EGN 3321 Final Exam Review Spring 2017
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1 EN 33 l Em Reew Spg 7 *T fshg ech poblem 5 mues o less o pcce es-lke me coss. The opcs o he pcce em e wh feel he bee sessed clss, bu hee m be poblems o he es o lke oes hs pcce es. Use ohe esouces lke he oes, emples, d homewok o bee pepe fo he em. *M soluos wll be posed fe he eew o m wodpess se hps://ucfs.wodpess.com/dmcs-wh-l/
2 Chpe : Kemcs of Pcles Kemcs: sud of geome of moo; o efeece o cuse of moo Kecs: sud of elos esg bewee foces cg o bod, mss of he bod, d moo of he bod pcle hs mss bu eglble se/shpe so oo c be egleced; gd bod hs dmeso so slo d oo e cosdeed Newo s s lw: pcle wll em cos se f hee e o ublced foces Newo s d lw: whe foce cs o pcle, wll ccelee he deco of he foce Newo s 3 d lw: foces of co d eco e equl, oppose d colle Recle: poso, eloc, d cceleo of pcle mog sgh le o No Ufom Moo ege eloc d seous eloc= d d d seous cceleo d d +: cesg + eloc o decesg eloc -: decesg + eloc o cesg - eloc o Ufom Moo: s cos o Rele moo ( )
3 o Depede moo Cble ssems d cod legh e cos Cule: poso, eloc, d cceleo of pcle mog log cued le o 3D o Recgul: pojecle moo g g Moo hool s cos; moo ecl s ufoml cceleed m hegh, V=; m ge: R=(V sq)/g; fee fll: V =(gy) / Veco fom j k d d d j k j k j k d d d d d d j k j k j k d d d Moo ele o mog fme: o o Tgel d oml compoes e d e e d o Rdl d sese e e e e e
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5 Chpe : Kecs of Pcles: Newo s d Lw he esul foce cg o pcle s o eo, he pcle wll he cceleo popool o he mgude of he esul d he deco of he esul m m m m m m m m m o The dee of gul momeum wh espec o me s equl o he mome bou O j k O mv mv V mv m O m m m M O o o bod mog ude cel foce, h cos, whee h=gul momeum/u mss Uesl o: Mm cos of go m m 3 kg s m f he esul foce s eo, le momeum ems cos o poblem solg, lws dw ou D d KD Noml d Tgel o Equos of Moo: m m d m m d Rdl d Tsese o Equos of Moo: gul Momeum mv O f 4 lb s 4
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7 Chpe 3: Kecs of Pcles: Eeg d Momeum Wok-Eeg mehods wok well whe ge eloces d dsplceme o Equo: T U T o Powe: e whch wok s doe du d d d o Effcec: oupu wok powe oupu effcec pu wok powe pu mpulse d momeum: mpulse s foud b egg boh sdes of Newo s d lw wh espec o me whee m s he le momeum. Ths mehod woks well whe ge d eloces d me. m d m d m d d m m o mpulse foce s foce h s lge eough o c o pcle oe sho me d cuse chge he momeum. The esulg moo s clled mpulse moo. m m mpc: collso bewee bodes. Lge foces oe smll me el o Le of mpc: oml o he sufces coc o Cel mpc: he mss cees of he bodes e o he le of mpc Dec mpc: he eloces of he bodes c log he le of mpc Peod of defomo peod of esuo: he fs occus fe mpc whe he bodes e coc d mog ogehe, he secod occus fe whe he ehe eg shpe o em defomed Coseo of momeum: m m m m e s he coeffce of esuo d s he sepo eloc/ppoch eloc. e o pefecl plsc: e= o pefecl elsc: e= (ol eeg d momeum coseed) Oblque mpc: oe o boh bodes moe log le ohe h he le of mpc he equos fom dec mpc e used fo he oml compoes m m m m e Tgel momeum s coseed (DON T ORET TS)
