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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
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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