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### Hukum Newton, Vektor

Pertemuan - 1

Mata Kuliah : Statika

Kode : TSP – 106

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• TIU :

• Mahasiswa dapat menjelaskan tentang prinsip keseimbangan, uraian, dan penjumlahan gaya.

• TIK :

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• Sub Pokok Bahasan :

• Definisi

• Uraian dan Penjumlahan

• Text Book :

• Hibbeler, R.C. (2004). Statics and Mechanics of Materials SI Edition.

• Hibbeler, R.C. (2010). Structural Analysis. 8th edition. Prentice Hall. ISBN : 978-0-13-257053-4

• Meriam, J.L., Kraige,L.G., (2006), Engineering Mechanics - Statics. 6th edition. John Wiley & Sons, Inc. ISBN : 978-0471739326

Bobot Penilaian :

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## Mechanics

Mekanika adalah sebuah divisi dari Ilmu Pengetahuan yang mempelajari perilaku sebuah objek akibat beban yang bekerja tehadapnya.

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Subdivisions of Mechanics

Mechanics

Deformable Bodies

Rigid Bodies Fluids

Statics (At Rest)

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• First Law

“A particle originally at rest, or moving in a straight line with constant velocity, will remain in this state provided the particle IS NOT subjected to an unbalanced external force”

Ne ton’s Three La s of Motion

Balanced Forces

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• Second Law

“A particle acted upon by an unbalanced force

(F) experiences an acceleration ( a ) that has the

same direction as the force and a magnitude that

is directly proportional to the force”. If ( F ) is

applied to a particle of mass (m), this law may be expressed mathematically as:

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• Third Law

“The mutual forces of action and reaction

between two particles are equal in magnitude, opposite in direction and collinear in

orientation”.

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A law governing the gravitational attraction between any two particles is mathematically stated as:

F = G [m1 m2 / r2]

Where F = force of gravitation between the two particles

G = A universal constant of gravitation; (66.73x10-12 m3/kg s2)

m1 and m2 = mass of each of the two particles r = the distance between the two particles

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Weight is the gravitational force between the earth and the particle. If we assume that:

W = weight of the particle

m = m1 = is the mass of the particle m2 = is the mass of the earth

r = is the distance between the earth’s center and the particle

Then:

W = G [m m2 / r2]

Letting:

g = G m2 / r2

Therefore, from the second law of motion ( F = ma ):

W = mg

Where

g = the acceleration due to gravity

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SI Units

SI is known as the International System of Units where Length is in meters (m), time is in seconds (s), and mass is in kilograms (kg) and force is in Newton (N)

(1 Newton is the force required to give 1 kilogram of mass an acceleration of 1 m/s2).

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Conversion Factors

Force; 1 lb = 4.4482 N

Mass; slug = 14.5938 kg

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Prefixes

giga = G = 109 = 1,000,000,000

mega = M = 106 = 1,000,000

kilo = k = 103 = 1,000

milli = m = 10-3 = 0.001

micro = μ = 10-6 = 0.000 001

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FORCE VECTORS

Scalars and Vectors

Scalar

• A quantity identified by positive or negative number.

• It is characterized by its magnitude only

• Elementary algebra is used when mathematical operations are

involved

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Vector

• A quantity by its magnitude and direction

• Examples include force, moment, and

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### Graphical Representation of a Vector

• Vectors are represented by ARROWS

• Magnitude is represented by the length of the

arrow

• Direction is defined by

• Vector A is written as A

Line of Action

A

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Multiplication and Division of a Vector by a Scalar • Vector A

• Scalar a

A a = aA

• Magnitude of aA

• Direction of A if a is positive (+)

• Direction of –A (opposite) if a is negative (-)

### Vector Operations

A

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• Vectors are added according to the parallelogram law

• The resultant R is the diagonal of the parallelogram

• If two vectors are co-linear (both have the same line of

A

B

A

B

R = A + B

A

B

R = A + B B A

R = A + B

A B

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• The resultant is the difference between vectors A and B

### Vector Subtraction

A

B -B

A

R R A

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If lines of action are known, the resultant R can be resolved into two components acting along those lines (i.e. a and b).

### Resolution of a Vector

a b

A

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### Analysis of Problems

• Two procedures to be followed:

Parallelogram law

Trigonometry

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### Cosine Law

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Example 1

• The screw eye in figure is subjected to two

forces F1 and F2. Determine the

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Using Parallelogram Law

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Example 2

• Resolve the 1000-N

force acting on the pipe, into components in the : (a) x and y direction; (b)

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Example 3

• The ring show in figure is subjected to two forces F1

and F2. If it is required that the resultant force have a magnitude of 1 kN and be directed vertically

downward, determine (a) the magnitudes of F1 and F2

provided  = 30o, (b) the magnitude of F1 and F2 if F2

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• In particular, the minimum length or magnitude of F2 will occur when its line of action is perpendicular to F1.

• Hence, when  = 90o – 20o = 70o, F

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