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## PowerPoint Slideshow about ' MECE 701 Fundamentals of Mechanical Engineering' - idola-carr

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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:
- 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 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

- 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 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 Motion

- Third Law

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

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 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

- 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

- 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 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

Cartesian Vectors

- Unit Vector

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

Unit vector is dimensionless.

Cartesian Vectors

- Unit vector of A

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

Cross Product

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

C = A x B

Magnitude:

C = ABsinθ

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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