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Lecture 4: Introduction to Physics PHY101

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

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Lecture 4: Introduction to Physics PHY101

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

  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. Addition of Vectors • Graphical: Tail-to-head method • Resultant of Forces (Addition of Vectors)

  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. Using components (A,B lie in x,y plane): C = A+B = Ax + Ay + Bx + By = Cx+Cy Cx and Cy are called vector components of C. They are two perpendicular vectors that are parallel to the x and y axis. Ax,Ay and Bx, By are vector components of A and B. Addition of Vectors

  6. Scalar Components of a Vector (in 2 dim.) • Vector components of vector A: A = Ax +Ay • Scalar components of vector A: A = Axx +Ayy Ax and Ay are called scalar components of A. x and y are unit vectors. Equivalently: A=(Ax,Ay) A is a vector pointing from the origin to the point with coordinates Ax,Ay.

  7. Scalar Components of a Vector (in 2 dim.) • Scalar components of vector A: A = Axx +Ayy |A|, q known: |Ax|= |A| Cos q |Ay|=|A| Sin q Ax, Ay known: A2=(Ax )2+(AY)2 q= Tan-1 |Ay|/|Ax|

  8. Using scalar components (A,B lie in x,y plane): C = A+B = Axx + Ayy+ Bxx+ Byy= Cxx+Cyy 1. Determine scalar components of A and B. 2. Calculate scalar components of C : Cx = Ax+Bx and Cy=Ay+By 3. Calculate |C| and q : C2=(Cx )2+(CY)2q= Tan-1 |Cy|/|Cx| Addition of Vectors

  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 ? • Determine scalar components of A,B,C: Ax=50 p. , Ay=0, Bx=38 p. cos 30 , By=38 p. sin 30 Cx=0, Cy=-30 p. • Determine Rx,Ry: Rx=Ax+Bx+Cx=83 p. Ry=Ay+By+Cy=-11 p. • Determine R: R=(Rx2+Ry2)1/2=84 p. q=Tan-1 Ry/Rx=7.5 degrees below the +x axis

  10. Addition of Vectors • vector sum

  11. Components of a Vector - Example • What is the magnitude of the vector F=-5 x-6 y ? • What angle does it make with the +x direction ? Answer: F=(-5,-6), Fx=-5, Fy=-6, F=(52+62)1/2= 7.8 q=Tan-1 |Fy|/|Fx| = 50 degrees Angle with the +x direction: (180+q) degrees=230 degrees

  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!

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