3.1 Velocity: m s. x t. dx dt. x t (1) 3.2 Acceleration: v t. v t. dv dt. (2) s. 3.3 Impulse: (3) s. lim. lim

Transcription

1 . unen n eie quniie n uni unen Phi quniie e hoe h n e ie efine, n fo whih he uni e hoen ii, inepenen of ohe phi quniie. o. unen uni Uni So Dienion engh Mee Tie Seon T M Kiog g M uen ineni Apee A igh ineni ne J 6 Tepeue Kein K 7 Soi nge Se-in S 8 Pne nge in The eiie phi quniie e hoe h e efine inie. The he he eueen uni funion of funen uni. f we he: U = U(, T, M,, J, ) [U] = T M J The hoogenei of phi equion: The phi fou e inin o he eueen uni nfoion. pe:. eoi: i T (). Aeeion: i T (). pue: p p g g M T ()

2 . oe:. Peue:.6 Mehni wo:.7 Kinei eneg: i p p p g g g M T () P g P g M T P P S S g g M T () J (6) ; g.8 Giion poeni neg:.9 i poeni neg: g M T ; g J p g h g h g g M T ; g J p p (7) (8). Powe: P. Deni: p,e g g M T ; g J p,e. Angu eoi: g J P g M T P W p,e (9) () g g M ()

3 . Soi nge: T () A A ein () ihe ino onn ppoiion he fou of giion (hei) penuu, T uing he hoogenei of he ienion equion. : o ie oeion he phi quniie h n ou e: he engh (), of he penuu (), giion eeion (g). T = g T T M T T M, hen ienifing he uppe oeffiien: T / g / T The of phue wih jupe (phui) i = g, n i unhe fo owe opee open wih no inii eoi. in he eoi epeion, () n he eoi ii if we now h he eine foe i popoion wih he eoi, =, whee = /. : f he foe i efine : Aong ei ieion n e ewien : The eun (ne) foe i g g e. G, hen: g n g g n g

4 f we wi epe he phi quniie wih ue we ge: e e o he ie goe o infini one oin: g i i i e i i 7. h in he eoi epeion n e wien : e i g 6. A ie wih he weigh G een hi h e n nge wih he hoizon pne. The oion equion e = Ag ong he hi n =, whee g i he giion eeion n A onn oeffiien. How uh i he fiion foe eween ie n now on he hi. (Piu e: he ie = 7 g, nge = ; A =.). : The eon pinipe of ni n e wien : G f The pojeion ong n e e: Gin f Go The oponen of eeion n e ue wih he foowing equion: Ag Ag Wih hoe: f f Gin g f 6. Ag G in A in A in A ei poin wih i oing ong jeo gien he ein oponen: Ao n o. heize he foe h poue hi pe of oion if we now h he foe epen on he ei poin poiion. Gie oe epe.

5 : The foe oponen ong O n O e e: The foe ouu i: Ain Ao in o whee i he ei poin poiion eo. The io: o, e he ieion oine of he foe. o, n he e ie e he nge eween he poiion eo n OX n OY e, epeie. o hee we n oee h he foe i ni-pe wih he poiion eo. Then he foe i poining o he ene of he efeene fe. Suh foe i e ion en foe. 8. On o wih = g e ing wo foe, = n =, whih e heize he nge = 6, n = epeie, wih he ieion of eoi. in he o eeion,, eoi, n he ine oee ino ie = ing fo he eginning of oion (Piu e = /). : f we e onieing efeene fe ee o eh hen he eeion oponen ong OX n OY e e: o o o 6 o... / in in n he eeion ouu: 7. / /

6 We oee h he eeion i onn in ie ( = on), he eoi equion n e ue fo: o oponen: u u n fo hee:.. /. 7. / n he eoi ouu: The eoi, ie e n nge u g g n oe o ue he ine we he:..99 / gien he equion:. g g.7 7. o 9 98". o oponen: A o i eing wih eoi of = 6 /h. f he iu of he whee i =. fin ou: ) The pei oion equion of poin fo he een whee iufeene. ) The ngeni eoi oponen n he ue of eoi. ) The ph ine poin eween wo on wih he o.. 6

