Vectors: Direction o. vector steps 2018.notebook. September 26, Quantities can either be scalar or vector. 90 o.

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1 Vectors: Quantities can either be scalar or vector Size only mass time speed Size and direction force velocity acceleration Vector quantities can be represented by an arrow called a vector. The vector has a tail and a head. The head of the vector shows direction. (tail marks origin) The length of the vector shows the size of the quantity. A scale is used to draw size/length. if the vector is to represent a force you could make it 3. cm long. The scale would be 1cm = 2 N Types of vectors: Components = vectors at act on an object Direction 36 o 9 o esultant = a single vector that is the vector sum of components that are acting 18 o o /36 o Equilibrant = equal and opposite to a resultant equal in size and opposite in direction E = 27 o 1

2 Quadrant N, S, E, W West of North N East of North 2 W of N N 2 21 N of E W North of West South of West North of East South of East E W E West of South East of South S of E S max angle of 45 o 25 W of S S F 1 = 55 N at. F 2 = 45 N at N 1) 2) 55 N Two forces act on an object. One force is 55 N acting at., and the second is 45 N acting at 9. What is the resulting force? 45 N. 55 N Point diagram: all components drawn from a single point Steps for solving vector problems using 1) List data "Graphical Analysis" 2) draw Point diagram listing angles freehand head of c 1 (from point diagram) 4) draw in all angles...use alternate interior/exterior and complimentary/supplementary angles 5) move tail of c 2 to head of c 1 at angle c 2 is from axis Picture diagram 3) 55 N. Vector Diagram 45 N Drawn according to the rules of vector addition! 6) calculate angle between c 1 and c 2 (happy angle) 2

3 vector steps 218.notebook 7. N at 32. 1) List data Two forces act on an object. One force is 6. N acting at 1., and the second is 7. N acting at 32. What is the resulting force? 7. N at 32. 1) List data Two forces act on an object. One force is 6. N acting at 1., and the second is 7. N acting at 32. What is the resulting force? point diagram 2) draw Point diagram listing angles 7. N at 32 4) draw in all angles...use alternate interior/exterior and complimentary/supplementary angles

4 5) move tail of c 2 to head of c 1 at angle c 2 is from axis 6) calculate angle between c 1 and c 2 Note how c 2 is 5 counterclockwise of "Y", ( clockwise from "X") Therefore, c 2' is also 5 counter clockwise of "Y" c 2 ' = c 2 c 2 ' c 2 7. N at 32. a) measure angle of C 1 7. N at 32. a) measure angle of C 1 b) draw C 1 to scale 4

5 7. N at 32. a) measure angle of C 1 b) draw C 1 to scale c) measure happy angle 1 a) measure angle of b) draw C 1 to scale c) measure happy angle d) draw C 2 to scale d) draw C 2 to scale e) draw from tail of C 1 to head of C 2 d) draw C 2 to scale e) draw from tail of C 1 to head of C 2 f) measure magnitude and direction of = 118 N 5

6 1 17 f) measure magnitude and direction of Two forces act on an object. One force is 85 N at 112 and the other is 77 N at 12. What is the resustant? 1 17 = 118 N at 343 = 118 N at = = 343 F 1 = 85 N at 1 F 2 = 77 N at Two forces act on an object. One force is 85 N at 112 and the other is 77 N at 12. What is the resustant? F 1 = 85 N at 1 F 2 = 77 N at 6

7 F 1 = 85 N at 1 F 2 = 77 N at F 1 = 85 N at 1 F 2 = 77 N at 4) draw in all angles...use alternate interior/exterior and complimentary and supplementary angles 78 4) draw in all angles...use alternate interior/exterior and complimentary/supplementary angles 5) move tail of c 2 to head of c 1 at angle c 2 is from axis F 1 = 85 N at 1 F 2 = 77 N at 4) draw in all angles...use alternate interior/exterior and complimentary and supplementary angles 5) move tail of c2 to at angle c2 is from axis F 1 = 85 N at 1 F 2 = 77 N at 4) draw in all angles...use alternate interior/exterior and complimentary and supplementary angles 8 5) move tail of c2 to at angle c2 is from axis 6) calculate angle between c1 and c ) calculate angle between c1 and c2 7

8 8 o 68 o vector steps 218.notebook F 1 = 85 N at 1 F 2 = 77 N at 4) draw in all angles...use alternate interior/exterior and complimentary and supplementary angles 8 5) move tail of c2 to at angle c2 is from axis 6) calculate angle between c1 and c2 F 1 = 85 N at 1 F 2 = 77 N at 3) o o 8 o 6) 5) = 14 at o 68 o 68 o F 1 = 85 N at 1 F 2 = 77 N at Same problem done slightly differently 68 o 8

9 vector steps 218.notebook 7. N at N at N at N 9