2002 November 14 Exam III Physics 191
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1 November 4 Exam III Physics 9 Physical onsans: Earh s free-fall acceleraion = g = 9.8 m/s ircle he leer of he single bes answer. quesion is worh poin Each 3. Four differen objecs wih masses: m = kg, m = kg, m = 3 kg, m D = 4 kg, were a res unil forces aced on hem. The graphs of force (in kn) versus ime (in µs) for each objec are displayed below. (F is he force acing on objec, ec.) Which objec ends up wih he mos kineic energy?. quarz fiber resiss being wised. The resoring orque (τ) is in proporion o he angle of wis θ (measured in radians): 4 F 4 F τ = κθ where he proporionaliy consan is κ. In a orsional oscillaor a disk of momen of ineria I oscillaes firs one way (wising he fiber) and hen he oher (unwising he fiber) aking a ime T o complee a cycle. Which of he below is a possible formula for T (i.e., has unis of ime)? 4 F 4 F D D κ. T = I. T = κ I. T = κ 3 I I D. T = κ quarz fiber oscillaing disk wih momen of ineria I. uniform bar resing on fricionless ice is kicked near is end providing a horizonal impulse J as shown below. The cener of mass (labeled below as M) will hen: M 4. Four pucks race on a fricionless surface. The pucks have masses: M = kg, M = kg, M = 3 kg, and M D = 4 kg. s shown below, hey are subjeced o differen forces and race lenghs. ircle he puck wih he larges momenum when i crosses is finish line. F F F F sar D finish finish J. remain a res wih he bar roaing around i.. move in a sraigh line a consan velociy.. wobble due o he unbalanced impulse. D. none of he above
2 5. In he below figure, suden has a mass of kg and suden has a mass of 75 kg. They si in idenical rolling office chairs facing each oher. Suden places his bare fee on he knees of suden, as shown. Suden hen suddenly pushes ouward wih his fee; as a resul, boh chairs o roll fricionlessly away from each oher. During he push (while he sudens are sill in conac):. suden exers a force on suden, bu is no exering any force on.. he sudens exer forces on each oher, wih he larger force on.. he sudens exer forces on each oher, wih he larger force on. D. none of he above 7. uniform square is spinning a a consan rae abou he pivo poin P on a fricionless surface. No forces are acing on square, excep perhaps a he pivo poin. The force a he pivo poin: ω P. provides a orque o mainain he spin.. poins down he page a he insan shown.. poins o he lef a he insan shown. D. is in fac zero. 6. Le p and v denoe respecively he momenum and velociy of suden afer he push; le p and v similarly denoe he momenum and velociy of suden. Which of he below saemens is correc?. p > p and v > v. p = p and v > v. p = p and v < v D. p < p and v < v 8. Four forces of equal magniude bu wih direcions as shown below ac a he corners of a square. The square has a fixed pivo poin P and is similar o he square in he previous problem, Rank (from leas o greaes) he orque produced by hese forces abou he pivo poin. We define a posiive orque as one in he couner-clockwise direcion. Noe: negaive numbers are smaller han any posiive number. (The orque produced by F is denoed τ, ec.) F 3 P F F F 4. τ = τ = τ 3 = τ 4. τ < τ = τ 4 < τ 3. τ < τ = τ 3 = τ 4 D. τ 4 < τ < τ < τ 3
