Chapter 4: Linear Momentum and Collisions
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1 Chater 4: Lear oetu ad Collsos 4.. The Ceter o ass, Newto s Secod Law or a Syste o artcles 4.. Lear oetu ad Its Coserato 4.3. Collso ad Iulse 4.4. oetu ad Ketc Eergy Collsos
2 4.. The Ceter o ass. Newto s Secod Law or a Syste o artcles 4... The ceter o ass (CO)
3 4... The ceter o ass Cosder a syste o artcles o asses ad searated by dstace d: d co I at ad at : co where s the total ass o the syste I the syste has artcles that are strug out alog the as: co... a. Systes o artcles
4 I the artcles are dstrbuted three desos: co co co z z y y,, k z j y r ˆ ˆ ˆ I the osto o artcle s ge by a ector: k z j y r co o co co ˆ ˆ ˆ The ceter o ass o the syste s detered by: co r r
5 b. Sold Bodes co d, y co yd, z co zd where s the ass o the object For uor objects, ther desty are: d d dv V dv V co V dv, y co V ydv, z co V zdv
6 Sale roble (. 04) Detere the ceter o ass o the late 0 S S S S S S 3 ) ( R R R area area thck ess thck ess S S S S S R R 3
7 Sale roble A syste cossts o three artcles located as show the gure. Fd the ceter o ass o the syste.
8 4... Newto s Secod Law or a Syste o artcles F a et co () F et co a : the et orce or all eteral orces : the accelerato o the ceter o ass o the syste. : the total ass o the syste. F a F a et, co, et, y co, y et, z F a co, z
9 4.. Lear oetu ad Its Coserato a. Lear oetu The lear oetu o a artcle s a ector quatty w h e re a d a re th e a s s deed as: (Ut: kg /s) a d th e e lo c ty o th e a rtc le, re s e c t e ly. Newto s secod law s eressed ters o oetu: w here F et s the et F et eteral For a syste o artcles: co o rce d dt o the artcle.... d dt d dt co... a The lear oetu o a syste o artcles s equal to the roduct o the total ass o the syste ad the elocty o the ceter o ass. co
10 b. Coserato o Lear oetu: I the et eteral orce actg o a syste o artcles s zero, F et 0 I, 0 ( X F et X, o r z) Questo: Why do we eed oetu? y, : X costat co stat Because oetu rodes us a tool or studyg collso o or ore objects.
11 4. Two artcles are lauched ro the org o the coordates syste at te t=0. =5.0 g s shot drectly alog the as wth a costat seed o 0 /s. =3.0 g s shot wth a elocty o agtude 0.0 /s, at a uward agle such that t always stays drectly aboe artcle durg ts lght. (a) What s the au heght H a reached by the CO o the two artcle syste? (b) I ut-ector otato, what are the (b) elocty ad (c) accelerato o the co whe the co reaches H a?, y, y 0 (a) At the au heght:, y 0 gy a gy artcle always stays drectly aboe.:,,, y 0,, y a 5.3 () 7.3 (/s) H a y a 5.74 ()
12 (b) co At the au heght,,y =0: (c) a co, y ; co,, 0 co, co a a co a co (0 /s) î a g a 3.68 (/s ), a co s dowward, hece : a co ( 3.68 /s ) ĵ
13 4.3. Collso ad Iulse Cosder a collso betwee a bat ad a ball: The chage the ball s oetu s: d F ( t ) dt ro a te t to a te t : t t t d F ( t) dt The ulse o the collso s deed by: t J F ( t) dt t J the chage the object s oetu I F(t) ucto s ukow: t (Ut: kg /s) the ulse o the object J F a g t
14 Eales:. A 0.70 kg ball s og horzotally wth a seed o 5.0 /s whe t strkes a ertcal wall. The ball rebouds wth a seed o.0 /s. What s the agtude o the chage lear oetu o the ball? ; Sce the ball s og horzotally, thereore, ths s oe desoal oto: ( ) /s; 5 /s : 0.7 (- - 5) (4.9 kg./s) ˆ 4.9 (kg /s)
15 . A 500-kg car traellg at a seed o 5.0 /s akes a 90 0 tur a te o 3.0 s ad eerges ro ths tur wth a seed o 3.0 /s: (a) What s the agtude o the ulse that acts o the car durg ths tur? Draw the ulse ector. (b) What s the agtude o the aerage orce o the car durg ths tur? (Fal ea, Jue 04) (a) (b) J F J ag J t (kg 95 J /s ) (N)
16 4.4. oetu ad Ketc Eergy Collsos Three tyes o collsos: We cosder a syste o bodes. Ielastc collso: costat : oetu total costat KE Soe eergy (KE) s traserred to other ors, e.g. heat, soud. costat co. Elastc collso: cosered. are ad KE K K K K
17 I oe deso: Secal cases: 0 : : ; 0 : ; : ;
18 3. erectly elastc collso: two bodes stck together ater collso: 3.. I oe deso: : cosered but ot KE. ) ( 3.. I two desos: ( ) Case 3
19 Eale: (erectly elastc collso) A 000-kg car traellg east at 80.0 k/h colldes wth a 3000 kg car traelg south at 50.0 k/h. The two cars stck together ater the collso. What s the seed o the cars ater the collso? (Fal ea, Jue 04) (kg k/h ) ( ) ( ) (k/h ) or.8 /s 80 k/h 50 k/h
20 Hoework:, 5, 3, 4,, 5, 38, 49, 56, 67, 60, 64, 74 (ages 30-37)
21 . Ceter o ass: 3. Iulse: Reew: r co r 4. Coserato o Lear oetu: Ielastc Collsos: Elastc Collsos:. Lear oetu t J F ( t) dt t J 5. oetu ad Ketc Eergy Collsos KE Ut: kg /s (lear J Foetu t ag costat ( a closed, solated syste) costat K K K K F et d dt
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