Physics 140 Fall 2014 Final Exam December 12 2014 Form 1 Mz Your name First Last U7 O Your UMID number S 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 120 minutes long There are 25 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 x x 0 v t at 0 I2 2 v at 7 7 vo 2a x xo 12 2 o o coot a t Os a t 2a O Oo v Roi at diildt Ra 7 7 arad irIR v vc VJB yB c continued on the next page Table 9 2 Moments of Inertia of Various Bodies b Slender rod a Slender rod ax is through center 1 1 e Hollow cylinder aus along edge axis through center ML d Thin rectangular plate c Rectangular plate ax s through one end f Solid cylinder 2 1 2 M i g Thin walled hollow 1 h Solid sphere 2 R M R 2 I MR I 2 Ma i Thin walled hollow sphere cylinder I 2 MR I 2 MR 2 MR Il 1 2O12Poar Educaion Inc continued from the previous page I 1 m m2r2 r 2 2 CM Md Fk f rdm a F A 1 8 Al b a YE Pd Po pgd pkN F kx Fg 2 r m 1 Gm Vorb 2 1 GIVI r Vesc 2 2GM r f W p Fb PfluidVdisplacedg A v 1 A v 2 2 P2 pgy2 pv 2 p pgyi pvi x t Acos cot x 2 co f my 1 zxi I f idt Paver1t 2 rcM miri m7r t rxF L r x p JO dPEIdx F TKE mv 2 2 RKE 1w 12 2 GPE Ir 2 m 1 Gm I mi 2 m cv k rn 2 or g L 2 or 2 0 rngd I cv 2irf 2r T k 27r cv k IT f F p 2 2 g 9 8 mIs kg m G 6 67 x 10h1 N 2 106 m RE 6 38 x 5 97 x 1024 kg 5 Pa Patm 1 atm 1 013 x i0 3 Ppure water 1000 kg rn MEh EPE 2 2 TKE RKE GPE 1 EPE TKEf RKEf GPEf EPEf 1 Two blocks lie atop each other on a frictionless horizontal surface The blocks have a coefficient of static friction at their interface A force F directed against the lower block as shown causes the pair to accelerate together to the right without relative slipping The force that causes the upper block to accelerate is F its weight the applied force F kinetic friction static friction the normal force a b c d e 4t tt VeJLJ ad Oo a ri pJ F ti t cie cu t 4 e C C CD L4 w ie7 1w kd ficJi ci e hadA w t 4 1t L JJ4 CLJLe d 7 V V 114 k 2i7 t g Z c 2 i c1t LeL 4t ct S1 a fr1Z44 t t e lt L 4 fl 2 A graph of the final steady state amplitude A of driven oscillations of a mass on a spring as a function of the angular frequency w of the applied driving force is shown at right A change in which physical quantity results in transition of the system behavior from one curve on this graph to another 0 a Natural frequency b Driving frequency Damping constant d Mass e Spring constant J4 hdL 1 L c ZA 14 a t L vz a dvi f4 c F j 0 cLw p M 7k yt t5 4 L t A C4 M4s kV A 1 L t4 c k fr VLC LC fretj lv iS 1 ag rj 7 Ufrt c12z vij hflX e VL Q tt L Ct LV 1 tI44r ft 3 An object can oscillate around a any equilibrium point any stable equilibrium point c any unstable equilibrium point d only a point where the exerted forces obey Hooke s law e any point at which the total exerted force is non zero t uJ eft c A cS c ie rec J 0 LX ArthicL b C eseLIodsy 1 4 1 c j te5iO 1 41 x C ict4 tC C c 3 1 k C rI 4 At what distance r from the center inside the Earth is the gravitational force due to the Earth the same as at a distance r 4R from its center outside the Earth Assume that the Earth s mass is distributed uniformly throughout its volume defined by a sphere of radius R JR 16 7 U a I CmM c R 4 d R12 1 I 3 p e R I kL X V Ofl t JzC iW A de d c i t4if LE f 310 k T z L 2 44 44 274 214t24 zj tt iAJI ft t C 1i6 4A r i L o M V ft L r C r R tLt M tZf c c 3 rv 4 H e r I C tv cc CD C C C CD C et 4 C t J Z c D C CD I 4 I CD CD Q CI C CI C CI C C C CD CI C CD C CD C CD Cd CD CD C CID 6 The dominant water waves in a particular patch of sea are observed to be sinusoidal with wavelength 1000 m frequency 0 07 Hz and amplitude of 2 m For this region what is the ratio of the wave speed to the maximum vertical velocity of water caused by the waves a 70 b 70 ir c 70r d 250 25O ir Tt ttte 4cJ Lww i4 7 Three same scales are attached along a straight line as shown The scale on the left is attached to a wall A force of 15 N is applied to the scale at the right What is the reading on the middle scale a b c d e T SJ 0 5N iON 15N 45 N MI 15 N y kQ Ctw tL 1k I n 4M J 4 CLass xJA S 1 15 S 4 74 A AL L 8 Three pieces of string each of length L are joined together end to end to make a combined string of length 3L The first piece of …