Graphical Addition.notebook February 05, 2016

same!origin

Graphical Addition.notebook February 05, 2016

Hi,

Next topic is adding vectors using scale diagrams and not mathematics.

When adding, we will use the "head-to-tail" method.

Graphical Addition.notebook February 05, 2016

Vector Addition ­ Graphical Method

Vectors are added "head­to­tail".

The first vector (A)  is drawn with the tail on the origin.

Put the tail of the second vector at the head of the first vector.

Draw the resultant vector from the origin to the head of the second vector.

Measure the length of the resultant and note direction.

Pick a scaling factor with which to draw the vectors.

let 1.0 cm =  5.0 km

In One Dimension

given ΔdA = 25.0 km [E]ΔdB =    15.0 km [E]

Ex 1.  Find the resultant displacement of the object:    ΔdA  +  Δd B = ΔdR

I offset the resultant displacement vectors from the original two being added so that you could see the head to tail method.

Graphical Addition.notebook February 05, 2016

Just a labelled compass will do here. Do not need graph paper.

let 1.0 cm = ___ units

N

S

EW

E

E

E

N

N

N

N

N

E

E

tail of vector two

head of vector one

head to head

tail to tail

A = 4.47 km [E 30 oN]

B = 3.61km [W 41.8o N]

R = A + B

Graphical Addition.notebook February 05, 2016

Graphical Addition.notebook February 05, 2016

Draw:

|ΔdA| = 3.0 cm

|ΔdB| = 2.0 cm

N

S

Ewθα

α

magnitude

ΔdR

Graphical Addition.notebook February 05, 2016

May try the next ones if you like.

I do have a print out of this worksheet to be handed out.

Graphical Addition.notebook February 05, 2016

a)

b) Draw the vector addition to find the resultant horizontal force acting on the object given the applied force is 3.6 N [E] and the force of kinetic friction is 4.3 N [W].

Draw the vector addition to find the resultant displacement given .Δd1 = 1.8 km [E] and Δd2 = 3.2 km [E].

answer [compass] =  _________________answer [ CCW]     =  _________________answer [ CW]     =    _________________

answer [compass] =  _________________answer [ CCW]     =  _________________answer [ CW]     =    _________________

Drawing Vector Addition - Linear • start addition at compass• draw each vector to scale with ruler• tail of second vector starts at the head of the first vector• measure the answer with ruler

scale let 1.0 cm = 1.0 km

Graphical Addition.notebook February 05, 2016

In Two Dimensions ­ head­to­tail

Ex. 2    Find the net applied force if person one exerts 2.5 N east and person two applies 3.5 N south?   

Graphical Addition.notebook February 05, 2016

Examples to do:

Find the displacement of an airplane that flies 50 km due east and then 77 km due north.

Graphical Addition.notebook February 05, 2016

Vector addition is commutative.  Can add vectors in any order.

http://physics.bu.edu/~duffy/semester1/semester1.html

Drawing A+ B and B + A completes the parallelogram.

not so good

http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Vectors/Add2Vectors.html

Animation to make our own examples:

http://comp.uark.edu/~jgeabana/java/VectorCalc.html

Graphical Addition.notebook February 05, 2016