Vector%20addition%20can%20be%20done%20geometrically%20with%20the%20triangle%20method%20or%20the%20parallelogram%20method%20for%20two%20vectors

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3.2 Vector Addition and Subtraction

• Vector addition can be done geometrically with
  the triangle method or the parallelogram method
  for two vectors
• Vector addition can be done geometrically with
  the polygon method for more than two vectors.
• Vector subtraction is a special case of vector
  addition because
• A B A (-B)
• where a negative vector has the same magnitude
  but opposite direction of the positive vector.
• Ex the negative vector of 45 m/s north is
• 45 m/s south

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Geometric methods of vector addition Triangle
method
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The parallelogram method can be used to sum two
vectors by placing both of their tails together
and sketching the two remaining sides that would
create a parallelogram. The diagonal with the
common tail represents the resultant vector,
whose direction is away from the initial vectors
common origin.
Geometric Methods of Vector Addition Parallelogram
Method
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Example 3

• Two displacement vectors A 5m and
• B 3m are given. Show
• A B with the triangle method
• A B with the parallelogram method
• A B with the triangle method
• A B with the parallelogram method

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Vector addition is conveniently done by the
analytical component method (See p. 78 in text)

• Resolve the vectors to be added into their x- and
  y- components. Include directional signs
  (positive or negative) in the components.
• Add, algebraically, all the x-components together
  and all the y-components together to get the x-
  and y- components of the resultant vector,
  respectively.
• Express the resultant vector using
• The component form, C Cxx Cyy or
• The magnitude-angle form,
• C sqrt(Cx2 Cy2), q tan-1(Cy/Cx)

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Vectors can be resolved into components and the
components added separately then recombine to
find the resultant.
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Use the analytical component method to find the
resultant velocity of the following two
velocities.V1 35 m/s 30o north of eastV2 55
m/s 45o north of west

• Resolve the vectors to be added into their
• x- and y- components
• Add x-components together and y-components
  together
• Express the resultant vector in component form
• In magnitude-angle form

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Concept Test slides 2-13

• D\Chapter_03\Assess\Assess_Present\WBL6_ConcepTes
  ts_Ch03.ppt
• Homework Problems p. 96-98 25, 27, 28, 31, 33,
  43, 44, 48, 49, 53