3 ω (rad/s) 9. The below diagram displays a racke balanced on a poin. How does he mass on one side of he fulcrum compare o he mass on he oher?. M < M M M. onsider he momen of ineria of a bicycle wheel roaed abou differen roaion axes:. is usual axle. abou a parallel axis on he edge. a diameer D. an axis parallel o a diameer, bu on an edge. Which roaion axis has he smalles momen of ineria?. M = M. M > M. (Mark wo leers!) The below graph displays he angular velociy, ω, of a roaing objec as a funcion of ime. onsider a poin on he rim of he roaing objec. ircle he leer where he magniude of he poin s cenripeal acceleraion is he larges. X he leer where he magniude of he poin s angenial acceleraion is he larges. D 3 D Time (s) 3. hoop (I hoop = MR ) is rolling wihou slipping on a horizonal surface. Which choice of fixed origin resuls in a oal angular momenum of zero? ω. bel drives (wihou slipping) a large radius pulley (#) from a small radius pulley (#) as shown below. Please compare he angular velociy of each pulley (ω, ω ) and he speed a he edge of each pulley (v, v ). Which combinaion of saemens is correc? D: no origin produces zero angular momenum # #. ω < ω, v = v. ω = ω, v = v. ω < ω, v > v D. ω = ω, v > v
4 The following quesions are worh 5 ps each 4. Erns Meissel (86 895) invened a sandard problem in celesial mechanics. He considered hree sars of mass m = 3 M, m = 4 M and m 3 = 5 M (M is he mass of he Sun) released from res a he iniial locaions described below. (Disances are measured in U, which is he average disance beween he Earh and he Sun.) The sars are assumed o be in deep space: he only forces are hose due o he graviaional aracion beween hese hree sars. The below picure shows how he sars move during he firs years. mass (M ) m = 3 m = 4 m 3 = 5 posiion (U) r = 4 ĵ r = 3 î r 3 = 4 3. Find he locaion of he cener of mass a he ime of release: Rcm (i.e., boh x and y componens).. Find he velociy of he cener of mass years afer he release: V cm (i.e., boh x and y componens)
5 5. Paricles and collide in space where no exernal forces are presen. Paricle, wih mass m = kg, moves parallel o he x axis and collides wih paricle (which has mass m = 3 kg). The below liss a pre-collision (unprimed) and a pos-collision (primed) posiion (in m) and velociy (in m/s). paricle mass pre-collision pos-collision m = r = 3 î + ĵ v = 5 î r = 9 5 î ĵ v = 5 î ĵ m = 3 r = v = r = 36 5 î 5 ĵ v = 8 5 î 6 5 ĵ. Show ha he iniial momenum in he x direcion equals he final momenum in he x direcion.. Show ha he iniial momenum in he y direcion equals he final momenum in he y direcion.. alculae he oal kineic energy in he pre-collision sae and in he pos-collision sae. Is his an elasic collision? D. alculae he relaive velociy vecor: v = v v in he pre-collision and pos-collision saes. Should he relaive speeds be equal? y ' ' x 6. The hin uniform rod in he below figure has a mass of kg and a lengh of m and can pivo abou a horizonal, fricionless pin hrough one end. I is released from an angle of 45 above he horizonal. Use he principle of conservaion of energy o deermine he angular speed of he rod as i passes hrough he horizonal posiion. Noe: I = 3 ML for a rod roaed abou one end. g 45
6 7. The plaer of a urnable is a uniform disk wih a mass of 3 kg and a diameer of 3 cm. The plaer had an angular speed of 45 rpm he insan i was urned off. consan fricional orque resuls in he plaer coming o res 5 seconds laer.. Wha is he magniude of he fricional orque? (Noe: I disk = MR.). How many radians did he plaer urn during he firs second of he deacceleraion? 8. n old sone well consiss of a bucke (mass M) and a reel wih crank (momen of ineria I and radius R ) o pull he bucke up. The bucke is released from he op of he well; as i falls i pulls he rope down and, as a resul, he crank assembly runs backward. Find he acceleraion of he bucke. Of course, your answer will include wo free body diagrams: one of he bucke and one of he reel. I, R g T M
2001 November 15 Exam III Physics 191
1 November 15 Eam III Physics 191 Physical Consans: Earh s free-fall acceleraion = g = 9.8 m/s 2 Circle he leer of he single bes answer. quesion is worh 1 poin Each 3. Four differen objecs wih masses:
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