Vector Final 2007

7/27/2019 Vector Final 2007

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VECTORS


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Scalars are quantities which are fully

described by a

magnitude alone.

Vectors are quantities which are fullydescribed by both a

magni tude and

a direction.

Do you remember the difference

between a scalar and a vector?


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1. The length of the line represents the

magnitude and the arrow indicates the

direction.2. The magnitude and direction of the vector is

clearly labeled.


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The magnitude of a vector in a scaled vectordiagram is depicted by the length of the arrow.

The arrow is drawn precisely to length in

accordance with a chosen scale.

Scaling!!!


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Direction!!!

Sometimes vectors will be directed

due East or due North. However we

will encounter vectors in all sorts ofdirections and be forced to find the

angle!

Compass Coordinate System


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Compass Coordinate System

x = 30 m @ 20 E of N

V = 20 m/s @ 30 W of N

a = 10 m/s2@ 40 W of S

F = 50 N @ 10 S of E

Navigational System?

Use the same scale for all vector magnitudes

E

S

N

W

To Draw direction:

Ex. 20 E of N: Start w/ North and go 20 East


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All these planes have the same reading on

their speedometer. (plane speed not speed

with respect to the ground (actual speed)

What

factor is

affecting

theirvelocity?


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A B C


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Easy Adding


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The resultant is the

vector sum of two or

more vectors.


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1. Select an appropriate scale (e.g., 1 cm = 5 km)

2. Draw and label 1st vector to scale.

*The tail of each consecutive vector begins at the head of

the most recent vector*

3. Draw and label 2nd vector to scale starting at the head of

the 1st vector.

4. Draw the resultant vector (the summative result of the

addition of the given vectors) by connecting the tail of the1st vector to the head of the 2nd vector. (initial to final pt.)

5. Determine the magnitude and direction of the resultant

vector by using a protractor, ruler, and the indicated

scale; then label the resultant vector.


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A. Tailwind(with the wind)

120 km/h20 km/h

80 km/h

100 km/h

100 km/h

20km/h

=

B. Headwind(against the wind)

=


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80 km/h

100 km/h

60 km/h

Resultant

C. 90 crosswindUsing a ruler and your

scale, you can determine

the magnitude of the

resultant vector. Or youcould use the

Pythagorean Theorem.

Then using a protractor,

you can measure the

direction of the resultant

vector. Or you could use

trigonometry to solve for

the angle.


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1. Find the resultant force vector of the two forcesbelow. 25 N due East, 45 N due South

25 N, East

45 N, South

Decide on

a scale!!!

51 N

59 S of E51 N

31 E of S

A i l i fl i 200 h t 50o

N f E Wi d l it


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0o

N

180o

270o

An airplane is flying 200mph at 50o

N of E. Wind velocity

is 50 mph due S. What is the velocity of the plane?

Scale: 50 mph = 1 inch

A i l i fl i 200 h t 50o

N f E Wi d l it


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E

N

W

S






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E

N

W

S





200 mph

50 mph

VR= 165 mph

@ 40 N of E


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2. Find the resultant velocity vector of the twovelocity vectors below.700 m/s @35 degrees E of N; 1000 m/s @ 30 degreesN of W

V1Vr

V2


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A bear walks one milesouth, then one milewest, and finally walksone mile north. Afterhis brisk walk, the bearends back where he

started.What color is thebear???

Intro to Vectors Warm-up


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In what direction is the leash pulling

on the dog?


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Wh t ld h t th d


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What would happen to the upward

and rightward Forces if the Force on

the chain were smaller?


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1) Find the resultant

Magnitude:__________

of the two vectors Direction:___________

Vector #1 = 20.5 N West

Vector #2 = 14.3 N North

Vector Diagram

24.99 N

34.90 N of W

V2

V1

VR=?


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2) Find the component of the

resultant = 255m 27 South of East

Vector # 1 _______ Direction__________

Vector # 2________ Direction__________

Vector Diagram:

115.8 m

227.2 m

South (-)

East (+)

Vr

V2

V1

Conventions:

+

+

-

-


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1. Draw vector diagram. (Draw axis)

2. Resolve vectors into components using trig:

Vadj = V cos Vopp = V sin 3. Sum x and y components:

Vxi Vyi4. Redraw!! Determine resultant vector using

Pythagoreans Theorem and trig:

Magnitude= ( Vxi) + ( Vyi)

Direction Action: = tan-1(opp/adj)

Practice: Find FR=Fnet =?

200 N due South,

100 N at 40 N of W

Answer: Fnet = N

@ W of S

Skip


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An airplane flies at an engine speed of 100 m/s

at 50 W of S into a wind of 30 m/s at 200 E ofN. What is the airplanes resultant velocity?

Solve using the components method!!

How far has the plane traveled after 1 hr??

Answer: 75.52 m/s @ 28.54 S of W

168.89 miles per 1 hour

You Try! ! !


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You Try! ! !

A motor boat traveling 4.0 m/s, East

encounters a current traveling 3.0 m/s,

North.

a. What is the resultant velocity of the motor boat?

b. If the width of the river is 80 meters wide, then how

much time does it take the boat to travel shore to

shore?

c. What distance downstream does the boat reach the

opposite shore?


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Equilibrium

Balanced? or Unbalanced?


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Balanced? or Unbalanced?


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Forces are in Equilibrium

A th Obj t i E ilib i ?


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Are these Objects are in Equilibrium?

50 N

151 N

25 N

15 N

10 N

102 N

5 kgCeiling


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The First Condition of Equilibrium: The upward forces must

balance the downward forces, and the leftward forcesmust balance the rightward forces.

SFx = 0 SFy = 0 at equilibrium

Solution of Problems in Static's:

1) Isolate a body. What point or object are you going to talk about?

2) Draw the forces acting on the body you have isolated, and label

them. (If their value is not know, give them a symbol

such as F1, FP, T1, etc.) Rememberthis is a free-body diag.
http://eta.physics.uoguelph.ca/cgi-bin/imagemap/ship


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3) Split each of the forces into its x and y

components, and label the components in termsof the symbols given in rule 2 and the proper sines

and cosines.

4) Write down your summation equations for the first

condition of equilibrium.

5) Solve the equations for the unknowns.

Cont.

Equilibrium problem


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Equilibrium problem

10 kg

300 N

Fy

Solve for Fx & Fy?

Fx

20

Ans: Fx = 102.61 N Fy = 183.91N

Equilibrium problem


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Equilibrium problem

Solve for F?

10 kg

200 N

50 NF

30

Answer: F = 88.34 N @ 60.65 S of W


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Tension Warm-up

Find the tension in eachrope if the weight (W) is

50 N.

Be sure to pick an

appropriate point to draw

your free-body-diagram.

Then sum your x forces

and then your y-forces.

W

37 45

Answers: T1= N, T2= N


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When the strongman suspends the10N telephone book with the ropeheld vertically the tension in eachstrand of rope is 5 N. If thestrongman could suspend the bookfrom the strands pulled horizontallyas shown, the tension in eachstrand would be:

a) About 5 Nb)About 10 Nc) About 20 Nd)More than a million Newtons...basically impossible.


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The two cars below are both accelerated by a 10 N force. Whichcar experiences the larger acceleration?a) Car 1b) Car 2c) Both cars accelerate similarly.

Explain

10

10

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Vector Final 2007