Physics 140 Winter 2014 Final Exam April 25 2014 Form 1 50L uTIO S Your name First Last M i A4 Your UMID number Fill in your name student ID number and form number on the scantron and in the spaces above All cell phones text massaging devices computers and communication devices of any type must be turned off and stowed out of sight The exam is closed book You may use four 3 x5 7 5 cm x 12 5 cm notecards both sides You may also use a calculator that cannot communicate with the outside world You cannot share calculators notecards scratch paper exam booklets or scantrons Exam responses must be based on your individual work only You must mark the correct answer on the scantron to get credit for each problem The exam is 125 minutes long There are 26 multiple choice questions All questions are of equal value There is no penalty for guessing At the end of the exam hand in your scantron and show your UM ID Constants and equations you may find useful xo x 2 Vx Ox 1 o 6 CO v j 0 2 at 2 V3 at WOz 2a x xo 2 2 a t w t 0 a t 2a O 6o Ro v dv dt Rc 7 7 arad v R VJC AIB VB C continued on the next page Table 9 2 Moments of Inertia of Various Bodies a b Slender rod LLXIS ii itiiih Slender rod axis hroiieli center I c OTIC end d Thin reetanirular plate ectangular plate a i tluoiili eefltet 2 ML I axis along edge 1 Ma I e I f Solid cylinder Hollov cx under w R I 2 MR I I sphere 1 2 MR I Thin walled holloxv h Solid sphere g Thin walled hollow cylinder 1 2 MR 2 S I R R 2 MR continued from the previous page 2 m r2 I rn r 1 1 1CM Md Fk L1kN F kx r m 1 Gm Fg 2 2 Vorb GM r 2 2GM r U Vesc f w p Irdm Fr A 0 E Al i a Y Pd PO pgd a Fb PfluidVdisplacedg v 2 v A 1 A 2 P1 pgyl pi x t Acos cot r 1 ar Co f OX 1 2 k rn k 2ic 2 dt PaverIt mi rn2 g 9 8m1s 2 kg N m G 6 67 x 10h1 2 r rxF L rxp 1o F dPE dx TKE mv 2 2 RKE 1w2 2 rn2 r 1 GFE Gm 106 MEth 5 97 x 1024 kg Pawn 1 atm 1 013 x 3 Pwater 1000 kg rn REarth 6 38 X EPE 1 TKE 2 2 RKEI 2 pV2 2 or 2 or gIL 0 rngd Iu 2rf 2 7 T 1 I r 2 i rn m r 1 rcM pgy2 dg my P2 GPE EPE TKEf RKEf GPEf EPEf Pa I Which of the following statements is false a Simple harmonic oscillations can only exist around a stable equilibrium point b A linear restoring force is required for simple harmonic oscillations to occur c The period of simple harmonic oscillations is determined by the properties of the system and does not depend on the initial conditions For a mass on a spring the frequency of the kinetic or potential energy oscillations is equal to the frequency of the position oscillations e Total mechanical energy of a simple harmonic oscillator is proportional to the oscillation amplitude squared LIA F b 4 C T d 1 t dJ v e ave A s s2 e 1 ccCae 42 FE so kM wt A 2 w KE Ce k x a o 4Ap e 4eii 1ci k AcsCwt ut kA 2r azt 4 1 x 2 2 Three identical blocks A B and C each having mass M are connected by massless strings as shown Block C is pulled to the right by a force F that causes the entire system to accelerate on a horizontal tabletop Neglecting friction the tension in the string connecting blocks B and C is a Zero b F 2 c F 3 2F 3 e F IA I I BII F T c k z p F F Thc C Fl 3 ttL L e tfAL F F 3 F21 3 3 F ci 3 Which of the following statements is false 1 Resonance occurs when the driving frequency matches the natural frequency of an oscillating system 2 In the absence of friction or fluid air resistance the amplitude of mechanical oscillations grows indefinitely at the resonant frequency 3 Destructive effects of mechanical resonance may be decreased by increasing damping 4 There must be an external source of energy to produce a resonance in an oscillating system a b c d h Statement I Statement 2 Statement 3 Statement 4 None all are true S A 2 2 2 z 3 4t A 3 ts owri 4 Block A on the table has weight 3w and the hanging weight in the figure has a weight w What is the minimLim coefficient of static friction between block A and the table for which the system remains in equilibrium a 0 250 0 333 0 463 c d 0 500 e 0 725 A S 45 0 x L e4 c Ta 15 3w C3 0 3 T V 4 o 33 2i CaS t4cf 35k1 S Cc tC4Ls L 3 3 5 Which of the following may describe a one dimensional travelling wave i e a disturbance propagating along a particular direction In all expressions below x is position t is time and A a and b are some positive constants not necessarily the same in all cases a b c d y x t y x t y x t y x t y x t A exp ax 4 bxt A cos at 4 bxt A sin ax t 4 A tan ax 4 bt 4 4 A ln ax bt 4 x x f Bt B 4 k1 L i41 2W 2 1 1 I jave t 4e xi x C v 6 Which of the following is false in a right handed coordinate system 1 a Ic k b jxI k I d j Ixj O e jXkI 7 Only conservative forces act on a certain one particle system The plot below shows the dependence of the potential energy on the particle s coordinate x The total mechanical energy of the statement about the system Choose the system is correct zero l E a The particLe has zero velocity at x 1 6 b x 0 is a point of stable equilibrium c The particle cannot possibly be located between x 1 and x 2 d The particle experiences zero force at x 2 None of the above x 0 5 o F KE P 0 efLV t L iQ t s E U KE k 0 o 0 5 cf rve tt1LVL D PQ x 1 C zJ Cd dU t x 4 PE Lst PE 3 V5 ot 2e z 71 I x 0 X I …