Vectors Serway and Jewett Chapter 3

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1 Vectos Sewa and Jewett Chapte 3 Scalas and Vectos Vecto Components and Aithmetic Vectos in 3 Dimensions Unit vectos i, j, k Pactice Poblems: Chapte 3, poblems 9, 19, 31, 45, 55, 61

2 Phsical quantities ae classified as scalas, vectos, etc. Scala : descibed b a eal numbe with units eamples: mass, chage, eneg... Vecto : descibed b a scala (its magnitude) and a diection in space eamples: displacement, velocit, foce... Vectos have diection, and obe diffeent ules of aithmetic.

3 Notation Scalas : odina o italic font (m, q, t...) Vectos : - Boldface font (v, a, F...) - aow notation (v, a, - undeline (v, a, F...) F...) Pa attention to notation : constant v and constant v mean diffeent things!

4 Magnitude : a scala, the length of a vecto. e.g., Speed, v = v (a scala), is the magnitude of velocit v Multiplication: scala vecto = vecto A 3 2 A 1 2 A Late in the couse, we will use two othe tpes of multiplication: the dot poduct, and the coss poduct.

5 Vecto Addition: Vecto + Vecto = Vecto e.g. A + B = C A B Tiangle Method Paallelogam Method A B A C = A + B C = A + B B

6 Quiz Two students ae moving a efigeato. One pushes with a foce of 200 newtons, the othe with a foce of 300 newtons. Foce is a vecto. The total foce the (togethe) eet on the efigeato is: a) equal to 500 newtons 2 2 b) equal to newtons c) not enough infomation to tell

7 Anothe Quiz Two students ae moving a efigeato. One pushes with a foce of 200 newtons, the othe with a foce of 300 newtons. The magnitude of the total foce the eet must be at least a) 500 newtons b) 300 newtons c) 200 newtons d) 100 newtons e) zeo

8 Quiz Conside two foces, F 1 and F 2, with F 1 =200N, and F 2 =300N, but with diections not specified. If we subtact the two foces, what is the lagest possible value of F 2 F 1? a) 500 newtons b) 300 newtons c) 200 newtons d) 100 newtons e) zeo

9 Question Two students ae moving a efigeato. One pushes with a foce of 200 newtons, the othe with a foce of 300 newtons. Is it possible fo the total foce the eet to equal 200 newtons?

10 Eample Poblem Two foces act on a block. One foce is 200N veticall downwads, the othe is 100N in magnitude, but can be in an diection. In what diection should the 100N foce be applied so that the total foce makes the lagest possible angle to the vetical?

11 Coodinate Sstems In 2-D : descibe a location in a plane b pola coodinates : distance and angle θ (, ) b Catesian coodinates : θ 0 distances,, paallel to aes

12 Components define the aes fist v v,(and v ) ae scalas, z aes don t have to be hoizontal and vetical v v the vecto and its components fom a ight tiangle with the vecto on the hpotenuse v

13 3-D Coodinates (location in space) We use a ight-handed coodinate sstem with thee aes: z z

14 Is this a ight-handed coodinate sstem? Does it matte? z

15 Unit Vectos A unit vecto u o û is a vecto with magnitude 1 : û = 1 (a pue numbe, no units) z k Define coodinate unit vectos i, j, k along the,, z ais. i j

16 A vecto A can be witten in tems of its components: A = A i + A j + A z k A j A A A j j i A i A i

17 Addition again: A A B B If A + B = C, A B then: C C C z = = = A A A z B B B z Thee scala equations fom one vecto equation! C A A A B B B C C

18 Difficult Quiz The foce of ai esistance on a cclist is equal to cv 2, in a diection opposite to v (c is some constant, v is the speed of the cclist). The -component of the foce will be: a) b) c) d) cv 2 cvv both of the above none of the above F θ v

19 Summa vecto quantities must be teated accoding to the ules of vecto aithmetic vectos add b the tiangle ule o paallelogam ule a vecto A can be epesented in tems of its catesian components using the unit vectos i, j, k C = A + B if and onl if: C = A + B C = A + B Cz = Az + Bz

Physics Tutorial V1 2D Vectors

Physics Tutorial V1 2D Vectors Physics Tutoial V1 2D Vectos 1 Resolving Vectos & Addition of Vectos A vecto quantity has both magnitude and diection. Thee ae two ways commonly used to mathematically descibe a vecto. y (a) The pola fom:,