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7/31/2019 PPTG101213 Scalars and Vectors GALLEGO
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Difference between scalar and vector |Representation of vectors |Resultant vectors
28 July 2012 REDG 2011 1
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Lolo Wacko got an
invitation from a
friend for Humba
Party. He was given
this instruction:
Our house is
located 8 km from
the signage in the
cross road.Which
way should he go?
28 July 2012 REDG 2011 2
Scalar vs Vector Quantities
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Lola Wacka also got
an invitation from
a friend for the
same Humba Party.
She was given this
instruction:Our
house is located 8
km west from the
signage in the
cross road.Whichway should he go?
28 July 2012 REDG 2011 3
Scalar vs Vector Quantities
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28 July 2012 REDG 2011 4
Scalar vs Vector Quantities
Ride on the School
Bus that is 8 kmfrom the house.
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28 July 2012 REDG 2011 5
Scalar vs Vector Quantities
Ride on the School
Bus that is 8 km,North from the
house.
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28 July 2012 REDG 2011 6
Scalar vs Vector Quantities
What is the difference betweenscalar quantity and vector
quantity?
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28 July 2012 REDG 2011 7
Scalar vs Vector Quantities
A scalar quantity is the aquantity that is described fully by
magnitude alone.
A vector quantity is a quantity
that is described fully by both
magnitude and direction.
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28 July 2012 REDG 2011 8
Scalar vs Vector Quantities
These are vector quantities;
1. Displacement2. Velocity
3. Acceleration
4. Force
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28 July 2012 REDG 2011 9
Scalar vs Vector Quantities
A quantity which is ignorant of direction is
referred to as _______________.
A quantity which is conscious of direction
is referred to as _______________.
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28 July 2012 REDG 2011 10
Distance vs Displacement
There are two quantities which are used
to describe the changing location.
Distance- refers to the total amount of
ground covered. Denoted by
Displacement- refers to the overall
change in position from start to finish.
Denoted by
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28 July 2012 REDG 2011 11
Distance vs Displacement
There are two quantities which are used
to describe the changing location.
Along whichpath(s) is the
distance travelled
different from thedisplacement?
1
2
3
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28 July 2012 REDG 2011 12
Distance vs Displacement
You run from your house to school that is
7 km away. You then walk home.
What distance did you travel?
What is the displacement of the entire trip?
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28 July 2012 REDG 2011 13
Distance vs Displacement
Observe the diagram below. A person
starts at A walks along the bold path andfinishes at B. Each square is 1 km long
along its edge.
A person walks atotal distance
of_______.
This person has adisplacement of
_________.
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28 July 2012 REDG 2011 14
Distance vs DisplacementDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
What is the total distance travelled by Deedee the Rider in the
3 minutes of driving?
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28 July 2012 REDG 2011 15
Distance vs DisplacementDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
What is his displacement in from t=0 to t=1?
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28 July 2012 REDG 2011 16
Distance vs DisplacementDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
What is his displacement in from t=1 to t=2?
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28 July 2012 REDG 2011 17
Distance vs DisplacementDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
What is his displacement in from t=2 to t=3?
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28 July 2012 REDG 2011 18
Distance vs DisplacementDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
What is the net displacement of Deedee the Rider in his 3-
minute joy drive?
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28 July 2012 REDG 2011 19
Distance vs Displacement
Change in distance (d) or change in
displacement () can be computed
d = |df-d
i|
= -
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28 July 2012 REDG 2011 20
Representing Displacement
All that are above is
NORTH
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28 July 2012 REDG 2011 21
Representing Displacement
All that are above isSOUTH
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28 July 2012 REDG 2011 22
Representing Displacement
All that are to the left isWEST
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28 July 2012 REDG 2011 23
Representing Displacement
All that are to the right isEAST
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28 July 2012 REDG 2011 24
Representing Displacement
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28 July 2012 REDG 2011 25
Representing Displacement
25 meters, 30o North of East (N of E)
always indicate
the description of
the vector
use scale
1cm=10m
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28 July 2012 REDG 2011 26
Representing Displacement
50 meters, 40o North of West (N of W)
always indicate
the description of
the vector
use scale
1cm=10m
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28 July 2012 REDG 2011 27
Representing Displacement
Illustrate the following vectors using
appropriate scaling.
1. 30 meters 30o west of north
2. 50 m, 40o east of south
3. 10 m, 60
o
south of west
always indicate the description
of the vector
use scale 1cm=5m
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28 July 2012 REDG 2011 28
Representing Displacement
Illustrate the following vectors using
appropriate scaling.
