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PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165

PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165. Dr. Derrick Boucher Assoc. Prof. of Physics. Session 2, Chapter 3. Chapter 3. READ IT Work out example problems Only a couple LON-CAPA questions come directly from this

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PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165

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  1. PHY 2048CGeneral Physics I with labSpring 2011CRNs 11154, 11161 & 11165 Dr. Derrick Boucher Assoc. Prof. of Physics Session 2, Chapter 3

  2. Chapter 3 • READ IT • Work out example problems • Only a couple LON-CAPA questions come directly from this • But, concepts are essential throughout this course and the next (PHY 2049)

  3. Chapter 3 Practice Problems Chap 3: 3, 7, 9, 11, 13, 15, 19, 25, 27 Unless otherwise indicated, all practice material is from the “Exercises and Problems” section at the end of the chapter. (Not “Questions.”)

  4. Outline • The need for vectors • Graphical representation • Mathematical formulation: components and unit vectors • Vector algebra with components

  5. Chapter 3. Reading Review Questions Starting next week, questions like the following could be quiz questions.

  6. PRS Clicker Questions

  7. What is a vector? • A quantity having both size and direction • The rate of change of velocity • A number defined by an angle and a magnitude • The difference between initial and final displacement • None of the above

  8. What is the name of the quantity represented as ? • Eye-hat • Invariant magnitude • Integral of motion • Unit vector in x-direction • Length of the horizontal axis

  9. To decompose a vector means • to break it into several smaller vectors. • to break it apart into scalars. • to break it into pieces parallel to the axes. • to place it at the origin. • This topic was not discussed in Chapter 3.

  10. Chapter 3. Basic Content and Examples

  11. EXAMPLE 3.2 Velocity and displacement QUESTION:

  12. EXAMPLE 3.2 Velocity and displacement

  13. EXAMPLE 3.2 Velocity and displacement

  14. EXAMPLE 3.2 Velocity and displacement

  15. EXAMPLE 3.2 Velocity and displacement

  16. Components • The x and y components of a vector tell us how much the vector lies along the x and y axes, respectively. • To calculate components of vectors you need a good diagram and some simple trigonometry. • There are no shortcuts here. The ONLY way to work with vectors are via components.

  17. Example problem Chapter 3 #6 (p. 87)

  18. Unit vectors • Unit vectors are a fancy way to say “thattaway” in mathematical notation. • Whichaway? Well, “north”, “west”, “up”, “right” are all examples of specific directions. These are, in a sense, unit vectors. • “West” doesn’t say how far, just what direction. • “Positive x direction”, etc. are also unit vector concepts. For the positive x, y and z directions, our text uses “eye hat”, “jay hat” and “kay hat.”

  19. Unit vectors Some math and science texts use these symbols

  20. Unit vectors If we want to express a particular distance, velocity, magnetic field, etc., etc. in a particular direction, we have to combine a magnitude and direction (with units!) For example, the displacement s is 14 meters in the +x direction: Or, the magnetic field, “B”, is has a strength of 0.073 teslas in the -y direction: Or, the nuclear bomber is 8 miles above the Earth’s surface:

  21. Unit vectors for oblique vectors If a vector doesn’t lie conveniently along a particular direction, it can be expressed as a sum of vectors that do lie along independent directions. If a vector lies 1 unit along the +x direction and 5 units along the +y direction, it would be expressed as: This contains the same information as: Or:

  22. Example problem Chapter 3 #10 (p. 87)

  23. Adding via components

  24. Unit vectors are orthogonal Orthogonal, or perpendicular in a multidimensional sense, means that x, y and z are completely independent directions. So, “i” terms can’t mix, algebraically, with “j” or “k” terms:

  25. Using Vectors

  26. Using Vectors

  27. Example problem Chapter 3 #12 (p. 87)

  28. PRS Clicker Questions

  29. Which figure shows ? (Assume A 3 has twice the magnitude of A1 and A2 . )

  30. Which figure shows 2 − ?

  31. What are the x- and y-components Cx and Cy of vector ? Cx = 1 cm, Cy = –1 cm Cx= –3 cm, Cy = 1 cm Cx = –2 cm, Cy = 1 cm Cx= –4 cm, Cy = 2 cm Cx= –3 cm, Cy = –1 cm

  32. Angle φthat specifies the direction of is given by tan–1(Cy /Cx) tan–1(Cx /|Cy|) tan–1(Cy /|Cx|) tan–1(Cx /Cy) tan–1(|Cx |/|Cy|)

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