PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, & 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 But, concepts are essential throughout this course and the next (PHY 2049)

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.”)

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

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

PRS Clicker Questions

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

What is the name of the quantity represented as ? A.Eye-hat B.Invariant magnitude C.Integral of motion D.Unit vector in x-direction E.Length of the horizontal axis

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

Chapter 3. Basic Content and Examples

EXAMPLE 3.2 Velocity and displacement QUESTION:

EXAMPLE 3.2 Velocity and displacement

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.

Example problem Chapter 3 #6 (p. 87)

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.”

Unit vectors XYZ Some math and science texts use these symbols

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 teslas in the -y direction: Or, the nuclear bomber is 8 miles above the Earth’s surface:

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:

Example problem Chapter 3 #10 (p. 87)

Adding via components

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:

Using Vectors

Example problem Chapter 3 #12 (p. 87)

PRS Clicker Questions

Which figure shows ? (Assume A 3 has twice the magnitude of A 1 and A 2. )

Which figure shows 2 − ?

What are the x- and y-components C x and C y of vector ? A. Cx = 1 cm, Cy = –1 cm B. C x = –3 cm, C y = 1 cm C. Cx = –2 cm, Cy = 1 cm D. C x = –4 cm, C y = 2 cm E. C x = –3 cm, C y = –1 cm

A.tan –1 (C y /C x ) B.tan –1 (C x /|C y |) C.tan –1 (C y /|C x |) D.tan –1 (C x /C y ) E.tan –1 (|C x |/|C y |) Angle φ that specifies the direction of is given by