exam3solutions

exam3solutions - PHYSICS-2161 Spring Semester 2011...

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Unformatted text preview: PHYSICS-2161 Spring Semester 2011 Instructor and section (circle yours) Examination 3 15 March 2011 Chastain (I) Chastain (6) Rupnik (3) Rupnik (4) Rupnfk (5) ' Giammanco (2) Jin (7) Plummer (9) Name (print) . K LSU ID Signature TURN OFF AND PUT AWAY ALL CELL PHONES, PAGERS, iPods, MP3s, OR ANY OTHER COMMUNICATIONS, AUDIO, OR VIDEO DEVICES Have your LSU ID ready when you turn in your paper. You may not use cell phone or smart phone application as your calculator. You may use an ordinary scientific or even graphing type calculator, as long as it is not of the "full keyboard" sort. Examine your paper to be sure it is complete and legible. There should be 3 problems and 3 questions, totaling 100 points. Examine your formula sheet as well. It should include only 1 page, stapled to the back of this test paper. For the three multiple choice Questions, clearly indicate your selected answer for each of the part(s) of the question by circling your selection. For these questions there will be only one correct response. There is room on the paper for scratch work or calculations, but that work will not be checked or graded. There is no partial credit awarded for multiple choice questions. For the three problems= show your work in the space provided. Even a correct answer, without supporting work, will receive little or no credit. Partial credit may be awarded for problems if warranted. Be-sure that numerical answers appear with appropriate SI units. Points will be deducted for missing, incorrect, or "silly" units. If the final answer is, in fact, a dimensionless quantity, please write the numerical result followed by the word ”dimensi0nless.” If you need more room for. your problem solution you may write on the back of the page, but be sure to add a note to look on the back. Otherwise anything on the back of the paper will be regarded as scratch work and will not be checked or graded. Solutions will be posted to the course web page within a few days. Question 1 (12 points) The figure shows a flywheel rotating counter-clockwise about a horizontal axis perpendicular to the page with an angular velocity of (D. The flywheel slows to a stop with a constant angular acceleration. P is a point on the rim of the flywhee- a: W a) (4 points) The direction of the angular acceleration of the flywheel is a} into the page ® beam} 53' «(‘0 G M 2 LS 0FP0£€7L€ dream-M W Wma Slows atom, b) out of the page 0 ) c) upward T d) downward J, b) (4 points) The direction of the net torque acting on the flywheel is _‘__ ' "> ‘ . into the page ® {the}; 7: I x 3 0g» .5, b) out of the page 0 M 0< 06‘6" “HOE c) upward T d) downward l .A A ‘—P c) (4 points) The approximate vector direction of the linear acceleration of point P is (circle one) i \ Problem 1 (22 points) The figure shows two blocks of mass M and 2M respectively, Where M = 3.0 kg. The blocks slide along frictionless surfaces. Initially, the block of mass 2M is moving to J the right with a constant speed of 4.0 m/s, and __ """"""""""""""""""""" " the block of mass M is at rest. The blocks ad: refi- collide completely ineIastically and slide as aflp the fiictionless inclined surface. W_ a :Hcl game i“ a) (7 points) Calculate the speed of the two blocks just after they collide. r r m LS welded 5194'. = if”? , because ZM—M $7346 2M4)“ = (amt/1)»? 45;: 7. b) (4 points) Calculate the kinetic energy of the two-block system just after they collide. K I Kg,JM : flam'ff: éMGZ-g’lr): 33:- M$1%@%)(4gy e 0 o gill/Qijk?“ :3 ll u) M93651: Golti'gfflfi PDL’ K- _ 1‘ M+2M Ll: J'afi‘i k( A]? 2.0} 242:»; #5563% 7: ‘—"“"—""’ :5 3 C: W l:— ‘ - z. in £2 ...__ we T3 ea 9% amt-9% d) (4 points) Compared to the kinetic ene gy of the two block system just before the collision, the kinetic energy just after the collision is a) larger A K4 0 gen ate/Mei Mme—t ‘ d)thesame ( Slug/f kl“ Question 2 (12 points) The figure shows an overhead View of a uniform disk rotating about a vertical axis through its center. Also pictured is one individual of the species Solenopsis invicta Buren, the common southern fire ant. The ant begins at the outer rim of the disk and crawls directly toward the center. a) (4 points) As the ant crawls towards the center, the rotational inertia (i. e. moment of inertia) of the disk—ant system about the axis through the center of the disk a) increases creases : 416 4115/ anvil, E r: c) remains constant