mece 701 fundamentals of mechanical engineering. mece 701 engineering mechanics machine elements...
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MECE 701 Fundamentals of Mechanical Engineering
MECE 701
MECE701
Engineering Mechanics
Machine Elements&
Machine Design
Mechanics of Materials
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 particlesG =Universal constant of gravitation
66.73(10-12)m3/(kg.s2)
m1,m2 =mass of each of the two particlesr = 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|
A2A -1.5A
Basic Vector Operations
Vector Addition
Resultant (R)= A+B = B+A
(commutative)
A
B
A
B
R=A+B
Parallelogram Law
A
B
R=A+B
Triangle Construction
A
B
R=A+B
Basic Vector Operations
Vector Subtraction
R= A-B = A+(-B)
Resolution of a Vector
b
a
B
AR
Trigonometry
Sine Law
c
C
b
B
a
A
sinsinsinA B
C
ab
c
Cosine Law
cABBAC cos222
Cartesian Vectors
Right Handed Coordinate System
A=Ax+Ay+Az
Cartesian Vectors
Unit Vector
A unit vector is a vector having a magnitude of 1.
Unit vector is dimensionless.
AuA
A
Cartesian Vectors
Cartesian Unit Vectors
A= Axi+Ayj+Azk
Cartesian Vectors
Magnitude of a Cartesian Vector
222zyx AAAA
Direction of a Cartesian Vector
A
AxcosA
AycosA
Azcos
DIRECTION COSINES
Cartesian Vectors
Unit vector of A
kA
Aj
A
Ai
A
A
A
Au zyxA ||||||||
kjiuA coscoscos
1coscoscos 222
kAjAiA coscoscos 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
Dot Product
Result is a scalar.
cosABBA
Result is the magnitude of the projection vector of A on B.
Dot Product
Laws of Operation
ABBA Commutative law:
Multiplication by a scalar:
Distributive law:
aBAaBABaABAa )()()()(
)()()( DABADBA
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
ABBA Commutative law is not valid:
Multiplication by a scalar:
Distributive law:
ABBA
a(AxB) = (aA)xB = Ax(aB) = (AxB)a
Ax(B+D) = (AxB) + (AxD)
Cross Product
)()( kBjBiBkAjAiABA zyxzyx
kBABAjBABAiBABABA xyyxxzzxyzzy )()()(
Cross Product
zyx
zyx
BBB
AAA
kji
BA
kBABAjBABAiBABABA xyyxxzzxyzzy )()()(
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