Addition of Vectors Imagine that you have a map that leads you to a buried treasure. Imagine that...

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Transcript of Addition of Vectors Imagine that you have a map that leads you to a buried treasure. Imagine that...
Addition of VectorsAddition of Vectors
Imagine that you have a map that Imagine that you have a map that
leads you to a buried treasure.leads you to a buried treasure.
This map has instructions such as 15This map has instructions such as 15
paces west northwestpaces west northwest
of the skull.of the skull.
The 15 paces is The 15 paces is
a distance and westa distance and west
northwest is a direction.northwest is a direction.
N
Quantities that are described by a Quantities that are described by a
magnitude (such as the distance on magnitude (such as the distance on
the previous slide) and a direction the previous slide) and a direction
are called are called vectorsvectors.. Those quantities that have no Those quantities that have no
direction are called direction are called scalarsscalars..
Examples of Examples of scalarsscalars in physics are in physics are
massmass timetime
distancedistance speedspeed
workwork energyenergy
Examples of Examples of vectorsvectors in physics are in physics are
displacementdisplacement velocityvelocity
accelerationacceleration forceforce
momentummomentum angular momentumangular momentum
The math associated with scalars The math associated with scalars
is familiar to everyone.is familiar to everyone. The math associated with The math associated with
vectors is more involved.vectors is more involved. Today you will explore the Today you will explore the
graphical addition of vectors.graphical addition of vectors.
Let’s use a treasure map again Let’s use a treasure map again
as an example of the addition of as an example of the addition of
vectors.vectors. Let’s imagine the instructions tell Let’s imagine the instructions tell
you to go 4 miles east then 3 you to go 4 miles east then 3
miles north.miles north.
4 miles
3 miles
5 miles
36.90
In this case you could have gone 3 In this case you could have gone 3
miles north first and then 4 miles miles north first and then 4 miles
east next and still end up at the east next and still end up at the
same location.same location. Your final position is 5 miles at Your final position is 5 miles at
36.936.900 north of east. north of east. It would have saved time if that It would have saved time if that
had been the one distance and one had been the one distance and one
direction traveled in the first place.direction traveled in the first place.
We say that the 5 miles at 36.9We say that the 5 miles at 36.900
north of east is the vector sum of the north of east is the vector sum of the
4 miles east vector and the 3 miles 4 miles east vector and the 3 miles
north vector.north vector. The order of the addition does not The order of the addition does not
matter.matter. Examples of addition of vectors Examples of addition of vectors
follows. The method used is thefollows. The method used is the
headtotailheadtotail method. method. You must know how to do these for You must know how to do these for
your lab exams.your lab exams.
HeadtoTail Method of Addition of Two Vectors
HeadtoTail Method of Addition of Three Vectors
You will need to use a scale when you You will need to use a scale when you graph your vectors.graph your vectors.
For example, you might set 10 cm to For example, you might set 10 cm to represent 100 grams.represent 100 grams.
How to ConstructHow to ConstructTwo Perpendicular LinesTwo Perpendicular Lines
(With a Protractor)(With a Protractor)
to form ato form aSet of Coordinate AxesSet of Coordinate Axes
45 @ N 3F1
W E
S
N
How to ConstructHow to Constructa Second Set of a Second Set of
Coordinate Axes Parallel toCoordinate Axes Parallel toan Initial Set of an Initial Set of Coordinate AxesCoordinate Axes
Mark the angle for the vector.
Remember the angle marked.
45 @ N 3F1
60 @ N 1F2
210 @ N 2F3
W E
S
N
321 FFFR
65.9 @ N 2.18R
Resultant
00
900
1800
2700
W E
S
N
321 FFFR
65.9 @ N 2.18R
Resultant
Equilibrant 45 @ N 3F1
60 @ N 1F2
210 @ N 2F3
3F
1F
2F