, and 3. (it may or may not involve all of these.) For full credit, show your work, sintplify your answer, and draw a box around your answer. Lacie xi firm (M objec'l': Hat'wa firm; 9’1, o I So '{wwi : mgksme ) Ema (’7 “‘3 < 9/.” WELL-a x-cuxis hmnga 9461‘, 5-0403 +0wa waiter-a? circle 930-6 \x ZFX : mam (90°- 6)= W3 case = max 30 «x wfi SincexMis is Wbpafltl'f‘ms is film: (0) At the instant the object has moved an angle 9 down the ramp as shown, what is the magnitude of the nomalforce that the ramp exerts on the object? Your answer should involve no quantities other than m, R, 0, and g. (It may or may not involve all of these.) For full credit, draw a free-body diagram of the object at this instant, label each force and state what object exerts that force, show your work, simplify your answer, and draw a box amund your answer. a ‘ (flaw Locilr afield aJQ' an object: _ I ZFLr :: 77- mg 005(90~6)= Wang Sli/ie: M447 wmr-Ma wi—Sfeecq V M 0194601? PM 2: V2. SubsHlml-a V=q/2823m6 {30m (30-): 01—.- masme +33 '23ESIM9= Physics I Final Exam (AM) 3l20/2009 Name: 2. (This problem is worth 40 points.) 1‘ T A ball of mass m is launched at an angle of 45° 213 from the horizontal toward a large cylindrical storage tank of diameter D and height 2D. The ball _;A4(§° u is launched from the same level as the base of the i . . . I< tank and 1s a distance 6D away. Ignore air resistance. l 1 Possibly useful information: sin 45° = T , cos 45° 2 -— , tan 45° 2 l 2 J5 (a) What are the minimum and maximum launch speeds that will cause the ball to go into the tank? Your answers should involve no quantities other than m, D, and g. (They may or may not involve all of these.) For full credit, show your work, simplify your answers, and draw a box around each answer. . _ 1‘” Ba." (3.233155 X-= 61)) (1:20 W‘ x=yfi=ép_3 ,t: QED 4-— 69 —a ——>x V2. 2 T v4: 2 v p 352-0 _ fi=&-%3t:2D«efi-6Jf _;*. V01 -21) or‘ so V01: = _’ VG r q _ - -vi: Eli/TD Wimuw: Wfizpax 34.“ 34}: la xr—TD; 3* 2D - X2431 .: 17-D—) ‘i:a V0 ‘--'=H>—-—9 ‘ q92_D2 ’- TT“ 1 «I? a 32 C -____L_ _ _.. 20 (b) [NOTE: You can do this part without first having done part (a).] You launch the ball with a speed such that F it is at the high point of its trajectory when it is directly over the leftmhand side of the storage tank. It turns out the ball is actually a small bomb, and at the high point of its trajectory it explodes into a piece of mass W3 and a piece of mass 2m/3. The piece of mass m/3 falls straight down and the piece of mass 2111/3 flies horizontally to the right. How far to the right of the launch point does the piece of mass 2m13 land? Your answer should involve no quantities other than m, D, and g. (It may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answor. 35L“ LS A'i' WM all». XI-‘éD all? D sz : V0.1: ~ : X W— GD —9 ‘i: V0 Vet-heave Valor/{3‘1 F: z—m a} W ‘ " - =- fi; 64}? 31> L__i VLF—4L 0 -) 4/: VO 6’- '— ~"’5<'“—-- ""—‘> W (9D sz {lava V02: \23D .—9 VozfiéaafB—T M “13%?”an Kamvx = "4;; =4f%' I23!) 2 MW All x~wowuauiwm 6°14 Mi-a pieces? mass 2.44/3 .- SD er-M‘féap .