1. Physics 101: Lecture 4, Pg 1 Lecture 4: Introduction to Physics PHY101 Chapter 1 : Scalars and Vectors (1.5)

2. Physics 101: Lecture 4, Pg 2 Vectors Vectors are graphically represented by arrows:  The direction of the physical quantity is given by the direction of the arrow.  The magnitude of the quantity is given by the length of the arrow.

3. Physics 101: Lecture 4, Pg 3 Addition of Vectors l Graphical: Tail-to-head method l Resultant of Forces (Addition of Vectors) Resultant of Forces (Addition of Vectors)

4. Physics 101: Lecture 4, Pg 4 Graphical Method - Example You are told to walk due east for 50 paces, then 30 degrees north of east for 38 paces, and then due south for 30 paces. What is the magnitude and direction of your total displacement ? Answer: magnitude: 84 paces direction: 7.5 degrees south of east

5. Physics 101: Lecture 4, Pg 5 Addition of Vectors l Using components (A,B lie in x,y plane): C = A+B = A x + A y + B x + B y = C x +C y Cx and Cy are called vector components of C. They are two perpendicular vectors that are parallel to the x and y axis. A x,A y and B x, B y are vector components of A and B.

6. Physics 101: Lecture 4, Pg 6 Scalar Components of a Vector (in 2 dim.) l Vector components of vector A: A = A x +A y l Scalar components of vector A: A = A x x +A y y A x and A y are called scalar components of A. x and y are unit vectors. Equivalently: A=(A x,A y ) A is a vector pointing from the origin to the point with coordinates A x,A y.

7. Physics 101: Lecture 4, Pg 7 Scalar Components of a Vector (in 2 dim.) l Scalar components of vector A: A = A x x +A y y | A|,  known: |A x |= |A| Cos  |A y |=|A| Sin  A x, A y known: A 2 =(A x ) 2 +(A Y ) 2  = Tan -1 |A y |/|A x |

8. Physics 101: Lecture 4, Pg 8 Addition of Vectors l Using scalar components (A,B lie in x,y plane): C = A+B = A x x + A y y+ B x x+ B y y= C x x+C y y 1. Determine scalar components of A and B. 2. Calculate scalar components of C : C x = A x +B x and C y =A y +B y 3. Calculate |C| and  : C 2 =(C x ) 2 +(C Y ) 2  = Tan -1 |C y |/|C x |

9. Physics 101: Lecture 4, Pg 9 Component Method - Example You are told to walk due east for 50 paces (A), then 30 degrees north of east for 38 paces (B), and then due south for 30 paces (C). What is the magnitude and direction of your total displacement R=A+B+C ? 1. Determine scalar components of A,B,C: A x =50 p., A y =0, B x =38 p. cos 30, B y =38 p. sin 30 C x =0, C y =-30 p. 2. Determine Rx,Ry: R x =A x +B x +C x =83 p. R y =A y +B y +C y =-11 p. 3. Determine R: R=(R x 2 +R y 2 ) 1/2 =84 p.  =Tan -1 R y /R x =7.5 degrees below the +x axis

10. Physics 101: Lecture 4, Pg 10 Addition of Vectors l vector sum vector sum

11. Physics 101: Lecture 4, Pg 11 Components of a Vector - Example l What is the magnitude of the vector F=-5 x-6 y ? l What angle does it make with the +x direction ? Answer: F=(-5,-6), F x =-5, F y =-6, F=(5 2 +6 2 ) 1/2 = 7.8  =Tan -1 |Fy|/|Fx| = 50 degrees Angle with the +x direction: (180+  ) degrees=230 degrees

12. Physics 101: Lecture 4, Pg 12 Lecture 4: Scalars and Vectors Vector addition using scalar components of a vector I strongly suggest that you try the example problems in the textbook. If you have trouble with any of them, please go to office hours for help!