1. 30 meters 30o west of north
2. 50 m, 40o east of south
3. 10 m, 60
o
south of west
always indicate the description
of the vector
use scale 1cm=5m
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28 July 2012 REDG 2011 29
Speed vs Velocity
These are two quantities which are used
to describe motion:
Speedis a quantity which describes how fast or
how slow the object is moving.
Velocity- is a quantity which describes how fast or
how slow and to what direction is the object moving.
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28 July 2012 REDG 2011 30
Speed vs Velocity
Path A
Path B
Path C
Suppose you are
considering 3 paths(A, B and C)
between the same
two locations.
Along which path
do you have to
move with the
greatest speed toarrive at the
destination at the
same amount of
time?
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28 July 2012 REDG 2011 31
Speed vs Velocity
distanceAverage speed (v) =
time
displacementAverage velocity (v ) =
time
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28 July 2012 REDG 2011 32
Speed vs Velocity
Path A
Path B
Path C
Suppose that you
run for 1 minutealong three
different paths.
Rank the three
paths from the
lowest to the
greatestspeed.
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28 July 2012 REDG 2011 33
Speed vs Velocity
Path A
Path B
Path C
Suppose that you
run for 10 secondsalong three
different paths.
Rank the three
paths from the
lowest to the
greatestvelocity.
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28 July 2012 REDG 2011 34
Speed vs Velocity
What is the unit of speed?
What is the unit for velocity?
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28 July 2012 REDG 2011 35
Speed vs Velocity
Each side of the square is 1 meter per second
A plane that is travelling at 70m/s
is influenced by a wind that blows
at a speed of 7m/s. What effect
does it give to the plane?
A plane that is travelling at 70m/s
to the east is influenced by 7m/stailwind. What effect does it give to
the plane?
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28 July 2012 REDG 2011 37
Speed vs Velocity
Each side of the square is 1 meter per second
What is the difference between
7 meters per second to the east
and
7 meters per second to the west?
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28 July 2012 REDG 2011 38
Representing Displacement
l
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28 July 2012 REDG 2011 39
Representing Displacement
S d V l i
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28 July 2012 REDG 2011 40
Speed vs Velocity
Each side of the square is 1 meter
per second
What is the difference between
7 meters per second to the east
and7 meters per second to the west?
S d V l i
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28 July 2012 REDG 2011 41
Speed vs Velocity
You run from your house to school that is 7 km away
for 30 minutes. Then you immediately to go taking 1hour in walking.
What is the average speed(in kilometer per hour) of
the entire trip?
S d V l i
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28 July 2012 REDG 2011 42
Speed vs Velocity
You run from your house to school that is 7 km away
for 30 minutes. The you immediately to go taking 1hour in walking.
What is the average velocity(in kilometer per hour)
of the entire trip?
S d V l it
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28 July 2012 REDG 2011 43
Speed vs VelocityDeedee the Rider moves from location A to location B to
location C to location D. each leg of the back-and-forth motion
takes 1 minute to complete. The total time is 3 minutes.
t=0 t=2 t=3 t=1
Calculate the average speed and velocity (in meters per
minute) of the three-minute drive.
S d V l it
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28 July 2012 REDG 2011 44
Speed vs Velocity
Is it possible for an object to be moving at a
high speed and end up with no overall changein position?
If YES, describe an example.
If NO, why?
A l ti
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28 July 2012 REDG 2011 45
Acceleration
Acceleration is the rate of change ofvelocity.
How will the velocity change?
A l ti
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28 July 2012 REDG 2011 46
Acceleration
Velocity = speed + direction
Cite instances where speed changes ?
A l ti
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28 July 2012 REDG 2011 47
Acceleration
Velocity = speed + direction
Is it possible for an object to be accelerating
without changing its speed?
If YES, cite a situation.
If NO, explain.
A l ti
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28 July 2012 REDG 2011 48
Acceleration
Rule of Thumb
The direction of the acceleration of anobject that is moving in straight line and
slowing down is opposite to the
direction the object is moving.
What is the direction of the acceleration
of an object that is moving in a straight
path and is speeding up?
Acceleration
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28 July 2012 REDG 2011 49
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
A car is moving eastward along Lake Avenue
and increasing its speed from 40 km per hour
to 70 km per hour.