-_- (Ba—w)sz ‘ ~ ~ - D ctr-LA szz—g—‘mgpl' Tth=i1mei~onse~ 54%: £513 = 551; ) So Pieced? (Mags 1442 W our «7? X2 6D‘i‘ KEV Physics 1 Final Exam (AM) 3/20/2009 Name: 3. (This problem is worth 49 points.) A block with mass m} is placed on an inclined plane with slope angle or. This block is connected to a second, hanging block with mass m1, mix, I by a ii ghtweight cord that passes over a small, frictionless pulley that 5 ’ I 1 :1 does not rotate. The coefficient of kinetic friction for the block of - xxx” WT ' mass m] on the inclined plane is ,uk. When the two blocks are reieased, ‘ ' . . the block of mass mI accelerates up the inclined plane and the block of X0! "'2 mass m,_. accelerates downward. (at) During the time that the block of mass m2 deseends a distance d, how much mechanical energy is lost? Your answer should involve no quantities other than m1, m2, 0:, ,uk, 3, and d. (It may or may not involve all of w these.) For full credit, show your work, simplify your answer, and draw a box around your answer. — positive since \ 5° Wvl/Uk 1/ ’3 ts rk $58 fi=flwg 603 W / 33 W W W ‘lwfifilm 5‘! imam" ’de " (b) Find the tension present in the cord while the two blocks are accelerating as described. Your answa should involve no quantities other than m1, mg, or, pk, and 3. (it may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answer. 4% x MW‘SMIMU': _T_7€(—thgswt‘¥= Mlax \ g \‘ [El-r _E M M Clan.” RT! .3 __§ QB S 2 ii 0 SO TflflkmlgmqawlgsiHW—Ml‘ix QM: mgr-fltw.3w-Maasw=0“.sz Mai we ] 5° T: “423"”424x: W‘zfl[’ "“ My 5H4 (Y Wyl-‘Mz (wz—flkm’ casM—wlsmor) Ml+wl { “4‘ng )(l-wkcoamsmcr Ml+m7a :Mrtzg Physics 1 Final Exam (AM) 3/20/2009 4. (This problem is worth 40 points.) A block of mass m is connected to two ideal horizontal springs having force constants k, and k2 as shown. The system is initially in equilibrium on a horizontal surface. The Name: coefficient of kinetic friction between the block and the horizontal surface is [1,. Initially neither spring is stretched or compressed. You now push the block a distance d to the right and release it from rest. (a) How much work did you do to push the block a distance d to the right? Your answer should involve no quantities other than k” 19, m, pk, g, and d. (It may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answer. In Low? 7m, £0: CWCA’WFM emit 73$. 4'? ")7 W3 7* thinning? (b) What is the acceleration of the block just after you release it from rest? Your answer should involve no quantities other than k,, k1, m, ,uk, 3, and d. (It may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answer. AA “’4 <——-"— 23: organza—75,: MK 75 k lg/‘fl‘flwa 50 Hal—PBX “flip/’48 : “Mix ax =3: (so, ) 7%? (c) After several back—and~forth oscillations, the block returns to rest at the position where neither spring is stretched or compressed. What was the total distance that the block traveled from when you released it from rest? Your answers should involve no quantities other than kl, kg, m, ,uk, 3, and 01. (They may or may not involve all of these.) For full credit, show your work, simplify your answer, and draw a box around your answers. 7%3/4? .. .L "‘2 an “*3 EW: E2 : E! + (Mariel-Tm 2 shall—s 1.242 (boa. awe afar col/h Stank?! sire/Maw? E2 :_ 0 (block wade @ rash mm 8,915“? Accident) Lelflzzfioflishmce Meal (Hg)? l E: wigs ( .— Z KEV Physics 1 Final Exam (AM) 3f20l’2009 Name: 5. MULTIPLE CHOICE. (This problem is worth 40 points.) For each question, draw a circle around the one best answer. Each question is Worth 4 points. There is no penalty for guessing. U58 the statements and diagram below to answer questions (a), (b), and (e). The diagram is a view from above of a hockey puck sliding, with a constant velocity, from point “a” to point “b” along a frictionless horizontal surface. When the puck reaches point “b”, it receives an instantaneous horizontal ‘kick’ in the direction of the heavy print arrow. (a) Along which of the frictionless paths below will the hockey puck move after receiving the “kick”? er it receives the “kick” @ (b) The speed of the puck just . I? (i) equals the speed v0 it had before it received the “kick”. (ii) equals