Physics 100

1
Physics 100

• Sections A1, A2, A3 and A4

2
Physics 100

• Chapter 1 Vectors (Sec 7, 8 and 9)

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Physical Quantities
Section 1.7

• Scalar quantity
• A physical quantity that can be described by a
  single number (magnitude).
• Vector quantity
• A physical quantity that has direction as well as
  magnitude.

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Scalar Quantities Examples
Temperature What is your temperature? 40
degrees
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Scalar Quantities Examples
Mass 160 kg !!!
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Vector Quantities Examples
Force 980 N (magnitude) Upward (direction)
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Vector Quantities Examples
Velocity 160 km/h (magnitude) East
(direction)
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Vector Quantities Examples

• Displacement the change in position of a point.
• Represented by a line directed from the initial
  point to the final point
• Vector represents the displacement from point
  P1 to point P2

P2
P1
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Vector Quantities Examples

• Going from Makkah to Buraidah
• Paths
• Path one
• Path two
• Two paths but same displacement.

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Parallel and Equal Vectors

• If two vectors have the same direction, they are
  parallel.
• If they have the same direction and the same
  magnitude, they are equal. (movement of a
  vector!!)

Parallel Vectors
Equal Vectors
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Antiparallel Vectors

• If two vectors have opposite directions, they are
  antiparallel.
• Negative of a vector is a vector with the same
  magnitude but opposite direction

Antiparallel Vectors
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Magnitude

• Magnitude of
• The magnitude is always positive
• Represents the length of the vector

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Vector Addition
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Vector Addition
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Vector Addition
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Vector Addition
The vector C is called the vector sum of resultant
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Vector Addition
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Vector Addition
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Vector Addition Commutative
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Vector Addition
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Vector Addition
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Vector Addition
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Vector Addition
CAUTION

• Vector Addition is different from number addition

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Vector Addition
CAUTION

• Vector Addition is different from number addition

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Vector Addition
CAUTION

• Vector Addition is different from number addition

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Vector Addition Associative
Need to find
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Vector Addition Associative
One way
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Vector Addition Associative
Another way
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Vector Addition Associative
Another way
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Vector Subtraction

• Vector subtraction is an addition of the vectors
  negative

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Vector Subtraction

• Vector subtraction is an addition of the vectors
  negative

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Vector Subtraction

• Vector subtraction is an addition of the vectors
  negative

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Vector Addition
Example 1.5

• A cross-country skier skies 1.00 km north and
  then 2.00 km east on a horizontal snow field.
• (a) How far and in what direction is she from the
  starting point?
• (b) What are the magnitude and direction of her
  resultant displacement?

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Vector Addition
Example 1.5

• A cross-country skier skies 1.00 km north and
  then 2.00 km east on a horizontal snow field.
• (a) How far and in what direction is she from the
  starting point?
• (b) What are the magnitude and direction of her
  resultant displacement?

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Vector Addition
Example 1.5

• A cross-country skier skies 1.00 km north and
  then 2.00 km east on a horizontal snow field.
• (a) How far and in what direction is she from the
  starting point?
• (b) What are the magnitude and direction of her
  resultant displacement?

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Vector Addition
Example 1.5
1.00 km
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Vector Addition
Example 1.5
2.00 km
1.00 km
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Vector Addition
Example 1.5
2.00 km
1.00 km
Resultant displacement
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Vector Addition
Example 1.5
2.00 km
1.00 km
The magnitude can be found using Pythagorean
Theory
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Vector Addition
Example 1.5
2.00 km
And the angle f
1.00 km
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Vector Addition
Example 1.5
2.00 km
1.00 km
2.24 km
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Components of Vectors
Section 1.8
y

• Any vector can be represented using its
  components. (more or less like the Cartesian
  coordinates of its tips if its tail is fixed on
  the origin of the system)

x
O
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Components of Vectors
y
x
O
44
Components of Vectors
y

• The resultant of the two components is the vector
  itself

x
O
45
Components of Vectors
y

• The components are named after their coordinates.

x
O
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Components of Vectors
y

• The vector components are named after their
  coordinates.

x
O
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Components of Vectors
y

• To be consistent, vectors angles will be taken
  always from ve x-axis.

x
O
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Components of Vectors
y

• To be consistent, vectors angles will be taken
  always from ve x-axis.

x
O
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Components of Vectors
y

• Components can be positive or negative

x
O
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Components of Vectors

• Components can be positive or negative

y
x
O
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Components of Vectors
y

• Components can be positive or negative

x
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors Angles
y
x
O
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Components of Vectors
y
x
O
Angle ? is measured from the x-axis, rotating
towards the ve y-axis
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Finding Components
Example 1.6

• ( a ) What are the x- and y- components of a
  vector of magnitude 3.00 m and angle 45 from the
  ve x-axis rotating clockwise?
• (b) What are the x- and y- components of a vector
  of magnitude 4.50 m and angle 37.0 from the -ve
  y-axis rotating counterclockwise?

