What’s Your Vector Victor?
or, in German, “ein-ge-vector”
Types of Quantities:

Scalar
– size only
 speed
 mass

Vector
– size and direction
– velocity, acceleration, momemtum
– force, pressure, torque, impulse
Expressing Vectors

Size:
Each unit represents a set magnitude
 if
one unit equals 10 newtons then the force
vector equals 100 N
Expressing Vectors:

Direction:
N
900
___0 ___ of ___
Deviation - major
1800
00
2700
E
W
S
Expressing Vectors
350 N of E
250 S of W
1200
3200
Rules for Vector Addition



#1 Draw first vector component to scale
#2 Start the tail of the second
component at the head of the first and
draw it
#3 Start the tail of the resultant at the
tail of the first component and end it at
the head of the last component
Vector Addition
C2
C1
R
C1
R
C2
C1
R
C3
C2
Two forces are applied to our little prankster!
Fb = 70 N
Fg = 65 N
Reduce our little prankster to a point and and
show both forces from that point!
Fb = 70 N
Fg = 65 N
Reduce our little prankster to a point and and
show both forces from that point!
P
Fb = 70 N
Fg = 65 N
Convert our point diagram to a vector diagram!
You do this by following the rules of vector addition.
P
Fb = 70 N
Fg = 65 N
Convert our point diagram to a vector diagram!
You do this by following the rules of vector addition.
Let’s consider Fg as component one and Fb as component
two.
P
Fb = 70 N
Fg = 65 N
Convert our point diagram to a vector diagram!
You do this by following the rules of vector addition.
Let’s consider Fg as component one and Fb as component
two.
Draw Fg first!
Then draw Fb
P
Remember, the tail
of Fb starts at the head
of Fg
Fg = 65 N
Fb = 70 N
Let’s consider Fg as component one and Fb as component
two.
Draw Fg first!
Then draw Fb
Remember, the tail
of Fb starts at the head
of Fg
Draw the resultant
Remember to start the tail
of the resultant from the tail of
Fg and ending at the head
of Fb
P
Fg = 65 N
Fb = 70 N
Wow, the family pet just won’t
budge! (da!)
Wow, the family pet just won’t
budge! (da!)
Dad pulls with 70 N
Ma pulls with 65 N
Fg = 65 N
Fb = 70 N
Reduce for pet to a point!
Fg = 65 N
Fb = 70 N
P
Now draw our vector diagram!
Fb = 70 N
R
Fg = 65 N
P
Resolving Vectors
A Resultant is broken down into two or more components
R
Cv
Ch
Sin 400 = CV / R or CV = Sin 400 (R)
Cos 400= CH / R or CH = Cos 400 (R)
R
400
CV
CH
Graphically Analysis of Vectors
F1
F1 = 85 N at 400
F2
F2 = 75 N at 2500
Graphically Analysis of Vectors
F1
F1Y
F1X
F2
F2Y
F2X
F1
F1Y
F1X
F2
SFX = FX1 + F X2
F2Y
F2X
SFY = FY1 + FY2
Fx1 = Cos q x F1 =
F1
F1Y
400
F1X
F2
200F
2Y
F2X
SFX = FX1 + F X2
SFY = FY1 + FY2
Fx2 = Sin q x F2 =
SFx = Fx1 x Fx2 =
Fy1 = Sin q x F1 =
Fy2 = Cos q x F2 =
SFy = Fy1 + Fy2 =
F1
F1X
F1Y
F2X
FX
F2Y
F1X
FY
F2
SFX = FX1 + F X2
F2Y
F1Y
F2X
SFY = FY1 + FY2
FR2 = FX2 + FY2
FX
Tan 0 = FY / FX
F1X
0
FR
F2X
FX
F2Y
FY
F1Y
FY
Equilibrant Vectors

E = -(R)

Same size and 1800 in direction
Two-Dimensional Motion


Projectile Motion
Periodic Motion
Projectile Moion
Vx
Vx
Vy
Vx
Vy
Vx = constant
Vy = varying
Vy
Vx
Vx
Vy
Vx
Vy
Formulas:
Vx = constant
therefore,
Vx = d/t
Vy
Vy = varying
therefore, acceleration
vf = vi + at
vf2 = vi2 + 2ad
d = vi + 1/2at2
Projectile Motion
vi
q
vx
vy
Vy = sinq(vi)
Vx = cosq(vi)
Vy controls how long
it’s in the air and how
high it goes
Vx controls how far it goes
Projectile Motion
“Range formula”
Remember!!!!!
yi
vi
vi is the velocity at an angle and the
sin2q is the sine of 2 x q
R = vi2 sin2q/g
Range formula works only when yi = yf
yf
Projectile Motion
“Range formula”
R = vi2 sin2q/g
vi
If vi = 34 m/s and q is 41o then,
R = (34 m/s)2 sin82o/9.8 m/s2
R = 1160 m2/s2 (0.99)/9.8 m/s2
R = 120 m
Projectile Motion
“Range formula”
Note that if q becomes the complement
of 41o, that is, q is now 49o, then,
vi
q
vi = 34 m/s and q is 49o then,
R = (34 m/s)2 sin98o/9.8 m/s2
R = 1160 m2/s2 (0.99)/9.8 m/s2
R = 120 m
So, both 41o and 49o yield “R”
Projectile Motion
“Range formula”
vi
vy
yi
vx
If vi = 34 m/s and q is 41o then,
vy = sin41o(34m/s) = 22m/s, and
t = vfy - viy/g = -22m/s - (22m/s)/-9.8m/s2 = 4.5 s
vx = cos41o(34 m/s) = 26 m/s, and
dx = vx(t) = 26m/s (4.5 s) = 120 m
yf
C1
E
C2
C1
E
C2
R
E
C1
C2
E
T1
T1
1/2
FW
T2
T2
Cos 400 = 1/2 FW / T1
T1
800
T2
Al’s Food Pit
T1 = 1/2 FW / Cos 400