FinalExam_solutions

FinalExam_solutions - Physics 2101, Final Exam, Spring 2008...

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Unformatted text preview: Physics 2101, Final Exam, Spring 2008 May 8, 2008 KEY Name: ______________________s-___hw_______________________u____m_______________ Section: (Circle one) 1 (Rupnik, MWF 8:40am) 2 (Giammanco, MWF 10:40am) 3 (Gonzalez, MWF 12:40pm) 4 (Rupnik, MWF 2:40pm) 5 (Rupnik, TTh 9:10am) 6 (Sheehy, TTh 12:10pm) 0 Please be sure to write your name and circle your section above. a For the questions, no work needs to be shown (there is no partial credit). 0 Please carry units through your calculations when needed, lack of units will result in a loss of points. a You may use scientific or graphing calculators, but you must derive your answer and explain your work. :- Feel free to detach, use and keep the formula sheet. No other reference material is allowed during the exam. 0 For the problems, explain your reasoning as much as possible. Partial credit will be awarded, and correct answers with no work shown will not receive full credit. a GOOD LUCK! Question 1 (7 pts): The figure shows a. plot of potential energy versus position U (at) of a conservative force F(m). A particle is at point x = b at t = 0, moving towards the left. It temporarily stops when it reaches 5': = a, and then it begins moving towards the right. I E, __ “(4) with W46 KM)" 0 (a) (3pts) What is the maximum kinetic energy that the particle will have ? EM: um) K: Eta/“Vb :hwr Jfozluf 1> (b) (2pts) Will the particle ever reach point :1? Yes We need more information to decide. (c) (2pts) What are the turning points for this particle’s motion? a,b,c a,c,f b,d,e Question 2 (6pts): In the figure shown, block 2, with mass M , is at rest on a frictionless surface and touching the end of a relaxed spring of constant k. The other end of the spring is fixed to a wall. Block 1, of mass 2M, traveling at speed in, collides with block 2, and the two blocks stick together, beginning an oscillation witgirequency w. The collision happens in a very short time. ‘ r ‘5" 40wa 16W? Mkfic 2M M . . 9| I (Lei/19m“. 2ft; == in if 11'; r: 5% ’U‘ 2. W 73- 1 (a) (2pts) What is the velocity of the two blocks together just after the collision? U1 2121 111/ 3 1.5/2 (b) (Zpts) If the collision happens at t = 0, and the origin of the 2: axis is at the position of block 2 before the collision, with the positive direction to the right. which of these expressions describe the oscillation after the collision? ascriber : (c) (2pts) Now imagine block 1 bounces off of block 2 instead of sticking. Which equation correctly describes the requency tug, of the resulting motion? “WW“‘ mi w e warm on, < w cut. = to It depends on the final velocity of block 1 Qution 3 (Bpts) The figure shows two blocks, with the same mass M,_COnnected by a massless string over a pulley with rotational inertia I. The string does not slip over the pulley, there is no friction force between the table and the sliding block; the pulley’s axis is frictionls. The system is released from rest, and the sliding block moves to the right. while the hanging block moves down. (a) (2pt) Which tension has larger magnitude? Ta. lmfifli‘fldfi 5' ; ® T2 The tens-ions are equal \i _. _. m, T mu amasse- =~r meet—R; >er I (b) (2pts) The net work done by the tension forces on the pulley is zero negative W:- Z’AB =(n—Tin9E— 43-71)“ >0 because ffhlil (c) (2pts) Assume that 'u is the velocity of the sliding block just before the other block strikes the floor, after traveling a distance H from rest. Assume that w is the angular velocity of the pulley at the same time. What is the kinetic energy of the system consisting of both blocks and the pulley at that time? «My: 1H FLT—1— %Mv2 Mu2 %M‘u2 + §Iw2 M‘s2 + ya? My? + Iwz .