PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165
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Transcript of PHY 2048C General Physics I with lab Spring 2011 CRNs 11154, 11161 & 11165
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PHY 2048CGeneral Physics I with lab
Spring 2011CRNs 11154, 11161 & 11165
Dr. Derrick BoucherAssoc. Prof. of Physics
Session 2, Chapter 3
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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)
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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.”)
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• The need for vectors• Graphical representation• Mathematical formulation: components and unit vectors• Vector algebra with components
Outline
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Chapter 3. Reading Review Chapter 3. Reading Review QuestionsQuestions
Starting next week, questions like the following
could be quiz questions.
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PRSClicker
Questions
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What is a vector?
A. A quantity having both size and directionB. The rate of change of velocityC. A number defined by an angle and a
magnitudeD. The difference between initial and final
displacementE. None of the above
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What is the name of the quantity represented as ?
A. Eye-hatB. Invariant magnitudeC. Integral of motionD. Unit vector in x-directionE. Length of the horizontal axis
i
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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.
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Chapter 3. Basic Content and Chapter 3. Basic Content and ExamplesExamples
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EXAMPLE 3.2 Velocity and displacement
QUESTION:
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EXAMPLE 3.2 Velocity and displacement
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EXAMPLE 3.2 Velocity and displacement
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EXAMPLE 3.2 Velocity and displacement
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EXAMPLE 3.2 Velocity and displacement
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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.
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Example problem Chapter 3 #6 (p. 87)
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Unit vectors
i j k
•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.”
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Unit vectorsX Y Z
i j k
x y z
Some math and science texts use these symbols
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Unit vectors
mis ˆ14
TjB ˆ073.0
mkh ˆ10287.1 4
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:
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Unit vectors for oblique vectors
jiB ˆ5ˆ1
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:
51 yx BandBThis contains the same information as:
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Example problem Chapter 3 #10 (p. 87)
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Adding via components
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Unit vectors are orthogonal
kjikjiji ˆ4ˆ2ˆ9ˆ4ˆ3ˆ8ˆ5ˆ1
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:
!!!!!!!!15ˆ4ˆ3ˆ8ˆ5ˆ1 kjiji
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Using Vectors
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Using Vectors
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Example problem Chapter 3 #12 (p. 87)
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PRSClicker
Questions
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Which figure shows ? A A A1 2 3
(Assume A 3 has twice the magnitude of A1 and A2 . )
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Which figure shows 2 − ?A
B
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What are the x- and y-components Cx and Cy of vector ?
C
A. Cx = 1 cm, Cy = –1 cmB. Cx = –3 cm, Cy = 1 cmC. Cx = –2 cm, Cy = 1 cmD. Cx = –4 cm, Cy = 2 cmE. Cx = –3 cm, Cy = –1 cm
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A. tan–1(Cy /Cx)
B. tan–1(Cx /|Cy|)C. tan–1(Cy /|Cx|)D. tan–1(Cx /Cy)E. tan–1(|Cx |/|Cy|)
Angle φ that specifies the direction of is given by
C