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Finding Components
Example 1.6
y

• ( a ) What are the x- and y- components of a
  vector of magnitude 3.0 m and angle 45 from the
  ve x-axis rotating clockwise?

x
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Finding Components
Example 1.6
y
x
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Finding Components
Example 1.6
y
x
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Finding Components
Example 1.6

• (b) What are the x- and y- components of a vector
  of magnitude 4.50 m and angle 37.0 from the -ve
  y-axis rotating counterclockwise?

x
y
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Finding Components
Example 1.6
x
y
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Finding Components
Example 1.6
x
y
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Using Components to Add Vectors
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Using Components to Add Vectors
y
x
O
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Using Components to Add Vectors
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Vector Addition
Problem-Solving Strategy

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)

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Problem-Solving Strategy
Vector Addition

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)
• EXECUTE the solution

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Problem-Solving Strategy
Vector Addition

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)
• EXECUTE the solution
• 1- Find x- and y-components of each vector AxA
  cos ?, AyA sin ?

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Problem-Solving Strategy
Vector Addition

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)
• EXECUTE the solution
• 1- Find x- and y-components of each vector AxA
  cos ?, AyA sin ?
• 2- Add the individual components to find Rx and Ry

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Problem-Solving Strategy
Vector Addition

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)
• EXECUTE the solution
• 1- Find x- and y-components of each vector AxA
  cos ?, AyA sin ?
• 2- Add the individual components to find Rx and
  Ry
• 3- R(Rx2Ry2) ½ ? arctan (Ry/Rx)

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Problem-Solving Strategy
Vector Addition

• IDENTIFY the relevant concepts and SET UP the
  problem
• Target variable (Magnitude of the sum, direction
  or both)
• EXECUTE the solution
• 1- Find x- and y-components of each vector AxA
  cos ?, AyA sin ?
• 2- Add the individual components to find Rx and
  Ry
• 3- R(Rx2Ry2) ½ ? arctan (Ry/Rx)
• EVALUATE your answer
• Compare your answer with your estimate.

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Adding Vectors with components
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Adding Vectors with components
?A
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Adding Vectors with components
Ay
Ax
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Adding Vectors with components
Ay
?B
Ax
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Adding Vectors with components
Ay
Ax
Bx
By
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Adding Vectors with components
AyBy
AxBx
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Adding Vectors with components
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Adding Vectors
Example 1.7

• The three finalists in a contest are brought to
  the center of a large flat field, Each is given a
  meter stick, a compass, a calculator, a shovel,
  and (in a different order for each contestant)
  the following three displacements
• 72.4 m east of north
• 57.3 m, 36.0 south of west
• 17.8 m straight south

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Adding Vectors
Example 1.7
y
72.4 m
32

• 72.4 m east of north

x
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Adding Vectors
Example 1.7
y
57.3 m, 36.0 south of west
36
57.3 m
72.4 m
32
x
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Adding Vectors
Example 1.7
y
36
57.3 m
72.4 m
17.8 m
32
x
17.8 m straight south
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Adding Vectors
Example 1.7
y
32
58
x
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Adding Vectors
Example 1.7
216
y
36
58
x
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Adding Vectors
Example 1.7
216
y
36
270
32
58
x
90
Adding Vectors
Example 1.7
216
y
36
57.3 m
270
72.4 m
17.8 m
32
58
x
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Adding Vectors
Example 1.7
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Adding Vectors
Example 1.7
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Adding Vectors
Example 1.7
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Adding Vectors
Example 1.7
95
Adding Vectors
Example 1.7
96
Adding Vectors
Example 1.7
y
36
57.3 m
72.4 m
17.8 m
32
? 129
x
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Adding Vectors
Example 1.7
Tryout Associative Addition
y
x
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Adding Vectors
Example 1.7
Tryout Associative Addition
y
x
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Unit Vectors
Section 1.9

• A unit vector is a vector that has a magnitude of
  1, with no units.

y
x
O
100
Unit Vectors

• It describes a direction in space.
• (pointers)

y
x
O
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Unit Vectors

• Vector components can be describe using
  components and unit vectors.

y
x
O
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Unit Vectors Vector Addition
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Unit Vectors Vector Addition
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Unit Vectors Vector Addition
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Unit Vectors Vector Addition
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Adding Vectors
Example 1.9
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Adding Vectors
Example 1.9
108
Adding Vectors
Example 1.9
109
Adding Vectors
Example 1.9
110
And the lessons continue