- = ‘L 7— 1... ‘2— Problem 1(13pts): A uniform beam of length L is supported by a cable perpendicular to the beam and a hinge at angle 9. The tension in the cable is T. Express your answers to the following questions in terms of T, g, L, 9 and numerical constants as needed. (a) (3pts) Next to the figure, draw a. ‘ee body diagram for the beam. (13) (3pts) What is the mass of the beam? , ,/ 1e. ‘ 22;,“ —o ~IfLT—M32 he (c) (4pts) What is the force of the hinge on the beam. rite an expressions for the magnitude of the horizontal and vertical compone orce. 2?; =0 :47“ eTaaG #11“; :1"le ' 21* _ Zfieo =fi+Tme—Mg=0 e2 ¥vzmquh€9= m T519 215' z_ : vfiT '—"""&Me 3&6 (d) (3pts) The cable snaps. Just after the cable snaps, what is the magnitude of the angular acceleration of the beam about the hinge? IA; m L’- L: : “L2- Ti" * 2- ’ ‘5‘ 4; Problem 2 (12pts): A solid disk of mass M = 1.5kg and radius R = 0.10111 is hanging from a massless thin rod of length D = 1.2m. (a) (2 pts) What is the rotational inertia of the disk-rod system with respect to the attachment point P? I z 110,“ + M “In” New MR f) If: “4;: Manse thesis-shawl; IF; awestm‘l— 2.51%” [b) (3 pts) A bullet with mass m = 20.05 is fired horizontally towards the center of mass of the disk with a speed of so = 500 m/s. In unit vector notation, what is the angular momentum E of the bullet with respect to point P just before it collides with the disk? Use the coordinate system with axes as shown in the figure. with the z—axis out of the page. 3 text’- = «(mam merges”) (1- @0500) ’3, If!” ‘1’”; t: ga'o ‘LJ where £=D+R ‘mfif meat arm for bki’é‘i'fs 2L1: = 2 Lee m?alar mmfmmrefaiivf “(v PM P (c) (4 pts) After the very short collision, the bullet gets embedded in the disk. In unit vector notation, what is the angular velocity :3 of the thin rod-bullet-disk system just after the collision? z':.- 2.94.2g+(0.02)(l. 3): 2.9763 (d) (3 pts) Find the distance h. to which the center of mass of the disk-bullet system swings after the collision. Problem 3 (12 pts): Three spheres with the same mass M are placed in the positiOns shown in the figure, with spheres B and C on the x-axis, and sphere A on the y axis. at a distance D from the origin- Express your answer to the following questions in terms of M , D, Newton’s constant G and numerical constants as needed. A- a [as i: “Muse (a) (5 pts) In unit-vector notation, what is the gravitational force on A due to B and C? F:F + F0: 2 gal-m9 (j) 176ng Gompomds 409ml M “'3 __ M we=-—-—D—=”Jl~£ M! l‘6 2- M 55 (Ni) -* M2" __ - GMQ' -4 ) (b) (5 pts) What is the total gravitational potential energy stored in the system? Assume U = 0 at infinity. ' ——._.—- __.—-—- Lewsé 19:“"6'fl‘r 6’ ML .- éwswa 59’ 52¢ Qa Mere g6: 2D (0) (2 pts) Initially, all Spheres were at rest at an infinite distance; you brought them one by one and set them at the positions shown in the figure, again at rest. What is the total work done by you to assemble the system? WEAK where W: W?+WW “202 AK-io) Wf *1”? it“: rwfzsu‘} : uwr ._= -— 52% (1+2VE> __._-—-- --—-‘“ “Axe— tame as-lfie cmwu;(b)* 7 Question 4 (6 pts) The figure shows a dark liquid and a. light liquid in static equilibrium in a. U-tube. (a) (2pts) Which liquid has a. higher density? fi)dmknqmd -- ' ' la feed (iii) They have the same density {(3 '4 (iv) We cannot tell from information given (b) (Zpts) Consider the horizontal level indicated by the lowest dashed line, at the deep end of the dark liquid. At that level, is the prsure in the left tube larger, smaller, or equal to the pressure on the right tube? larger smaller W527 «fiafi'lfi’iéfflaeironi’ one /‘ ‘aé/ES‘JDI‘E has +0 Be- ‘lfie Came rng4 f (c) (2pts) Assume the density of th - a 1: liquid is pd, the density of the light liquid is .01. and gig is atmospheric