7 : ) W w in o w w W W.in..o hi i he equion of oi. ) o o o in in in W in W o o in o in in ) in in o in 8. A o wih = g n ie wih fiion on hoizon ufe if i puhe pi ping, wih n ei onn = /, n whih w opee hf of hi engh =. in ou: ) he ehni wo of fiion foe uing epnion. ) how uh u i he fiion oeffiien if in he fin poiion he ping in no ee. : ) e W W W W 8 W 8 J 7

8 ) f f i f g A onee ue wih he ie of =.8 n eni of g/ u e ippe oun n ege. ue: ) Poin of ppiion ieion n ue of he ini foe neee o un un-oe; ) The epeion of hoizon foe h n un-oe he onee o if hi i ppie on upeio ege funion of oion nge. ) The ehni wo pen fo uning oe he onee o. : ) M o o M o M M G G g g g ) M M G G o o M M G o G o g o o o ) W M g in in g g 678. g W M W W M W g g 8

9 W g o g in g W g W 8.8 J. On n inine pne wih ininion = in(/) n engh =. i oing wih no iing fiion n hoogeneou phee of = g n iu =. How uh i he ne eoi, ngu eoi n fequen he e of he pne. :,A,,A, p, A in,, gh g in in,o, in,, in,o,, 7 g in Hz 7 g in Deone h fe pefe ei oiion of wo hoe pu of he e inii : one eing e he nge eween he ieion of pu i 9. How uh e he eoiie n e nge if he inii eoi of pojeie pu i = /h n = 6?,i pi pf,f p p p p p p o p p p p p p p p p p p p p p p p o 9 p p 9 9 6

10 o o o o.6. On he efeion pe of hoi oioope wih eniii of / on oh e O n O i i ppie iuneou he eei oge o n U in U. ue: i. The po equion of oion on O n O e. ii. quion of he jeo. U : ) S S U o o S U S U in 8in : ) o 8in o o 8 o o. A ei poin eeue oion eie he equion: in. Show h hi i honi oio oion. in he piue n peio of oion, he eoi n eeion of he ei poin. in in o Ain in 6 o 6 A 6 o 6 T 6 in 6 T. Ain Ao 6o 6

11 6 in 6 6. A ei poin wih he = g i oiing une he w: : o ) o. ue:. The ie nee o eh he iu eoi, n he ie nee o eh he iu eeion;. The iu ue of he ei foe h on he ei poin;. peion of inei, poeni n o eneg. o o o 6 in 6 6 o n o 6 in in 6 6 6n n n ) Ain in e ) p A A A o A in o. 6 in o J 6 in J 6. 6 J

12 7. A honi oio whih oie wih he piue, A of 8 i fe. fo he eginning of oion (fo equiiiu poiion) he ine eue fo equiiiu poiion. ue:. oio puion;. oio peio;. oio fequen;. eoi of oiion in he gien poiion; e. eeion of oiion in he gien poiion. : ) Ain Ain in A ) T T. T ) 8. Hz T. ) π ωaoω τ π8 o π..9o 6 τ.6 ω Ain ω τ π 8 in π. τ 9 Ain in The oni oo ee n ipne i i he in he oen in whih he ieion oee ipne e n nge = 6 wih he ei. How uh i he ipne pee? ( = /) : 9. in A AA in o 68 Mh 9. How uh i he funen fequen of iion of oppe wie ( = 8.9 g/ ) wih eion of n he engh of when i e wih foe of 7.8.