the speed v it acquires from the “kick”, and is independent of the speed v0. (iii) equals vn + v. (iv is smaller than either 3 eed v or v. (v) is greater than either of the speeds v0 or 12, but smaller than v0 + v. (e) Along the frictionless path you have chosen, how does the speed of the puck vary after receiving the “kick”? (i) No change. (ii) .on inuously increasing. (iii) Continuously decreasing. (iv) Increasing for a while, and decreasing thereafter. (v) Constant for a whiie, and decreasing thereafter. (CONTINUED ON NEXT PAGE) Physics 1 Final Exam (AM) 3/20/2009 Name: 5. (continued) Refer to the drawing on the right when answering questions (d), (e), and (f). The drawing depicts a block sliding along a frictionless ramp. The eight numbered arrows in the diagram represent directions to be referred to when answering the questions. > (d) When the block is at position I, which of the arrows in the diagram best represents the direction of the net force on the block? . (i) 1 (ii) 2 (iii 3 (v) 5 (vi) 6 (vii) 7 (viii) 8 (ix) None of the arrows, the net force is zero. @ (e) When the block is at position II, which of the arrows in the diagram best represents the direction of the net I force on the block? (ii) 2 (iii) 3 (iv) 4 (v) 5 (vi) 6 (vii) 7 (viii) 8 (ix) None of the arrows, the net force is zero. @ (f) When the block is at position 111, which of the arrows in the diagram best represents the direction of the net force on the block? (i) 1 (ii) 2 (iii) 3 (iv) 4 (v1) 6 (Vii) 7 (viii) 8 (ix) None of the arrows, the net force is zero. (CONTINUED ON NEXT PAGE) Physics 1 Final Exam (AM) 3/2012009 Name: 5. (continued) (g) The positions of two blocks at successive 0.20-second time intervals are represented by the numbered squares in the diagram below. The blocks are moving to the right. Do the blocks ever have the same speed? (i) No. (ii) Yes, at instant 2. (iii) Yes, at instant 5. ' Yes at instants 2 and 5. (v) Yes, at some time during the interval between instants 3 and 4. (h) A ball of mass m, radius R, and moment of inertia 1 begins rolling from rest with constant angular acceleration down a hill. If it takes a time T for the ball to make the first complete revolution, how long will it take the ball to make the second complete revolution? 2 (i)2T _._._‘O(4; '2. (ii)T«E 9— £41,- (“DT 6:0—5 211-: 21r=?'_°<'T '9 T: y . T ()— 2. w J5 0:0etlrr: Nitric/Jr: ‘9 “E: «5&1 = 4/2 T %4fimfir6:’2r+LiWi5 fiT—T=T[4/2fi-l) (VDTl—fi] A —.3 q {g (i) The drawing to the right depicts the paths of two colliding steel balls, P and Q. Jipfi . PQZ k? Which of the arrows below best represents the direction of the impulse applied to ball Q ‘\ x' by ball P during the collision? an if, (ii) (iii) (iv) (V) I, ‘\ I ‘ / \- __._.__.. X ‘A (CONTINUED ON NEXT PAGE) ._‘x (22 ‘ Pact ._':.‘- Physics 1 Final Exam (AM) 3/20/2009 Name: 5. (continued) Ls b (j) Consider the vectors :4 = 31° +4} , E :51: +2]; , and C = 2 j— I}. Which statement about the angle 0 ~ between the vector 24 X if and the vector (3' is correct? (09:0 f A Q (ii)0<0<90° .3 _. J A A A (iii)e=9o° AXE: 3 4 o : 8c -4>J “ZOL (iv) 90° < 0<180° 5 0 2 (v) 9: 180° (vi) not enough information given to decide (reg) . a: (ea—ejazoa), (2ft) ENDOFTHEEXAM : 4242028” <0 0< 6(90 ° ...
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This note was uploaded on 04/24/2011 for the course PHYS 1 taught by Professor Fridluund during the Winter '08 term at UCSB.

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Final Exam 8-9 - Physics 1 Final Exam (AM) 3!20i2009 Name;...

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