Chapter 8. Momentum, Impulse and Collisions (continued) 10/22/2014 Physics 218
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1 Chater 8 Moentu, Iulse and Collsons (contnued 0//04 Physcs 8
2 Learnng Goals The eanng of the oentu of a artcle(syste and how the ulse of the net force actng on a artcle causes the oentu to change. The condtons under whch the total oentu of the syste of artcles s constant (consered. How to sole two-body collson robles. The dstncton between elastc, nelastc and coletely nelastc collsons. The defnton of the center of ass of a syste and what deternes how the center of ass oes. Lastly, a ery bref ntroducton to rocket roulson. 0//04 Physcs 8
3 Stats fro re-lectures 0//04 Physcs 8 3
4 Defnton of Moentu d d F Net ( dt dt wedefned thequantty as the oentu of as d F Net dt an alternate for of (rested the artcle Newton's nd Law 0//04 Physcs 8 4
5 The Defnton of Iulse 0//04 Physcs 8 5 assung a constant net force ( t F t t F J net ( ths becoes ng for the ulse, substtut J t t F t t F Net net
6 Conseraton of Moentu If the ector su of the external forces on a syste s zero, the total oentu of the syste s consered. d F Net 0 dt and the oentu of the systes constant 0//04 Physcs 8 6
7 Exale of a -body collson (Note:usng dfferent nuber fro Y&F Moentu before 0.4 kg /s to Rt Moentu after 0.4 kg /s to Rt.0 /s 0//04 Physcs 8 7
8 Now n -densons. 0//04 Physcs 8 8 constant constant after total before total y y x x x 0 we hae searatng out thecoonents
9 Now on to a dscusson of Elastc and Inelastc Collsons For an solated syste wth no external forces actng on t and wth nternal forces that are only conserate, we fnd that no echancal energy s lost or ganed n the collson. We call these collsons, Elastc Collsons. collson n whch the knetc energy after the collson s less than before the collson we call, an Inelastc Collson. n nelastc collson where the bodes stck together and go off as a sngle object after the collson we call a Coletely Inelastc Collson. 0//04 Physcs 8 9
10 Note In any collson n whch external forces can be neglected, oentu s consered and the total oentu before equals the total oentu after; ONLY n elastc collsons wll the total knetc energy before and after the collson be the sae! 0//04 Physcs 8 0
11 Elastc collsons n -D 0//04 Physcs 8 before and for the eloctes after the collson We can sole these equatons after after total before total KE KE
12 Fgure 8.8 Is ths collson elastc (a or nelastc (b? What s consered n ths collson? a Moentu b Mechancal energy c Moentu and echancal energy d None of the aboe
13 0//04 Physcs 8 3 cos ( ( ( ( energy as t swngs. Now we can consere echancal bedded? the block swng after the bullet s How hgh wll ( so ( gl gh after total before total
14 Elastc Collsons Only conserate forces actng on the artcles noled n these collsons. 0//04 Physcs 8 4
15 Fgure 8.4
16 Center of Mass of a syste r centerof ass r r 3r3 3 r Where s ths ont located n a syste of dscrete asses? In a contnuous ass dstrbuton? 0//04 Physcs 8 6
17 reakng down by coonents x y z centerof ass centerof ass centerof ass x x z z y y 3 y3 3x z3 x z y 0//04 Physcs 8 7
18 Takng the derate wth resect to te ges nterestng results ( center of ass d dt center of ass r r 3r3 ( 3 total dr dt a ( center of ass a d dt center of ass 33 ( 3 a F nternal d dt F External F a NetExternal 0//04 Physcs 8 8
19 ( then for two artcles ( the oentu as Fndng the total oentu of the syste n the center-of-ass ( ( ( centerof ass c c ( ( easured n the c becoes c ( ( 0//04 Physcs 8 9 so total c 0!!
20 Fgure 8.9
21 Fgure 8.3a
22 Fgure 8.30
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