W M R; +0 Lu, ‘ ‘ “area A“ «as: (1) cannot be determined 6 ‘HLE. ‘L afi/ dirk scarf: Hie £qM€ a» IS S 4%; Isys j ‘ Lelé’gre b) (4 points) As the ant crawls towards the center, the magnitude of the angular momentum of the disk-ant system about the axis through the center of the disk C - c t - * %I4éfl;&14 Mattie MS “‘7 , a WM boo a) increases —-—> b) decreases 3%? :1 9410 0) remains constant d) cannot be determined : 3 e) (4 points) As the ant crawls towards the center, the magnitude of the angular speed of the disk-ant system b) decreases c) remains constant. . a Cu” WWW szujo d) cannot be deterrnrned 90 g6 # was: Lama: (LL War #3664 Problem 2 (20 points) In the figure a block of mass M hangs at the end of a cord of negligible mass that is wrapped around a uniform solid disk also of mass M and radius R that is free to rotate about a horizontal frictionless axis through its center. The cord does not slip. It simply unwinds as the system moves. The system is released from rest. _ a) (10 points) Obtain an expression for the angular acceleration of the disk. Express your answer in terms (as needed) of M, R, g, and numerical constants. » eomflctoes mot at}: ea :— at = 04 R c) (4 points) The direction of the block’s angular momentum, about the center of the disk, while the block is moving, is a) towards the top margin of this paper b) towards the bottom margin of this paper 0) out of the paper ) 1nto the paper e) the block has no angular momentum Question 3 (12 points) The figure shows a cross section View of a unique salad bowl. The left-hand side of the bowl is rough, and the right-hand side is smooth and frictionless. A uniform object that rolls without slipping begins from rest at a height, H, above the bottom of the bowl. The object will roll without slipping to the bottom of the bowl and then slide upwards along the frictionless ri t—hand side. ' —-- gh r‘ollrm e> 412m *' ‘0 K a) (4 points) Which kind of uniform object (all with identical masses and radii) would roll to the bottom of the bowl first? I(°M a) a thin hoop l 0.5, Miler“ 'i’hé KWX ’5: 0,87 - t c)ahollow sphere 97/ ‘ Sowd dick has [a SMHQSrf/S so (1L (1) all reach the bottom at the same time W fig KL!“ 9? 591146 b) (5 points) if the object were a solid sphere, the total kinetic energy as it is rolling would be expressed as M a) éMvEm =35: tortfie 80:4 sphere ’2- b) évam K‘iKa‘L KM=?LM%W+-é(§gfizj(%>7 . gl+el=i%'§ d) 1—76Mv fl— e) 2M»); 0) (3 points) As the object slides upwards along the right-hand side, the maximum height attained, with respect to the position of its center of mass when at the bottom, is a)equaltoH . here {3 no Weill-,6 deéjiéo rite wit? 94370 its Mafia—mat mam (arr—c) 12a- 0+ we saw owe weft KW wet/mam loom a he hwaaeum +07% W We < H be ‘ Mo : R Mu Crew“ f Wfifim b4 c) greater than H d) none of the above Problem 3 (22 points) In the figure a plastic block of mass 010 kg is sliding with velocity v on a frictionless surface towards an initially stationary uniform thin rod with length, L, of 2.4 In and rotational inertia, I, of 2.0 kg—In2 about the frictionless ivot at the upper end. The block collides with the lower end of the rod. After a very short collision, the block is at rest and the rod swings upwards. The rod stops when its center of mass rises to a height fd=0.15 .' a. O m :0: atom a) (4 points) Use the Parallel Axis Theorem to Show that the rotational inertia of the thin rod rotating about its upper end is I 2 1MB __ “’ij ‘m/KL-r3 IO“ ICW+ M x?» Mere h: E = HL" L“: '2' L 2 Ta: + Mesa—wens b) ( 7 no" ts) Calculate the angular velocity of the rod just after the collision. - mi notes (mares) 50W “+2 MM «is by i=1 was Wfififl‘ltwc Cu. W pogfi‘w " K o o . at;ng W {S ij ?C2— fiqomgQZ-Plgfimé Khoifiwt.’ W Khém5§19w+ M4?— I :::l’ll_.2",7s> “-31; 22,30 ng)‘ We? ing fi%?dg%, cht ‘ gwfiflslia’hhzfit mi:- ll “2% a!“ $308+!“ c) (7 points) Calculate the initial speed, v, of the sliding block, PMé‘t’Mtwtgo g 2&- =Z7Qf .. _ QW’WWL MW. 9M} blade mugs mt 4.3 cut tail“ 2 ) M ) M 612: £6414 W a=ID¢o¥JaLW.HMfif W/ ,7 Mag-lelowp - , Iowa =M/= 4’" on (margin) (1) (4 points) What quantity or quantities is/are conserved during motion of the rod AFTER the collision between the block and the rod? 3) angular momentum & cliff We? 72,6 21:3 0) both mechanical energy and angular momentum E d) neither mechanical energy nor angular momentum ...
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exam3solutions - PHYSICS-2161 Spring Semester 2011...

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