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

head-to-tailhead-to-tail method. method. You must know how to do these for You must know how to do these for

your lab exams.your lab exams.

Head-to-Tail Method of Addition of Two Vectors

Head-to-Tail 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