Review. Physics 231 fall 2007

Transcription

1 Reew Physcs 3 all 7

2 Man ssues Knematcs - moton wth constant acceleaton D moton, D pojectle moton, otatonal moton Dynamcs (oces) Enegy (knetc and potental) (tanslatonal o otatonal moton when detals ae not mpotant) Momentum and systems o patcles (collsons, systems o objects) Equlbum (equatons om equlbum condtons) Gataton (mostly moton o planets and satelltes) Peodc moton (SHM, spngs, pendulum) luds (pessue, oce, pncple o buoyancy)

3 Poblem solng Phase : You hae to undestand the poblem Phase : Desng a plan Phase 3: Cayng out the plan Phase 4: Lookng back 3

4 Pactcal adse (phase ) Stat om the statement o the poblem. I you cannot undestand the poblem, ty to estate the poblem Vsualze the poblem as a whole as clealy and as dly as you can. Daw a dagam. Isolate the pncpal pats o you poblem. Do not concen yousel wth detals o the moment. Go though the pncpal pats o you poblem Good questons: What s the unknown? What ae the data? What s the condton? Is the condton sucent to detemne the unknown? O s t nsucent? O edundant? O contadctoy? 4

5 Pactcal adse (phase ) Desng a plan s a heustc easonng (ncludes: ealuatng possble answes o solutons, tal and eo) Eamne pncpal pats, detals and the connectons. Consde them om aous sdes, combne them deently. Seek connectons wth you omely acqued knowledge. Eamne you guess. Look at the unknown. Ty to thnk o a amla poblem hang the same o smla unknown. You may be oblged to consde aulay poblems an mmedate connecton cannot be ound 5

6 Phase 3: Cayng out the plan Ths phase s ease than the st two, what we need s manly patence. Pactcal adse: ollow you plan and check each step 6

7 Pactcal adse (phase 4) Check the esult usng omely acqued knowledge (ncludng common sense!). Poblem n lettes ae susceptble o moe tests than poblems n numbes. Can we dee the esult deently? 7

8 8 ) ( gt t y y t g t a at t at g a y y y y D pojectle moton ) D moton (o ee all Knematcs

9 Dynamcs Second Newton's Law o D/D moton : net, N Tenson T g s e net ma ma o unom ccula moton : oces : Gatatonal oce Nomal oce ctonal oce Spng oce, net, net, y mg mg cos(θ ) μsn and k m k ma / y etenal μ N k 9

10 Enegy Knetc enegy K m Change n knetc enegy ΔK K K W d cosϑ Gatatonal potental Elastc potental enegy enegy U( y) U( ) Conseaton o Mechancal Enegy mgy k K U K U Conseaton o Enegy (cton noled) K U Powe : P K U dw dt k ΔW Δt ( )

11 τ θ θ τ α τ φ τ θ θ α α θ θ α π π π α θ P W I m K I I t t t T T a s cm cm net ) ( ) sn( ) ( /, Wok and powe : knetc enegy Total neta) s otatonal (whee law Second Newton's toque equency peod moton : and tanslatonal otatonal Rotatonal knematcs, dynamcs & enegy

12 Moment and Impulse Lnea momentum p m, nd Newton's Law dp ma dt Impulse : J p p aeδt Conswaton o lnea momentum : net then p p Elastc collson : p p and E E Inelastc collson : p p and E E Angula momentum : patcle L p, gd body L I Conseaton o angula momentum : o τ L const net net

13 System o patcles Cente o mass net M a net CM CM CM, n m m... m m m... M Second Newton's Law o a system o patcles o CM const 3

14 Equlbum Two Condtons o Equlbum : n physcs 3 o most poblems net τ and τ net, net,y net,z net Choose ONE object n a tme o consdeaton Daw a ee-body dagam (show ALL oces actng ON that object) Choose (wsely) a coodnate system and esole oces n the components Geneate equlbum equatons usng the condtons o equlbum 4

15 Gataton mm Newton's Law o gataton G GM The ee - all acceleaton g R 4π 3 4π o M ρv ρ R then g Gρ R 3 3 GMm Gatatonal potental enegy U R Escape speed : GM R Obtal moton : c GM R h and T π GM ( R h) 3/ 5

16 Peodc moton Peodc Moton Any moton that epeat tsel at egula nteals Restoaton oce ma c c T π m m c Smple hamonc moton ( t) cos( t φ) m π π T ( t) ( t) Equatons cos( t φ) m m a( t) ( t) sn( t φ) Spng Enegy Pendlum k T π m k E m c mg L T π 6 L g

17 luds m Densty ρ V Pessue p A Pessue at depth Pascal s pncple : h : A A Achmedes pncple o buoyancy p p ρgh b m g ρ Vg 7