13 : T T S S T S ; T S Hz. ue he weengh ue of oun of Hz in i ( = /) n ino ine ( = /). ue he ee Young ouu if he eni i ( = 8 g/ ). : n he iqui Heiu (eow. K) he oun eoi i /. f we now he He eni =. g/ fin he opeiii ouu. ope hi eu wih he we opeiii ouu if we now h he oun eoi i 6 /. He 6 : He He He 7.6 W W W He oppe wie wih he engh = 6 n iee = i upene o wih g. f he oppe wie eongion i.6 fin ou:. The e,, in, S. The Young ouu, ; n ei onn, ; o A. How uh i he ine-oi ine if in he unee ei i.6 ;

14 g g : ). 6 S.6.6.6%.6 g 9.8 e g ) 7.8 S.6 ) n fon of iophone oun h he peue of. P (/ ). How uh we he o pif he oun in oe o eh he pin heho, pin = W/? We now he i oui ipene Z = = g/. How uh i he peue n he oun ee? : A A g g A A g g g pin p p Z.. W A A g g.. 6 g.. in he eion eween he ineni of we ino n oe ei funion of eph : of peneion n opion oeffiien. n e. Hogen o i oniue fo poon n n eeon wih equ eei hge u oppoie ign, n oue ue e =.6-9. n he funen e, he iu of eeon fi oi oun poon i =. -. ue he ion foe eween poon n eeon.

15 : e Wh i he ue of equ eei hge, whi whih wo ieni, hing he e : g, u e hge, if hee e iue in i ine, n he ouoin foe h on eh i equ in ue wih he weigh ino pe in whih he giion eeion i g = 9.8 /. e p e G g pp pp G G e e pp.8 6 g p pp e g e p Two ieni phee pe in oi, hing he e =. g e upene fo inge poin wih he hep of wo ioe wie, no eenie, of negee n wih he e engh =. Wh i he ue of he equ hge wih whih he wo phee u e hge i uh w h he nge eween he fie hou e = 9? The giion eeion i oniee g = 9.8 /. (in =.77; g = ). q : e G g in 98 q e g G g q. in q.9.8 g 9 9 g g in e q..77 g g e q.9 6

16 8. ue he epenene of eei fie ineni n eei poeni on he ene of phee hing he eei hge unifo iiue in he enie oue. The o hge i enoe n he phee iu. : ) < ; i n i i i i i ) > ; i n i 9. ue he eei fie ineni ine fo o, unifo hge wih o hge. 8 6

17 7 : in in in. e onie oi e oniue fo wo onuo hing he iu n, wih <. Ue he Gu heoe o eeine he epenene of eei fie ineni n eei poeni fo he oi e e. ue he oi e pi. The e engh i ee i hge wih n eei hge q. : ) < ; i on

18 ) > ; i ) < < ; i i n i i i n on n n n U n U n. Ue he Gu heoe o ue he epeion of pne pio pi. : i n i n n n i S S S i S S i S ; S i ; i S S S i i S S 8

19 9 U S U S U. App he Apee w o ue he gnei inuion ) ine fo n infinie ong onuo ) n inie of n infinie ong oenoi (oi). : ) ) n. Two eei uen = A n = A of he e ene e fowing hough wo pe onuo, iue ine = one fo eh ohe. ue: ) The foe pe uni engh wih whih he wo onuo e uu ing; ) ue he ehni wo pe uni engh pen o oe he onuo ine = one fo eh ohe. ( = -7 H/). : ) 7 )

20 n n 7.6 n n J.6 6. An eei uen wih = A i fowing hough igh ine infinie ong onuo whih i pe in he pne of engu fe pe wih wo of hi ie, ie in he figue. We now he = = n =. ue: ) he gnei fu hough he engu fe; ) he foe h on eh ie of he fe; ) he o foe h on he fe when hough hi = A eei uen i ping hough. Wh i he ene of hi eei uen o oee n ion foe? : ) S S S W n. n ) n n )

21 . The eei uen ineni h fow hough onuo i ie epenen oing o he foowing w: () = ++. ue: ) The eei hge h p hough iui uing he ie fo = o =. ) The eei uen ineni of onn uen, whih e o he e oun of eei hge in he gien ie. : ) ) A 76..