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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
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