MECE 701 Fundamentals of Mechanical Engineering

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MECE 701 Fundamentals of Mechanical Engineering
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MECE 701
Engineering Mechanics
Mechanics of Materials
MECE701
Machine Elements Machine Design
Materials Science
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Fundamental Concepts
Idealizations Particle A particle has a mass
but its size can be neglected. Rigid Body A
rigid body is a combination of a large number of
particles in which all the particles remain at a
fixed distance from one another both before and
after applying a load
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Fundamental Concepts

• Concentrated Force
• A concentrated force represents the effect of
  a loading which is assumed to act at a point on
  a body

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Newtons Laws of Motion

• First Law
• A particle originally at rest, or moving in a
  straight line with constant velocity, will
  remain in this state provided that the particle
  is not subjected to an unbalanced force.

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Newtons Laws of Motion

• 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.
• Fma

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Newtons Laws of Motion

• Third Law
• The mutual forces of action and reaction between
  two particles are equal, opposite, and collinear.

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Newtons Laws of Motion

• Law of Gravitational Attraction
• FG(m1m2)/r2
• F force of gravitation btw two particles
• G Universal constant of gravitation
• 66.73(10-12)m3/(kg.s2)
• m1,m2 mass of each of the two particles
• r distance between two particles

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Newtons Laws of Motion

• Weight
• Wweight
• m2mass of earth
• r distance btw earths center and the particle
• ggravitational acceleration
• gGm2/r2
• Wmg

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Scalars and Vectors

• Scalar
• A quantity characterized by a positive or
  negative number is called a scalar. (mass,
  volume, length)
• Vector
• A vector is a quantity that has both a magnitude
  and direction. (position, force, momentum)

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Basic Vector Operations

• Multiplication and Division of a Vector by a
  Scalar
• The product of vector A and a scalar a yields a
  vector having a magnitude of aA

2A
-1.5A
A
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Basic Vector Operations

• Vector Addition
• Resultant (R) AB BA
• (commutative)

Parallelogram Law
Triangle Construction
B
RAB
A
A
RAB
A
A
RAB
B
B
B
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Basic Vector Operations

• Vector Subtraction
• R A-B A(-B)
• Resolution of a Vector

a
R
A
b
B
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Trigonometry

• Sine Law

A
B
c
a
b

• Cosine Law

C
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Cartesian Vectors

• Right Handed Coordinate System

AAxAyAz
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Cartesian Vectors

• Unit Vector
• A unit vector is a vector having a magnitude of
  1.
• Unit vector is dimensionless.

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Cartesian Vectors

• Cartesian Unit Vectors

A AxiAyjAzk
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Cartesian Vectors

• Magnitude of a Cartesian Vector

• Direction of a Cartesian Vector

DIRECTION COSINES
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Cartesian Vectors

• Unit vector of A

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Cartesian Vectors

• Addition and Subtraction of Cartesian Vectors
• RAB(AxBx)i(AyBy)j(AzBz)k
• RA-B(Ax-Bx)i(Ay-By)j(Az-Bz)k

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Dot Product

• Result is a scalar.

Result is the magnitude of the projection vector
of A on B.
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Dot Product

• Laws of Operation

Commutative law
Multiplication by a scalar
Distributive law
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Cross Product

• The cross product of two vectors A and B yields
  the vector C
• C A x B

• Magnitude
• C ABsin?

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Cross Product

• Laws of Operation

Commutative law is not valid
Multiplication by a scalar
a(AxB) (aA)xB Ax(aB) (AxB)a
Distributive law
Ax(BD) (AxB) (AxD)
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Cross Product
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Cross Product