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# MECE 701 Fundamentals of Mechanical Engineering - PowerPoint PPT Presentation

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 701Fundamentals of Mechanical Engineering

Engineering Mechanics

Mechanics of Materials

MECE701

Machine Elements

&

Machine Design

Materials Science

• 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

Concentrated Force:

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

• 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.

• 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

• Third Law

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

• 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

• Weight

W=weight

m2=mass of earth

r = distance btw earth’s center and the particle

g=gravitational acceleration

g=Gm2/r2

W=mg

• 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)

• 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

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

• Vector Subtraction

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

• Resolution of a Vector

a

R

A

B

b

• Sine Law

A

B

c

a

b

• Cosine Law

C

Right Handed Coordinate System

A=Ax+Ay+Az

• Unit Vector

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

Unit vector is dimensionless.

• Cartesian Unit Vectors

A= Axi+Ayj+Azk

• Magnitude of a Cartesian Vector

• Direction of a Cartesian Vector

DIRECTION COSINES

• Unit vector of A

• 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

Result is a scalar.

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

• Laws of Operation

Commutative law:

Multiplication by a scalar:

Distributive law:

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

C = A x B

Magnitude:

C = ABsinθ

• 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)