What’s Your Vector Victor? or, in German, “ein-ge-vector”

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

E

S

W

900

2700

1800 00

___0 ___ of ___

Deviation - major

Expressing Vectors350 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

C1

C2

R

C1

C2

R

C1

C2C3

R

Two forces are applied to our little prankster!

Fg = 65 N

Fb = 70 N

Fg = 65 NFb = 70 N

Reduce our little prankster to a point and andshow both forces from that point!

Fg = 65 NFb = 70 N

Reduce our little prankster to a point and andshow both forces from that point!

P

Fg = 65 NFb = 70 N

P

Convert our point diagram to a vector diagram!

You do this by following the rules of vector addition.

Fg = 65 NFb = 70 N

P



Let’s consider Fg as component one and Fb as componenttwo.

Fg = 65 N

P



Let’s consider Fg as component one and Fb as componenttwo.Draw Fg first!

Then draw Fb

Remember, the tailof Fb starts at the headof Fg

Fb = 70 N

Fg = 65 N

P

Let’s consider Fg as component one and Fb as componenttwo.

Draw Fg first!

Then draw Fb

Remember, the tailof Fb starts at the headof Fg

Draw the resultant

Remember to start the tailof the resultant from the tail ofFg and ending at the head of Fb

Fb = 70 N

Wow, the family pet just won’tbudge! (da!)

Wow, the family pet just won’tbudge! (da!)

Ma pulls with 65 NDad pulls with 70 N

Fb = 70 NFg = 65 N

Reduce for pet to a point!

Fb = 70 NFg = 65 N

P

Now draw our vector diagram!

Fb = 70 N

Fg = 65 N

P

R

Resolving VectorsA Resultant is broken down into two or more components

R

Ch

Cv

R

CH

CV

Sin 400 = CV / R or CV = Sin 400 (R)

Cos 400= CH / R or CH = Cos 400 (R)

Graphically Analysis of VectorsF1

F2

F1 = 85 N at 400

F2 = 75 N at 2500

Graphically Analysis of VectorsF1

F2

F1X

F1Y

F2Y

F2X

F1

F2

F1Y

F1X

F2Y

F2X

FX = FX1 + F X2

FY = FY1 + FY2

F1Y

F1X

FX = FX1 + F X2

FY = FY1 + FY2

F2Y

F2

F2X

F1 Fx1 = Cos x F1 =

Fx2 = Sin x F2 =

Fx = Fx1 x Fx2 =

Fy1 = Sin x F1 =

Fy2 = Cos x F2 =

Fy = Fy1 + Fy2 =

400

200

F1Y

F1X

F1X

FX

FX = FX1 + F X2

FY = FY1 + FY2F2Y

F2Y

F1Y

FY

F2

F2X

F1

F2X

FR2 = FX

2 + FY2

Tan 0 = FY / FX

F1X

FX

F2Y

F1Y

FY

F2X

FX

FY

FR

0

Equilibrant Vectors

E = -(R)

Same size and 1800 in direction

Two-Dimensional Motion

Projectile Motion Periodic Motion

Projectile MoionVx

Vx

Vx

Vy

Vy

Vy

Vx = constant

Vy = varying

Vx

Vx

Vx

Vy

Vy

Vy

Formulas:

Vx = constant therefore,

Vx = d/t

Vy = varying therefore, acceleration

vf = vi + atvf

2 = vi2 + 2ad

d = vi + 1/2at2

Projectile Motion

vi vy

vx

Vy = sin(vi)

Vx = cos(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”

vi R = vi2 sin2/gyi

yf

Range formula works only when yi = yf

Remember!!!!! vi is the velocity at an angle and the sin2 is the sine of 2 x


vi

R = vi2 sin2/g

If vi = 34 m/s and is 41o then,

R = 1160 m2/s2 (0.99)/9.8 m/s2

R = 120 m

R = (34 m/s)2 sin82o/9.8 m/s2


vi

Note that if becomes the complementof 41o, that is, is now 49o, then,

vi = 34 m/s and is 49o then,

R = 1160 m2/s2 (0.99)/9.8 m/s2

R = 120 m

R = (34 m/s)2 sin98o/9.8 m/s2

So, both 41o and 49o yield “R”


vi

yiyf

If vi = 34 m/s and is 41o then,vy

vy = sin41o(34m/s) = 22m/s, andvx

dx = vx(t) = 26m/s (4.5 s) = 120 m

vx = cos4 m/s) = 26 m/s, and

vy

t = vfy - viy/g = -22m/s - (22m/s)/-9.8m/s2 = 4.5 s

C1

C2

E

C1

C2

R E

C1

C2

E

Al’s Food Pit

800T1 T2

T1 T2

E

T2T1

1/2FW

Cos 400 = 1/2 FW / T1

T1 = 1/2 FW / Cos 400

What’s Your Vector Victor? or, in German, “ein-ge-vector”

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