Chapter 3 - Vectors. I. Definition. Arithmetic operations involving vectors. A) Addition and subtraction

Transcription

1 Chpter 3 - Vectors I. Defnton II. Arthmetc opertons nvolvng vectors A Aton n sutrcton - Grphcl metho - Anltcl metho Vector components B Multplcton

2 Revew of ngle reference sstem 9º º<θ <9º 9º<θ <8º 8º θ θ º Orgn of ngle reference sstem 8º<θ 3 <7º 7º θ 3 θ 4 7º<θ 4 <36º Angle orgn Θ 4 =3º=-6º

3 I. Defnton Vector quntt: quntt wth mgntue n recton. It cn e represente vector. Emples: splcement, veloct, ccelerton. Dsplcement oes not escre the oect s pth. Sme splcement Sclr quntt: quntt wth mgntue, no recton. Emples: temperture, pressure

4 Rules: 3. lw commuttve 3. lw ssoctve c c II. Arthmetc opertons nvolvng vectors - Geometrcl metho s Vector ton: s

5 Vector sutrcton: 3.3 Vector component: proecton of the vector on n s. sn 3.4 Sclr components of tn 3.5 Vector mgntue Vector recton

6 Unt vector: Vector wth mgntue. No mensons, no unts.,, unt vectors n postve recton of,, es 3.6 Vector component Vector ton: - Anltcl metho: ng vectors components. r 3.7

7 Vectors & Phscs: -The reltonshps mong vectors o not epen on the locton of the orgn of the coornte sstem or on the orentton of the es. - The lws of phscs re nepenent of the choce of coornte sstem. ' 3.8 ' ' Multplng vectors: - Vector sclr: - Vector vector: Sclr prouct = sclr quntt s f 3.9 ot prouct

8 9 Rule: 3. 9 Multplng vectors: - Vector vector Vector prouct = vector sn c c cross prouct Mgntue Angle etween two vectors:

9 sn sn 9 Vector prouct Drecton rght hn rule Rule: 3. c perpenculr to plne contnng, Plce n tl to tl wthout lterng ther orenttons. c wll e long lne perpenculr to the plne tht contns n where the meet. 3 Sweep nto through the smllest ngle etween them.

10 Rght-hne coornte sstem Left-hne coornte sstem

11 sn

12 P: If B s e to C = 3 + 4, the result s vector n the postve recton of the s, wth mgntue equl to tht of C. Wht s the mgntue of B? Metho Metho Isosceles trngle B C B 3 4 D D θ C D C tn 3/ B B 3 D B 9 3. B / sn B Dsn 3. D P: A fre nt goes through three splcements long level groun: for.4m SW,.5m E, 3 =.6m t 6º North of Est. Let the postve recton e Est n the postve recton e North. Wht re the n components of, n 3? Wht re the n the components, the mgntue n the recton of the nt s net splcement? c If the nt s to return rectl to the strtng pont, how fr n n wht recton shoul t move? m N m D m D m E.4sn 45.8 D m.5m 45º tn 4.8 North of Est m 3 3.6sn 6.5m B c Return vector negtve of net splcement, D=.57m, recte 5º South of West

13 P ?,??? 3 of plne n n to perpenculr of Component long of Component c n r etween Angle r θ r m r r r m m c // // perp m m perp perp // P3 If 5 4 3? 4 Tp: Thn efore clculte!!! 4 9, 4 4 4, to perpenculr plne to perpenculr plne n contne

14 P4: Vectors A n B le n n plne. A hs mgntue 8. n ngle 3º; B hs components B =-7.7,B = -9.. Wht re the ngles etween the negtve recton of the s n the recton of A, the recton of AB, c the recton of AB+3? A 3º Angle etween n A B Angle, A B C ngle plne A, B 9, ecuse C perpenculr c Drecton A B 3 D E B D A E D D D 99 D 97.6

15 P5: A wheel wth rus of 45 cm rolls wthout sleepng long horontl floor. At tme t the ot P pnte on the rm of the wheel s t the pont of contct etween the wheel n the floor. At lter tme t,the wheel hs rolle through one-hlf of revoluton. Wht re the mgntue n the ngle reltve to the floor of the splcement P urng ths ntervl? Vertcl splcement: R. 9m Horontl splcement: R. 4m r.4m.9m r m R tn 3.5 R P6: Vector hs mgntue of 5. m n s recte Est. Vector hs mgntue of 4. m n s recte 35º West of North. Wht re the mgntue n recton of +?. Wht re the mgntue n recton of -?. c Drw vector grm for ech comnton. W - - N 5º + S E 5 4sn tn m m 3.8 tn or North of West