Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration

Transcription

1 Mh Csquee

2 Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc*

3 The componens e he legs of he gh ngle whose hpoenuse s A A A A n A A A nd Acos ) Asn ) A A A A n A A A A A o n A A O,

4 Knemc bles n one dmenson Poson: ) m Veloc: ) m/s Acceleon: ) m/s Knemc bles n hee dmensons ) zk Poson: ) zk Veloc: Acceleon: ) zk m/s All e ecos: he decon nd mgnudes m m/s z k

5 In one dmenson ) ) ) = - 3. m, ) = +. m Δ = +. m + 3. m = +4. m In wo dmensons Poson: he poson of n obec s descbed b s poson eco ) lws pons o pcle fom ogn. Dsplcemen: ) ) ) )

6 Aege eloc g Insnneous eloc lm d d lm g d d d d g g, d d g, s ngen o he ph n - gph;

7 Emple : Moon of Tule A ule ss he ogn nd moes wh he speed of = cm/s n he decon of 5 o he hozonl. ) Fnd he coodnes of ule seconds le. b) How f dd he ule wlk n seconds?

8 Emple : The egle descend An egle peched on ee lmb 9.5 m boe he we spos fsh swmmng ne he sufce. The egle pushes off fom he bnch nd descends owd he we. B dusng s bod n flgh, he egle mnns consn speed of 3. m/s n ngle of. deg below he hozonl. ) How long does ke fo he egle o ech he we? b) how f hs he egle eled n he hozonl decon when eches he we?

9 Emple : The egle descend An egle peched on ee lmb 9.5 m boe he we spos fsh swmmng ne he sufce. The egle pushes off fom he bnch nd descends owd he we. B dusng s bod n flgh, he egle mnns consn speed of 3. m/s n ngle of. deg below he hozonl. ) How long does ke fo he egle o ech he we? b) how f hs he egle eled n he hozonl decon when eches he we?

10 Aege cceleon g g, g g, Insnneous cceleon lm lm g d d d d d d d d The mgnude of he eloc he speed) cn chnge The decon of he eloc cn chnge, een hough he mgnude s consn Boh he mgnude nd he decon cn chnge

11 Poson Aege eloc Insnneous eloc Acceleon e no necessl sme decon. ) d d d d d d lm ) g g g,, d d d d d d lm ) d d d d d d d d d d d d ) nd ),, )

12 Moons n hee dmensons e ndependen componens Consn cceleon equons Consn cceleon equons hold n ech dmenson = begnnng of he pocess; whee nd e consn; Inl eloc nl dsplcemen ; ) )

13 Defne coodne ssem. Mke skech showng es, ogn. Ls known qunes. Fnd,,,, ec. Show nl condons on skech. Ls equons of moon o see whch ones o use. Tme s he sme fo nd decons. = = ), = = ), = = ), = = ). He n s pon long he decon of f s consn. ) )

14 Emple 3: A Humme Accelees A hummngbd s flng n such w h s nll mong ecll wh speed of 4.4 m/s nd cceleng hozonll m/s. Assumng he bd's cceleon emns consn fo he me nel of nees, fnd ) he hozonl nd ecl dsnces hough whch moes n.55 s nd b) s nd eloc componens he me =.55 s. c ) wh s he bd s eloc?

15 -D poblem nd defne coodne ssem: - hozonl, - ecl up +) T o pck =, = = Hozonl moon + Vecl moon Hozonl: =, consn eloc moon Vecl: = -g = -9.8 m/s, = Equons: g f ) ) Hozonl Vecl

16 X nd Y moons hppen ndependenl, so we cn e hem sepel Hozonl g g Vecl T o pck =, = = Hozonl moon + Vecl moon Hozonl: =, consn eloc moon Vecl: = -g = -9.8 m/s nd e conneced b me ) s pbol

17 -D poblem nd defne coodne ssem. Hozonl: = nd ecl: = -g. T o pck =, = =. Veloc nl condons: cn he, componens. s consn usull. cos chnges connuousl. sn Equons: Hozonl Vecl g g

18 Inl condons = ): =, = = cosθ nd = snθ Hozonl moon: Vecl moon: Pbol; θ = nd θ = 9? g g cos n g

19 Inl condons = ): =, = = cosθ nd = snθ, hen g h sn g g Hozonl Vecl R cos sn sn g g g g

20 Inl condons = ): =, = = cosθ nd = snθ, hen Hozonl Vecl g g g sn g g h h h g h sn g g g h g g

21 Complemen lues of he nl ngle esul n he sme nge The heghs wll be dffeen The mmum nge occus poecon ngle of 45 o R sn g

22 Poson Aege eloc Insnneous eloc Acceleon e no sme decon. ) d d d d d d lm ) g g g,, d d d d d d lm ) d d d d d d d d d d d d ) nd ),, )

23 If pcle moes wh consn cceleon, moon equons e Poecle moon s one pe of -D moon unde consn cceleon, whee =, = -g. f f f ) ) f f f ) ) ) f