HW9.2: SHM-Springs and Pendulums

Transcription

1 HW9.: SHM-Sprin and Pendulum T S m T P Show your wor clearly on a eparate pae. Mae a etch o the problem. Start each olution with a undamental concept equation written in ymbolic ariable. Sole or the unnown ariable in a tep-by tep equence.. You want to build a randather cloc with a pendulum (a weiht on the end o a liht cable) that ha a one econd period. a) How lon do you mae the cable? T b) Suppoe the cable tretche a bit rom the weiht on the end. Will the cloc run at or low?? lower, loner ie larer period. What i the period o a imple pendulum 5 cm lon a) on Earth.5 T m b) on a reely allin eleator reely allin eleator, i apparently, T would be ininite c) on the Moon (Moon = /6 th Earth) i i /6 th Earth, then T i 6 time T on Earth or The lenth o a imple pendulum i.66 m, the pendulum bob ha a ma o 3, and it i releaed at an anle o to the ertical. a) With what requency doe it ocillate? ume SHM. 9.8 / T. 63Hz.66 b) What i the pendulum bob peed when it pae throuh the lowet point o the win? (Enery i conered) E mh E.53m c) What i the total enery tored in the ocillation aumin no loe? (9.8)(.66.66co) E E (.3)(.53 ). 439J.66co= X.66-x= h.66m

2 4. Suppoe you notice that a 5- weiht tied to a trin win bac and orth 5 time in econd. How lon i the trin? T T = ec/5win=4ec 4 4.m The period o a pendulum i obered to be T. Suppoe you want to mae the period T. What do you do to the pendulum? Increae by 4 6. (a) ma o 4 i upended rom a prin hanin ertically, and the prin i ound to tretch 8. cm. ind the prin contant. m m (.4)(9.8).8 49N.8 p (b) How much will the prin tretch i the upended ma i 575? m m (.575)(9.8) 49.5m ma i attached to a prin and pulled out horizontally to a imum diplacement rom equilibrium o.5 m. =.5m p (a) What prin contant mut the prin hae i the ma i to achiee an acceleration equal to that o raity? ma m m (b) What i it period o ibration? ma (3)(9.8) N m 3 T S

3 8. When a 4.- ma i hun ertically on a certain liht prin that obey Hooe law, the prin tretche.5 cm. I the 4.- ma i remoed, (a) how ar will the prin tretch i a.5- ma i hun on it? The amount that the prin tretche i directly proportional to the ma o the hanin object ince the weiht i balanced by the prin orce. I 4 tretche the prin.5cm, then.5 will tretch the prin (.5/4)x.5 cm =.94cm m m.5m p b) How much wor mut an external aent do to tretch the ame prin 4. cm rom it untretched poition? We need to determine the prin contant o thi prin irt. m m (4)(9.8).5 568N W ( ) (568)(.4 ). 5J 9. prin o prin contant 9.6 N/m i compreed 5. cm. ma o.3 i attached to the prin and releaed rom ret. =5 cm p C 4.cm ind (a) the imum elatic potential enery tored in the prin I there i no riction or air reitance, then the enery o the prin/ma i conered. t the diplacement (at ), there i no inetic enery and all o the enery i in the orm o prin potential enery. Since we now and (5cm), we can ind the enery at that point E U ( ) (9.6)(.5 ). 45J (b) the imum peed o the ma and Max peed and inetic enery occur at =, when US =. Then all o the.45j o enery i in the orm o inetic enery. E E.45 K.44m (c) the period o ibration o the ma. m.3 T S

4 . In an arcade ame a.- di i hot acro a rictionle horizontal urace by comprein it aaint a prin and releain it. I the prin ha a prin contant o N/m and i compreed rom it equilibrium poition by 6. cm, ind the peed with which the di lide acro the urace. Since there are no nonconeratie orce =6 cm doin wor on the hocey puc, the prin, earth and puc are an iolated ytem in which mechanical enery i conered. p E E K i i U i K ( ) m i U ()(.6 ).5 C 4.cm. The aboe raph how the motion o a. object attached to a prin. The ma i underoin imple harmonic motion. Determine the ollowin a) The period o the motion 5 b) The amplitude o the motion 3m c) The prin contant T 5 m 8.9N

5 d) The total mechanical enery in the ma-prin ytem E i the ame at all point. t the diplacement (at ), there i no inetic enery and all o the enery i in the orm o prin potential enery. Since we now and (5cm), we can ind the enery at that point E U ( ) (8.9)(3 ) 85. J e) What i the imum PE in the prin, and at what time() doe it hae thi imum enery? US=85.J - Max US when K = at diplacement. Thi occur at.5 and 3.75 ) What i the imum KE o the object, and at what time() doe it hae thi imum enery? K=85.J - Max K when US = at equilibrium. Thi occur at,,5 and 5 ) What i the imum peed o the object, and at what time() did it occur? Max peed occur when K i, at = at,.5 and 5. K m h) What i the peed o the object when it i.5 meter rom the equilibrium poition? t.5m, ome o the 85.J o enery i in the orm o US and ome i in orm o K E K.5 3.6m.5 U.65 i) What i the imum acceleration o the object? Max acceleration i where i which i at = S.5.5 (.5 ) ma ma a S ma ma 4.73m m j) Durin what interal in the irt 5. econd doe the object hae poitie elocity? Poitie elocity occur when the lope o the x-t raph i poitie (-.5 and ) ) Durin what interal in the irt 5. econd i the object peedin up? Speedin up when the diplacement, elocity and acceleration are in the ame direction. -.5: dipl and elocity +direction / acceleration i - SOWING DOWN.5-.5: dipl and elocity -direction / acceleration i - SPEEDING UP : dipl and elocity -direction / acceleration i + SOWING DOWN : dipl and elocity +direction / acceleration i + SPEEDING UP 5-5.5: dipl and elocity +direction / acceleration i - SOWING DOWN l) Determine the eneral equation or the diplacement o the object a it relate to time. Ue the appropriate numerical alue or and. i 3m and i /5 x( t) in(t) 3in( ) 5 t

6 m) Determine the poition o the ma at 3.3. The ine unction mut be ealuated in RDINS x( t) 3in( t) x(3.3) 3in( 5 5 (3.3)).3m Thi reult aree with the x-t cure. Decribe two experimental method to determine the prin contant o a prin. e peciic about what you would meaure, what equipment you would need to tae your meaurement, what are the independent and dependent ariable. What you would raph and how you would analyze your raph to determine the prin contant.