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MECE 701 Fundamentals of Mechanical Engineering. MECE 701. Engineering Mechanics. Mechanics of Materials. MECE701. Machine Elements & Machine Design. Materials Science. Fundamental Concepts. Idealizations: Particle: A particle has a mass but its size can be neglected. Rigid Body:

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Mece 701 fundamentals of mechanical engineering

MECE 701Fundamentals of Mechanical Engineering


Mece 701
MECE 701

Engineering Mechanics

Mechanics of Materials

MECE701

Machine Elements

&

Machine Design

Materials Science


Fundamental concepts
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


Fundamental concepts1
Fundamental Concepts

Concentrated Force:

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


Newton s laws of motion
Newton’s 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.


Newton s laws of motion1
Newton’s 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.

    F=ma


Newton s laws of motion2
Newton’s Laws of Motion

  • Third Law

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


Newton s laws of motion3
Newton’s Laws of Motion

  • Law of Gravitational Attraction

    F=G(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


Newton s laws of motion4
Newton’s Laws of Motion

  • Weight

    W=weight

    m2=mass of earth

    r = distance btw earth’s center and the particle

    g=gravitational acceleration

    g=Gm2/r2

    W=mg


Scalars and vectors
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)


Basic vector operations
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


Basic vector operations1
Basic Vector Operations

  • Vector Addition

    Resultant (R)= A+B = B+A

    (commutative)

Parallelogram Law

Triangle Construction

B

R=A+B

A

A

R=A+B

A

A

R=A+B

B

B

B


Basic vector operations2
Basic Vector Operations

  • Vector Subtraction

    R= A-B = A+(-B)

  • Resolution of a Vector

a

R

A

B

b


Trigonometry
Trigonometry

  • Sine Law

A

B

c

a

b

  • Cosine Law

C


Cartesian vectors
Cartesian Vectors

Right Handed Coordinate System

A=Ax+Ay+Az


Cartesian vectors1
Cartesian Vectors

  • Unit Vector

    A unit vector is a vector having a magnitude of 1.

    Unit vector is dimensionless.


Cartesian vectors2
Cartesian Vectors

  • Cartesian Unit Vectors

A= Axi+Ayj+Azk


Cartesian vectors3
Cartesian Vectors

  • Magnitude of a Cartesian Vector

  • Direction of a Cartesian Vector

DIRECTION COSINES


Cartesian vectors4
Cartesian Vectors

  • Unit vector of A


Cartesian vectors5
Cartesian Vectors

  • Addition and Subtraction of Cartesian Vectors

    R=A+B=(Ax+Bx)i+(Ay+By)j+(Az+Bz)k

    R=A-B=(Ax-Bx)i+(Ay-By)j+(Az-Bz)k


Dot product
Dot Product

Result is a scalar.

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


Dot product1
Dot Product

  • Laws of Operation

Commutative law:

Multiplication by a scalar:

Distributive law:


Cross product
Cross Product

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

C = A x B

Magnitude:

C = ABsinθ


Cross product1
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(B+D) = (AxB) + (AxD)




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