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9 Chpe 4: Ssems of Pcles Usg Newo s Lw d momeum, he ssem of eel foces (cg o pcle) d he ssem of effece foces (m of he pcle fe he foce) e equpolle, o equle. Equpolle mes he he equl powe o effec. Le momeum: he esul of he eel foces = e of chge of le momeum. f hee e o eel foces, L=cos (coseo of momeum) gul momeum: he mome esul bou po = e of chge of gul momeum. f hee e o eel foces, o=cos (coseo of momeum) Mss cee: he mss cee moes s f ll eel foces wee coceed h po Eeg mehods: he kec eeg = kec eeg of he mss cee + kec eeg ele o ceodl fme. ll of he eeg d momeum mehods fom C3 c be ppled o ssem of pcles. L d L d M O m m L m L L O O m m m m M O O m m L m L m m m m m m
10 Chpe 5: Kemcs of Rgd odes Tslo s. oo: slo, ll pcles o he bod moe pllel phs whch c be ecle o cule; wh oo, pcles moe pllel ccul phs o Do cofuse cule slo wh oo o Tslo: ll pcles he bod he he sme eloc d cceleo o Roo: bou fed s k k d d o o ufoml cceleed oo: To coe fom ds o eoluos, dde b *p; o coe fom pm o d/s, mulpl b *p/6. eel ple moo s cosdeed o be he sum of slo d oo wh espec o b po. cceleo compoe gel k k k
11 seous cee of oo: we c fd he CR b fdg he po whee he pepedcul dsce fom he eloc ecos esec o The pcle he cee of oo hs eo eloc bsolue d ele cceleo k Re of chge wh espec o og fme: Q Q Q Q Q Q O Re of chge wh espec o fed po: j Q j Q k Ple moo ele o og fme P OXY O P O O k Q Q Q OXYZ O P P c O P P P P P eloc of P o ph P P O c O P bsolue eloc of P P' cools
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14 m m m Δ Δ Δ Chpe 6: Ple Moo of Rgd odes: oces d cceleos Kecs of gd bodes: eloshp bewee foces o gd bod d he shpe, mss d moo poduced. Use he fomo fom hs chpe whe ge foces d cceleos Equos: d lembe s Pcple: he eel foces cg o gd bod e equle o he effece foces of he pcles fomg he bod Ple moo s he sum of slo d oo o ou D: sole he bod, dw s, dw foces, dw suppo ecos, d dd dmesos; o KD: sole he bod, dw m d α Kemc elo bewee he moo of he mss cee d moo of he bod bou po s: fo ollg moo: o ollg whou sldg: o ollg, sldg mpedg: o Rog d sldg: o cceleo of mss cee: M m d m Δ s N s N N k O O O O O
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16 Chpe 7: Ple Moo of Rgd odes: Eeg d Momeum Pcple of Wok d Eeg woks fo poblems olg dsplcemes d eloces T U o The e wok of el foces eo o Wok of foce dug dsplceme U U T d M d M f M s cos o Kec eeg of gd bod T m Tslo + oo Ol use he ool compoe whe hee s fed s of oo o Powe s he e whch wok s doe du Powe d o M Pcple of mpulse d Momeum woks fo poblems olg eloces d me s cos s ds L d L O M Od O o Reew week slde 34 fo mpulse momeum dgms o gul momeum bou fed s O: m d m Whe hee e o eel foces cg o gd bod: L L Eccec mpc poblems e soled wh mpulse d Momeum d Coeffce of Resuo Rd e coeffce of esuo M d O Pd m m m
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18 Chpe 8: Kecs of Rgd odes 3D The mehod o fd befoe s o ld fo 3D bodes d moo. o he gul momeum bou, he cee of mss: m m Δ o o he pcpl es of e, o d ω he he sme deco f d ol f ω s deced log pcpl s of e o he gul momeum bou some po O: O m The pcple of mpulse d momeum c be ppled o he ssem o eeg mehods, he kec eeg s: es coespod seousl o pcple es: ) ( m T Rgd bod wh fed po: ) ( T f O coespods seousl wh O : ) ( T o e of chge of gul momeum, k j Eule s Equos: M M M
19 o gd bod oo bou fed s, M M M o f smmec bou ple, ΣM=, ΣM= o f o smmec, ee f α=, he sum of eel momes wll o be goscope hs oo wh fed mss cee bu c sp feel d ssume oeo o φ, θ, d ψ e clled he Eule gles e of pecesso e of uo e of sp K j k s j cos k M M s cos cos s cos s cos cos d M d o Reew Week 3 slde 35 fo sed pecesso of goscope o smmecl bod ude o foce, hee e cses: sp bou s of smme o sp bou ese s s s cos cos
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