chapter2.1-4 statics

8/10/2019 Chapter2.1-4 Statics

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SCALARS AND VECTORS

(Section 2.1)

Scalars Vectors

Examples: Mass, Volume Force, Velocity

Characteristics: It has a magnitude It has a magnitude

(positive or negative) and direction

Addition rule: Simple arithmetic Parallelogram law

Special Notation: None Bold font, a line, an

arrow or a carrot

In these PowerPoint presentations, a vector quantity is represented li ke this(in bold,

italics, and yellow).


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VECTOR OPERATIONS(Section 2.2)

Scalar Multiplicationand Division


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VECTOR ADDITION USING EITHER THE

PARALLELOGRAM LAW OR TRIANGLE

Parallelogram Law:

Triangle method

(always tip to tail):

How do you subtract a vector?

How can you add more than two concurrent vectors graphically ?


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Resolution of a vector is breaking up a vector into components.

It is kind of like using the parallelogram law in reverse.

RESOLUTION OF A VECTOR


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Cosine LawC =Sqrt(A2+B2-2AB Cos c)Sine Law: A/Sin a = B/Sin b = C/Sin c

A B

C

b

c

a

ABCoscBA 222

ABCoscBA 222


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READING QUIZ

1. Which one of the following is a scalar quantity?A) Force B) Position C) Mass D) Velocity

2. For vector addition, you have to use ______ law.

A) Newtons Second

B) the arithmetic

C) Pascals

D) the parallelogram


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APPLICATION OF VECTOR ADDITION

There are three concurrentforces acting on the hook

due to the chains.

We need to decide if the

hook will fail (bend orbreak)?

To do this, we need to know

the resultant force acting on

the hook.

FR


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ADDITION OF A SYSTEM OF COPLANAR FORCES

(Section 2.4)

Each component of the vector is

shown as a magnitude and a

direction.

The directions are based on the x and y axes. We use the

unit vectors iandjto designate the x and y axes.

We resolve vectors intocomponents using the x and y

axis system.


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For example,

F= Fx i + Fyj or F '= F'x i + ( F'y )j

The x and y axis are always perpendicular to each other.

Together, they can be directed at any inclination.


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ADDITION OF SEVERAL VECTORS

Step 3 is to find the magnitude

and angle of the resultant vector.

Step 2 is to add all the x-

components together, followed by

adding all the y components

together. These two totals are the

x and y components of the

resultant vector.

Step 1 is to resolve each forceinto its components.


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Break the three vectors into components, then add them.

FR= F1 + F2 + F3

= F1xi + F1yjF2xi + F2yj+ F3xi F3yj

= (F1xF2x+ F3x)i+ (F1y+ F2yF3y)j

= (FRx)i+ (FRy)j

An example of the process:


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Components of Force Vector:

Fx = FCos () FFy= F Sin (theta) 5 4

If slope of a vector given:

Fx= F( 3/5) 3Fy= F (4/5)


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EXAMPLE

Plan:

a) Resolve the forces into their x-y components.

b) Add the respective components to get the resultant vector.

c) Find magnitude and angle from the resultant components.

Given: Three concurrent forces

acting on a tent post.Find: The magnitude and

angle of the resultant

force.


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EXAMPLE (continued)

F1= {0i +300j} N

F2= {450 cos (45) i+ 450 sin (45)j} N

= {318.2 i+ 318.2j} N

F3= { (3/5) 600 i+ (4/5) 600j} N

= { 360 i+ 480j} N


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EXAMPLE

(continued)

Summing up all the iandjcomponents respectively, we get,

FR= { (0318.2 + 360) i+ (300 + 318.2 + 480)j} N

= { 41.80 i+ 1098j} N

x

y

FRUsing magnitude and direction:

FR= ((41.80)2+ (1098)2)1/2= 1099 N

= tan-1(1098/41.80) = 87.8


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CONCEPT QUIZ

1. Can you resolve a 2-D vector along two directions, which

are not at 90 to each other?

A) Yes, but not uniquely.

B) No.

C) Yes, uniquely.

2. Can you resolve a 2-D vector along three directions (say

at 0, 60, and 120)?

A) Yes, but not uniquely.B) No.

C) Yes, uniquely.


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GROUP PROBLEM SOLVING

Plan:

a) Resolve the forces into their x and y components.

b) Add the respective components to get the resultant vector.

c) Find magnitude and angle from the resultant components.

Given:Three concurrent

forces acting on a

bracket

Find: The magnitude and

angle of the

resultant force.


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F1 = { (5/13) 300 i + (12/13) 300j } N

= { 115.4 i + 276.9j} N

F2 = {500 cos (30) i + 500 sin (30)j} N

= { 433.0 i + 250j } N

F3 = { 600 cos (45) i 600 sin (45)j } N

{ 424.3 i 424.3j} N

GROUP PROBLEM SOLVING (continued)


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GROUP PROBLEM SOLVING (continued)

Summing up all the iandjcomponents respectively, we get,

FR = { (115.4 + 433.0 + 424.3) i+ (276.9 + 250424.3)j}N

= { 972.7 i + 102.7j } N

Now find the magnitude and angle,

FR = ((972.7)2 + (102.7)2) = 978.1 N

= tan1

( 102.7 / 972.7 ) = 6.03

From Positive x axis, = 6.03

x

y

FR


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ATTENTION QUIZ1. Resolve Falong x and y axes and write it in

vector form. F= { ___________ } N

A) 80 cos (30) i 80 sin (30)j

B) 80 sin (30) i + 80 cos (30)j

C) 80 sin (30)i 80 cos (30)

j

D) 80 cos (30) i + 80 sin (30)j

2. Determine the magnitude of the resultant (F1+ F2) force in N

when F1= { 10 i+ 20j} N and F

2= { 20 i + 20j} N .

A) 30 N B) 40 N C) 50 N

D) 60 N E) 70 N

30

xy

F = 80 N


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chapter2.1-4 statics

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