Separation of vectors into
components
(Component = part)
Consider the dog below. What
direction is the force on the dog?
Up & to Right
Up & to Left
Down & right
Down and left
ft
nd
le
na
30
Do
w
Do
w
n&
rig
ht
eft
to
L
Up
&
to
R
ig h
t
0% 0% 0% 0%
Up
&
A.
B.
C.
D.
NOW, if the leash were held in the direction of
the red arrow, predict how the force on the
dog would be different?
More L less up
More R less up
More up less R
More up more
R
ore
R
ss R
re
u
pm
p le
30
Mo
re
u
Mo
re
R
Mo
re
L
les
les
su
su
p
p
25% 25% 25% 25%
Mo
A.
B.
C.
D.
NOW, if the leash were held in the direction of
the red arrow, predict how the force on the
dog would be different?
More L less up
More R less up
More up less R
More up more
R
ore
R
ss R
re
u
pm
p le
30
Mo
re
u
Mo
re
R
Mo
re
L
les
les
su
su
p
p
25% 25% 25% 25%
Mo
A.
B.
C.
D.
NOW, if the leash were held in the direction of
the red arrow, predict how the force on the
dog would be different?
A. Just up, no L or
R
B. Just down, no L
or R
C. No force at all
ea
ta
No
for
c
rR
Lo
wn
, no
do
Jus
t
Jus
t
up
, no
Lo
rR
ll
33% 33% 33%
30
NOW, if the leash were held in the direction of
the red arrow, predict how the force on the
dog would be different?
A. Just L no up nor
down
B. Just R no up nor
down
C. No force
whatsoever.
hat
soe
ver
.
ew
for
c
30
No
ou
pn
or
Rn
Jus
t
Jus
t
Ln
ou
pn
or
do
w
do
wn
n
33% 33% 33%
• Vector Components:
–In many (most) real world situations,
forces, velocities, accelerations etc. are
NOT parallel to the horizontal and
vertical planes and have a Vertical and
Horizontal component simultaneously.
–In order to describe or predict motion
and forces, it is necessary to consider
each component separately
Consider the following example of a stone
thrown at an angle and a velocity, v.
• v = 10m/s
v = 10 m/s
• Hypothesize which stone stays in the air the
longest?
• Justify your hypothesis.
Consider the following example of a stone
thrown at an angle and a velocity, v.
• v = 10m/s
v = 10 m/s
• Hypothesize which stone is travelling
horizontally the fastest?
• Justify your hypothesis.
Estimate the horizontal component of
the 10 m/s velocity vector
/s
25%
2m
/s
25%
12
m
25%
/s
/s
25%
8m
10m/s
8m/s
12m/s
2m/s
10
m
A.
B.
C.
D.
:30
Estimate the horizontal component of
the 10 m/s velocity vector
/s
25%
2m
/s
25%
12
m
25%
/s
/s
25%
8m
10m/s
8m/s
12m/s
2m/s
10
m
A.
B.
C.
D.
:30
Estimate the vertical component of the
10 m/s velocity vector
/s
25%
2m
/s
25%
12
m
25%
/s
/s
25%
8m
10m/s
8m/s
12m/s
2m/s
10
m
A.
B.
C.
D.
:30
Estimate the vertical component of the
10 m/s velocity vector
/s
25%
2m
/s
25%
12
m
25%
/s
/s
25%
8m
10m/s
8m/s
12m/s
2m/s
10
m
A.
B.
C.
D.
:30
How do we figure out the horizontal and
vertical components (we need numbers!)
• Draw a rough sketch of the vector SHOWING the
magnitude and the angle made with the
horizontal.
• Sketch a rectangle around the vector
• Beginning with the tail, sketch the first
component of the vector along the rectangle,
then continue from the corner and sketch the
second component showing direction with
arrows.
• Calculate components using SOH CAH TOA
DIRECTION!
• Components to the RIGHT or UP are ____ive .
• Components to the LEFT or DOWN are ___ive.
Here is one example
Lets do the example in the homework
• The physics classroom link from my website
has a GREAT tutorial on vectors. Just take yout
time and go through it when you have a
chance.
• This powerpoint in on my website.