Physics 1710 Chapter 3 Vectors

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Physics 1710Chapter 3 Vectors

• 1' Lesson
• A Vector is a quantity that requires two or
• more numbers to define it and acts like the
• displacement vector.
• The magnitude of a vector is the square root
• of the sum of the squares of its
• components.
• A vector makes an angle to the x-axis whose
• tangent is equal to the ratio of the
• y-component to the x-component.

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Physics 1710Chapter 3 Vectors

• 80/20 Quiz
• How fast was Dr. M going when he hit the concrete
  after a fall of 1.0 meter?
• (1 m/s 2.24 mph)

v v2gd v2(9.8m/s2 )(1.0 m) 4.4 m/s
9.9 mph
Why did this break his leg?
a v2/2d (4.4 m/s)2 /(2 ? 0.02 m) 110
m/s2
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Physics 1710Chapter 3 Vectors

• Demonstration
• Egg Toss

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Physics 1710Chapter 3 Vectors

• Seat belt
• Air Bag Video

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Physics 1710Chapter 3 Vectors

• A Scalar is a entity that requires only one
  number to characterize it fully. (Like a scale.)
• Examples
• What time is it?
• What is your weight?
• What is the temperature of the room?

What is the weight of 100. Kg man? Weight g m
9.80 N/kg (100. kg) 980 N.
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Physics 1710Chapter 3 Vectors

• A vector is a quantity that requires more than
  one component to tell the whole story.
• Example
• Where is the treasure buried in the field?

Use orthogonal, that is perpendicular
axes. Example 104 Street and 102 Avenue
(104,102) 102 Street and 104 Avenue (102,104)
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Physics 1710Chapter 3 Vectors

• Position in 2-Dimensions or higher is a VECTOR.
  We use boldface, not italic to denote a vector
  quantity, italics to denote the scalar
  components.
• We often represent a vector as a position on a
  graph with an arrow connecting the origin to the
  position.

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Physics 1710Chapter 3 Vectors

• Position in 2-Dimensions or higher is a VECTOR.
  We use boldface, not italic to denote a vector
  quantity, italics to denote the scalar
  components.
• We often represent a vector as a position on a
  graph with an arrow connecting the origin to the
  position.

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Physics 1710Chapter 3 Vectors
80/20 Fact

• The length of the arrow represents the magnitude
  of the vector. In orthogonal coordinates, the
  magnitude of vector A given by
• A v Ax2 Ay2 Az2

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Physics 1710Chapter 3 Vectors
80/20 Fact

• The direction of the vector A is characterized
  (two dimensions) by the angle ? it makes with
  the x-axis.
• tan ? Ay / Ax

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Physics 1710Chapter 3 Vectors
80/20 Fact

• One may combine vectors by vector addition
• C A B
• Then
• C x Ax Bx Cy Ay By
• Key point
• Add the components separately.
• Observe strict segregation of x and y parts.

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Physics 1710Chapter 3 Vectors
80/20 Fact

• The magnitude and direction of the sum is given
  by
• ?A B? v(Ax Bx ) 2 (Ay By ) 2
• Tan ? (Ay By ) / (Ax Bx )

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Physics 1710Chapter 3 Vectors
80/20 Fact

• We often designate the components of the vector
  by unit vectors ( i, j, k ) the x,y, and z
  components, respectively.
• Thus, 2.0 i 3.0 j has an x-component of 2.0
  units and a y-component of 3.0 units.
• Or (2.0, 3.0)

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Physics 1710Chapter 3 Vectors

• Summary
• To add vectors add the components.
• Use the Pythagorean theorem for the magnitude.
• Use trigonometry to get the angle.