10/2/2003 PHY Lecture 9 1

Transcription

1 Announceents. Exa wll be returned at the end of class. Please rework the exa, to help soldfy your knowledge of ths ateral. (Up to 0 extra cre ponts granted for reworked exa turn n old exa, correctons on a separate paper due Tuesday, Oct. 7.). Physcs colloquu today 4 PM Oln 0 SPS eetng at :30 AM (free pzza for physcs ajors and potental physcs ajors) 3. Today s topc Chapter 9 HRW Center of ass Defnton of oentu Conseraton of oentu 0//003 PHY 3 -- Lecture 9

2 Exa -- PHY 3 D Grade 0//003 PHY 3 -- Lecture 9

3 ŷ of ass r r j xˆ r COM r 0//003 PHY 3 -- Lecture 9 3

4 Exaple:.kg.5kg 3 3.4kg x y co co x x 3x y y y 3 0//003 PHY 3 -- Lecture 9 4

5 0//003 PHY 3 -- Lecture 9 5 Another exaple of center of ass: x y (,) (,) M 0 4M 0 ( ) M M M M M M co j j r

6 Poston of the center of ass: r co r Velocty of the center of ass: co Acceleraton of the center of ass: a co a 0//003 PHY 3 -- Lecture 9 6

7 Physcs of coposte systes: F a d dp Center-of-ass elocty: Note that: F F total M d co co M 0//003 PHY 3 -- Lecture 9 7

8 0//003 PHY 3 -- Lecture 9 8

9 A new way to look at Newton s second law: F a d d( ) dp Defne lnear oentu p Consequences:. If F 0 dp 0 p constant. For syste of partcles: If F 0//003 PHY 3 -- Lecture 9 9 dp F 0 0 p dp constant

10 Conseraton of (lnear) oentu: If dp F 0, p constant Exaple: Suppose a olecule of CO s ntally at rest, and t suddenly decoposes nto separate C and O atos. In ths process the checal bndng energy E 0 s transfored nto echancal energy of the C and O atos. What can you say about the oton of these atos after the decoposton? Before After C O C C - O O 0 C O O / C 0//003 PHY 3 -- Lecture 9 0

11 Further analyss: E 0 ½ C C ½ O O ½ C C ( C / O ) ½ C C E 0 /( C / O ) ~ E 0 /( /6) 4/7 E 0 ½ O O 3/7 E 0 Extra cre opportunty: Work through the detals of the aboe analyss and erfy the results for yourself ( perhaps wth a dfferent datoc olecule). 0//003 PHY 3 -- Lecture 9

12 Peer nstructon queston: Suppose a nucleus whch has an ntal ass of M 38 0 (where 0 denotes a standard ass unt),suddenly decoposes nto two saller nucle wth M 34 0 and M 4 0. If the elocty of nucleus # s V what s the elocty of nucleus #? (a) -0.07V (b) -V (c) -59.5V After the decoposton whch nucleus has ore energy? (a) M (b) M (c) The nucle hae the sae energy. (d) Not enough nforaton s gen. 0//003 PHY 3 -- Lecture 9

13 Peer nstructon queston: Roeo (60 kg) entertans Julet (40 kg) by playng hs gutar fro the rear of ther boat (00 kg) whch s at rest n stll water. Roeo s away fro Julet who s n the front of the boat. After the serenade, Julet carefully oes to the rear of the boat (away fro shore) to plant a kss on Roeo s cheek. How does the boat oe relate to the shore n ths process? (Intally Julet s closest to the shore.) (a) 0. away fro shore (b) 0.4 away fro shore (c) 0. toward shore (d) 0.4 toward shore x CM x d x-x d J /M total 0.4 CM 0//003 PHY 3 -- Lecture 9 3

14 Another exaple: In ths case, echancal energy s not consered. (Where does t go?) Howeer, to our leel of approxaton, we wll assue that oentu s consered. Before: After: c 0c T 0T c c T 0//003 PHY 3 -- Lecture 9 4

15 0//003 PHY 3 -- Lecture 9 5 Note: In general, oentu s a ector quantty. c 0c T 0T ( c T ) f j T T c T c T c c f 0 0

16 0//003 PHY 3 -- Lecture 9 6

17 Stateent of conseraton of oentu: 0 f f cosθ snθ f f snφ cosφ If echancal (knetc) energy s consered, then: f f 0//003 PHY 3 -- Lecture 9 7

18 Peer nstructon queston: Gen the preous exaple, suarzed wth these equatons: 0 f cosθ snθ f snφ cosφ f f f f whch of the followng stateents are true? (a) It s n prncple possble to sole the aboe equatons unquely. (b) It s not possble to sole the aboe equatons unquely because the atheatcs s too dffcult. (c) It s not possble to sole the aboe equatons unquely because there s ssng physcal nforaton. 0//003 PHY 3 -- Lecture 9 8

19 0//003 PHY 3 -- Lecture 9 9 One densonal case: Conseraton of oentu: f f Conseraton of energy: ½ ½ ½ f ½ f Extra cre: Show that f f

20 Lnear oentu: p F dp Generalzaton for a coposte syste: F dp Suary Conseraton of oentu: dp If F 0; 0; p (constant) Energy ay also be consered ( for exaple, n an elastc collson) 0//003 PHY 3 -- Lecture 9 0

21 Another exaple h h. falls a dstance h energy consered. colldes wth oentu and energy consered 3. oes back up the nclne to a heght h Extra cre: Show that h h 0//003 PHY 3 -- Lecture 9

22 Noton of pulse: F dp F t p Exaple: p f - θ p( f sn θ f f sn θ f ) (- f cos θ f f cos θ f ) j f θ f p p f 0//003 PHY 3 -- Lecture 9

23 Noton of pulse: F dp cause effect p f - Exaple: p( f sn θ f f sn θ f ) (- f cos θ f f cos θ f ) j θ p p f -p F t f θ f p p f 0//003 PHY 3 -- Lecture 9 3