2. What’s Your Vector Victor? or, in German, “ein-ge-vector”

3. Types of Quantities: s Scalar –size only u speed u mass s Vector –size and direction –velocity, acceleration, momemtum –force, pressure, torque, impulse

4. Expressing Vectors s Size: Each unit represents a set magnitude u if one unit equals 10 newtons then the force vector equals 100 N

5. Expressing Vectors: s Direction: N E S W 90 0 270 0 180 00 ___ 0 ___ of ___ Deviation - major

6. Expressing Vectors 35 0 N of E 25 0 S of W

7. 120 0 320 0

8. Rules for Vector Addition s #1 Draw first vector component to scale s #2 Start the tail of the second component at the head of the first and draw it s #3 Start the tail of the resultant at the tail of the first component and end it at the head of the last component

9. Vector Addition C1C1 C2C2 R

10. C1C1 C2C2 R

11. C1C1 C2C2 C3C3 R

12. Two forces are applied to our little prankster! F g = 65 N F b = 70 N

13. F g = 65 N F b = 70 N Reduce our little prankster to a point and and show both forces from that point!

14. F g = 65 N F b = 70 N Reduce our little prankster to a point and and show both forces from that point! P

15. F g = 65 N F b = 70 N P Convert our point diagram to a vector diagram! You do this by following the rules of vector addition.

16. F g = 65 N F b = 70 N P Convert our point diagram to a vector diagram! You do this by following the rules of vector addition. Let’s consider F g as component one and F b as component two.

17. F g = 65 N P Convert our point diagram to a vector diagram! You do this by following the rules of vector addition. Let’s consider F g as component one and F b as component two. Draw F g first! Then draw F b Remember, the tail of F b starts at the head of F g F b = 70 N

18. F g = 65 N P Let’s consider F g as component one and F b as component two. Draw F g first! Then draw F b Remember, the tail of F b starts at the head of F g Draw the resultant Remember to start the tail of the resultant from the tail of F g and ending at the head of F b F b = 70 N

19. Wow, the family pet just won’t budge! (da!)

20. Wow, the family pet just won’t budge! (da!) Ma pulls with 65 N Dad pulls with 70 N F b = 70 N F g = 65 N

21. Reduce for pet to a point! F b = 70 N F g = 65 N P

22. Now draw our vector diagram! F b = 70 N F g = 65 N P R

23. Resolving Vectors A Resultant is broken down into two or more components R ChCh CvCv

24. R CHCH CVCV   Sin 40 0 = C V / R or C V = Sin 40 0 (R) Cos 40 0 = C H / R or C H = Cos 40 0 (R)

25. Graphically Analysis of Vectors F1F1 F2F2 F 1 = 85 N at 40 0 F 2 = 75 N at 250 0

26. Graphically Analysis of Vectors F1F1 F2F2 F 1X F 1Y F 2Y F 2X

27. F1F1 F2F2 F 1Y F 1X F 2Y F 2X  F X = F X1 + F X2  F Y = F Y1 + F Y2

28. F 1Y F 1X  F X = F X1 + F X2  F Y = F Y1 + F Y2 F 2Y F2F2 F 2X F1F1 F x1 = Cos  x F 1 = F x2 = Sin  x F 2 =  F x = F x1 x F x2 = F y1 = Sin  x F 1 = F y2 = Cos  x F 2 =  F y = F y1 + F y2 = 40 0 20 0

29. F 1Y F 1X FXFX  F X = F X1 + F X2  F Y = F Y1 + F Y2 F 2Y F 1Y FYFY F2F2 F 2X F1F1

30. F R 2 = F X 2 + F Y 2 Tan 0 = F Y / F X F 1X FXFX F 2Y F 1Y FYFY F 2X FXFX FYFY FRFR 0

31. Equilibrant Vectors s E = -(R) s Same size and 180 0 in direction

32. Two-Dimensional Motion s Projectile Motion s Periodic Motion

33. Projectile Moion VxVx VxVx VxVx VyVy VyVy VyVy V x = constant V y = varying

34. VxVx VxVx VxVx VyVy VyVy VyVy Formulas: V x = constant therefore, V x = d/t V y = varying therefore, acceleration v f = v i + at v f 2 = v i 2 + 2ad d = v i + 1/2at 2

35. Projectile Motion vivi vyvy vxvx V y = sin  (v i ) V x = cos  (v i ) V y controls how long it’s in the air and how high it goes V x controls how far it goes 

36. Projectile Motion “Range formula” vivi R = v i 2 sin2  /g yiyi yfyf Range formula works only when y i = y f Remember!!!!! v i is the velocity at an angle and the sin2  is the sine of 2 x 

37. Projectile Motion “Range formula” vivi R = v i 2 sin2  /g If v i = 34 m/s and  is 41 o then, R = 1160 m 2 /s 2 (0.99)/9.8 m/s 2 R = 120 m R = (34 m/s) 2 sin82 o /9.8 m/s 2

38. Projectile Motion “Range formula” vivi  Note that if  becomes the complement of 41 o, that is,  is now 49 o, then, v i = 34 m/s and  is 49 o then, R = 1160 m 2 /s 2 (0.99)/9.8 m/s 2 R = 120 m R = (34 m/s) 2 sin98 o /9.8 m/s 2 So, both 41 o and 49 o yield “R”

39. Projectile Motion “Range formula” vivi yiyi yfyf If v i = 34 m/s and  is 41 o then, vyvy v y = sin41 o (34m/s) = 22m/s, and vxvx d x = v x (t) = 26m/s (4.5 s) = 120 m v x = cos    4 m/s) = 26 m/s, and vyvy t = v fy - v iy /g = -22m/s - (22m/s)/-9.8m/s 2 = 4.5 s

40. C1C1 C2C2 E

41. C1C1 C2C2 R E C1C1 C2C2 E

42. Al’s Food Pit 80 0 T1T1 T2T2 T1T1 T2T2 E T2T2 T1T1 1/2 F W Cos 40 0 = 1/2 F W / T 1 T 1 = 1/2 F W / Cos 40 0