pressure. What ‘ o express the pressure at the lowest point inside the tube? ¢L=F+g;53:fo+ggé,+fi?fiz W “*4”? ‘fifdkfiwwfip i) P0 + glplhz + Pdhi i1 1):; + p19(h1 + hz) film+flmm+mMJ (1") Po + 91053 - he) Question 5 (Tpts): The figure showa three waves, #1, #2 and #3, that are separately sent along the same string that is stretched under the same tension 1', along the z axis. The grid shows equal divisions in the vertical and horizontal scales. (a) (2pts) Which wave has has the largest speed? (1) (2) (3) (1) and (2) are equal (2) and (3) are equal All are equal (b) (2pts) Which wave has the shortest period? 22413 ’1? 1331:4745 (2) and (3) are equal All are equal (c) (3pts) In which wave is the maximum vertical velocity of the string particles the largest? Afl=$w==mh [We/f?“ fiaqflr? j. l T p 7__ 7. m 2 2.51 335,, ® (2) (3) (1) and (2) are equal (2) and (3) are equal All are equal Lb? wiped-(50k of he flo'l’ ”' Md: Q #Ec‘ce x/ war Problem 4 (12pts) : A 40g piece of ice is taken from the freezer at —15.0°C, and drOpped in to 200g of water in a thermally insulated container, initially atwAfter a. while, the system reaches an equilibrium temperature T; > 0°. Aw- ; ?/1)Tm1 3Q :; Z. Z Z fig; 3 33 (a) (3pts) What is the heat absorbed by the ice after it warmed up to 0° C? Q? “m 0m [Orr—15426 ):(407)(2.22%A{0"1 19%): 1332 2/ w}; (b) (3pts) What is the heat absorbed by the ice to completely melt at T = 0°C? Qm’z ; «Ital; {flog/333 7/? )2: 3520} QM = lazy/3320 #4652} (c) (3pts) What would be the heat released by the water if it had cooled down to freezing temperature, 0°C? 62% W =- mam m'c "25°C):(2003){4,/67é:§1){#2§)= #20 (730 EL inmlflthQ’ 3—" W “au""“w mm tam;- ' tenpémfifi (d) {3pts) What is the actual final equilibrium temperature T}? iahe 2'" (“>69 4 “(10) (11¢ 7;; [Quail “"‘che M 6.25% gag. 3°C [wafCQ-‘F em (4./8’é5%):277 K fifl—F terse: and 4‘66 meet“? "Tun; ) + “14¢ 2% (aw—594) + “9"” L? + “45¢ fay-(Ed C) :0 T f 7;”; “#4:: (0?”751' im‘ L := Wfié‘aof IF..— (“#4. m“. (2W7)(4:/8’é’722) =1” 10 Question 6 (7pts) : In the p—V diagram shown in the figure, an ideal gas undergoes an isothermal expansion. then a pressure reduction at constant volume, and finally an adiabatic compression to the initial volume. (a) (2pts) In which of the three processes is the gas absorbing heat? m—-—-—-———-——-——-" 2 —* 3 3 —> 1 All of them None of them 1m; {'50 fraud! “WHOM 11v K66? W6 tow and do #3 Poi-Hike Work, 345 MC '5 assorb flame! ate/~93. (b) (3pts) In which of the three processes is the gas decreasing entropy? «He‘s—fie Q4 o a 62" ,3 AS =5ng 1 —v 2 o 3 ~—+ 1 All of them None of them Cfiurw} lessons reduafi‘on «f Mai!— Mmé‘; gas has 7%: P662121 had gym/Arm) ’9 (Q40 )fiffigudeS c‘r‘fflfW6 a-F‘fiF {c} (2pts) The cycle1—+2~+3—b1is:i {01‘ Q3 )3 a heat engine a refrigerator neither a heat engine nor a refrigerator bemce #6 jaw? does Pogmfif tow-é m aye/é 11 Problem 5 (12 pts): In the p—V diagram shown in the figure, two moles of an idea] diatomic gas undergo the processes shown in the figure. The initial pressure and temperature at point 1 are p1 = latm and T1: 300K. 1 46:2214-6' v, aoov1 Volume. V1: V3: 3v; R" 9’3, g/m-K (a) (4pts) What is the initial volume, at point 1? V; 91—8-1; 3 W :.0. 0493571414,!3 003mg I ff LNKIO FE, ) Er. 0 (b) (4 pts) What are the pressure and temperature at point 3? 3" {WV/r: 3"HL'" Wbafi‘c Frames; (or Pvt-Cond- r 4? k H- usk/0&2 2,;é7xm CL one": we; H) H (c) (4 pts) What are the work done by the gas and the change in internal energy of the gas in the process 3 —» 1? AE;;‘%” W3; A2,?mév(flr'fé):l{£){5"39(soo»M23) Ag]: 41,353, I (mhfik (K3 :3” w :-4433}- 12 I 3! ...
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FinalExam_solutions - Physics 2101, Final Exam, Spring 2008...

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