Acceleration
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28 July 2012 REDG 2011 50
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
A northbound car skids to stop to avoid a
reckless driver.
Acceleration
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28 July 2012 REDG 2011 51
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
An Olympic diver slows down after splashing
into the water.
Acceleration
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28 July 2012 REDG 2011 52
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
A southward-bound free kick of Don Bosco
Team is slowed down and stopped by USC
Team.
Acceleration
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28 July 2012 REDG 2011 53
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
A downward falling parachutist pulls the chord
and rapidly slows down.
Acceleration
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28 July 2012 REDG 2011 54
Acceleration
Tell the direction (left, right, up, down, east, west,
north or south) of the acceleration in the
example below:
A falling-bungee jumper slows down at she
nears concrete sidewalks below.
Force
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28 July 2012 REDG 2011 55
Force
Force
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Force
Representing Vectors
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28 July 2012 REDG 2011 57
Representing Vectors
In illustrating vectors, the length of the arrow
representing them is scaled down so that theproportion with other vectors is preserved.
Real size of the vector is represented by a shorter size. For
instance, 1cm: 10km
Representing Vectors
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Representing Vectors
Representing Vectors
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displacement
velocity
force
acceleration
28 July 2012 REDG 2011 59
Representing Vectors
Vector Notations
Representing Vectors
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28 July 2012 REDG 2011 60
Representing Vectors
Illustrate the following vectors in a single
graph
= 200km, 45o N of E
= 75km, 30o S of W
= 100km, 25o W of N
= 125km, 60o E of S
Representing Vectors
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28 July 2012 REDG 2011 61
Representing Vectors
Representing Vectors
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28 July 2012 REDG 2011 62
Representing Vectors
A curious students was
patiently observing themotion of an ant crawling
on the floor. The ant
traveled 7 cm due east
then 3cm due north, then
4 cm due east, then 7cmdue north, then 8 cm due
east.
Illustrate the path traveled
by the ant?
Representing Vectors
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28 July 2012 REDG 2011 63
Representing Vectors
A curious students was
patiently observing themotion of an ant crawling
on the floor. The ant
traveled 7 cm due east
then 3cm due north, then
4 cm due east, then 7cmdue north, then 8 cm due
east.
What is the total distance
travelled by the ant?
Resultant Vectors (Graphical Method)
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28 July 2012 REDG 2011 64
Resultant Vectors (Graphical Method)
A curious student was
patiently observing themotion of an ant crawling
on the floor. The ant
traveled 7 cm due east
then 3cm due north, then
4 cm due east, then 7cmdue north, then 8 cm due
east.
What is its displacement?
use 1cm=2cm
Resultant Vectors (Graphical Method)
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28 July 2012 REDG 2011 65
Resultant Vectors (Graphical Method)
The Resultant Vector can
be determined usinggraphical and component
method.
Resultant VectorVector sum of
two or more
vectors
Resultant Vectors (Graphical Method)
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Resultant Vectors (Graphical Method)
The Resultant Vector can
be determined usinggraphical and component
method.
Resultant VectorVector sum of
two or more
vectors
Resultant Vectors
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28 July 2012 REDG 2011 67
Resultant Vectors
A flock of birds follows the same
migratory pattern every year. Biologists
noted that they originate from Japan andflies 2500 km 60o S of W to Taiwan for a
stopover. The flock will then turn 400 E of
S and cover a distance of 1500 kmtowards the Batanes Islands in the
Philippines. How far are they from Japan?
Represent the vectors in the problem below and
determine the resultant vector.
Resultant Vectors (Graphical Method)
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28 July 2012 REDG 2011 68
Resultant Vectors (Graphical Method)
A sailboat is cruising up the Amazon
River. Its sails embraces a 40 km/hr wind
directed at 60o W of N and another windthat is moving at 35 km/hr towards the
West. If the downstream current is
moving at 10 km/hr directed at 20o Eastof South, what is the resultant velocity of
the ship.
Represent the vectors in the problem below and
determine the resultant vector.
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Resultant Vectors (Graphical Method)
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Resultant Vectors (Graphical Method)
Resultant Vectors (Graphical Method)
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( p )
No matter how you
arrange the vectors aslong as it is head to tail,
you will always get the
resultant vector.
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Most explanation and examples in this presentation are based
of the lesson presentation ofThe Physics Classroom &
Conceptual Physics. The clip arts used were taken from
different sites that I thought are free to use. This is for
classroom use only.