Physics 140 Fall 2013 Third Midterm Exam November 21 2013 Form 1 50L a T O5 Your name Last First MIKE Your UMID number M 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 site The exam is closed book You may use three 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 oniy You must mark the correct answer on the scantron to get credit for each problem The exam is 90 minutes long There are 20 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 v0t at I2 2 at 7 7 xO vo 2a x 6 8o wot at 2 2 xo wz cooz Uct 2a O Rw at dvldt Ra 7 2 arad vIR w R vNc VNB YB C Oz z 0 0 v 6o continued on the next page ibe 9 2 Moments of Inertia of Various Bodies a Slender rod axis tlirotih center b Slender nd I N T axis through 1 12 center 2 1 Solid cylinder e llollosv cylinder d Fh in rectangu In r plate c Reln ngn lar plate throuch one end 2 IlL I I i is axis along edge ii b g Thinwalled hollow cylinder h Solid sphere i ThinwalJed hollow sphere I N O1 PCaSCn rO IcaIorI Inc continued from the previous page 2 I mr 2 ln7r7 2 1 CM Md Fg Gin r rxF L r x p JO 2 Vorb Gi14 r 2 Vesc 2GM r Pd PU pgd Fk UkN w p 1 P d j my B pfluidVdisplacedg v 2 v A 1 A 2 P2 pgy2 pv2 2 P1 pgyl pvi x atrn 1 1 013 Pa Patm fPdt avert 2 m m m2r r 1 F dPE dx 2 2 TKE mv RKE GPE Gin EPE TKEI RKE GPEI EPEI rCM m2 3 Pwater 1000 kg rn g 9 8m1s 2 H G 6 67 x 10 kg Nm 2 m 6 RE 6 38x 10 x ME 5 97 1024 kg TKEf RKEf GPEf EPEF 1 Which of the following statements about unstable equilibrium is true I If deviated from unstable equilibrium an object experiences a restoring force or a restoring torque directed to bring it back to equilibrium 2 Unstable equilibrium corresponds to a local minimum of potential energy 3 The sum of all forces and all torques acting on a body is zero at unstable equilibrium a Statement 1 b Statement 2 Statement 3 d None e More than one w CL 4 Lt L L C2 hd z cf kQ 4 c J4 q t LLAA a 4 1 3 T 4 czt LLAL tl tQ t 2 g 411 LJ e 2 A stray asteroid moves around a lonely star in a hyperbolic trajectory There are no other celestial bodies nearby Which conservation laws apply to the motion of the asteroid a Conservation of energy only b Conservation of momentum only c Conservation of angular momentum only Conservation of energy and conservation angular momentum e Conservation of energy conservation of momentum and conservation of angular momentum e c t L4 14 t e 0 t L i7 4 e 3 L A OT M 0 e1 2ct iz z L l 2 A stray asteroid moves around a lonely star in a hyperbolic trajectory There are no other celestial bodies nearby Which conservation laws apply to the motion of the asteroid a b c d e Conservation of energy only Conservation of momentum only Conservation of angular momentum only Conservation of energy and conservation angular momentum Conservation of energy conservation of momentum and conservation of angular momentum C h z h t 2 he Ck td C Ved i e4t c 1 wtJ c t c 3 Imagine that the air in our atmosphere is replaced with an ideal fluid of the density of Styrofoam Estimate the thickness height of the atmosphere needed to produce the atmospheric 3 p 102 kg rn pressure of 1 atm 100 000 Pa at the surface of our planet a I m b lOm j3 100 m d l000m e 10 000m I jaC d9 7c Vacwi fOo all pi 4 Suppose that you want to make a plastic replica of Earth so that your weight on the new planet is exactly half of your weight on the real Earth Due to government regulations suppose also that your new plastic planet must have the same radius as Earth What density should you use Assume uniform distribution of mass within both the real Earth and your new plastic replica a b c d e same density as Earth twice the density of Earth four times the density of Earth half the density of Earth one fourth the density of Earth WE WE 1 Gin Vip a fr R L R 5 An ice skater holds dumbbells weights in her hands When her hands are in close to her body her moment of inertia is I but when her arms are spread out her moment of inertia is 1 7 If she is initially spinning with angular speed w with her arms spread apart how fast will she spin when she brings her arms inward to her body b c d e Her angular velocity will increase by a factor of 1 7 due to conservation of angular momentum Her angular velocity will decrease by a factor of 1 7 due to conservation of angular momentum Her angular velocity will increase by a factor of 1 3 1 71 2 due to conservation of energy Her angular velocity will decrease by a factor of 1 3 1 71 2 due to conservation of energy Her angular velocity will stay the same I KE 1 6 A block of mass M hangs in static equilibrium from two massless ropes as shown in the diagram The other rope puils upward with tension T 1 2 at angle 0 Which One rope is horizontal with tension T tension the greatest rope has a 1 T T 7 2 T T c T 1 T 2 d The answer depends on the value of the mass M e The answer depends on the value of the angle 0 54e v I c L X t44 ce 44 Z y a X hk 6Zg 4 f 4 x 2 Qs 43 4 7 A physics minded artist has created an abstract sculpture titled A spherical cow in vacuum a simplified picture of which is shown in the diagram The sculpture is symmetric with respect to a vertical plane it has mass M 1000 kg height h 2 m width w …