Interfacing Analog to Digital Data Converters ee3404.pdf
ME2201_Unit 1.pdf
1. UNIT I
BASICS AND STATICS OF
PARTICLES
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ENGINEERING MECHANICS
Mr.B.K.Parrthipan, M.E., M.B.A., (Ph.D).,
Assistant Professor / Mechatronics Engineering,
Kamaraj College of Engineering and Technology.
3. Units - Definition
Units may be defined as those standards in terms of
which the various physical quantities like length,
mass, time, force, area, volume, velocity,
acceleration etc., are measured.
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4. Units - Types
Fundamental units
• The units which are
independent of all other units
are known as fundamental
units
• 1. Length
• 2. Mass
• 3. Time
• 4. Temperature
• 5. Electric Current
• 6. Amount of substance
• 7. Luminous Intensity
Derived units
• The units which are dependent
of one or more fundamental
unit is known as derived units.
• 1. Area
• 2. Volume
• 3. Velocity
• 4. Acceleration
• 5. Force
• 6. Pressure
• 7. Density
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5. System of Units
• 1. CGS Units
• 2. FPS Units
• 3. MKS Units
• 4. SI Units
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6. System of Units
The C.G.S. system of units (Centimetre, Gram, Second
system) is a French system. This system deals with only three
fundamental units – the Centimetre, Gram and the Second for
length, mass and time respectively.
The F.P.S. system of units (Foot, Pound, Second system) is a
British system. This system deals with only three fundamental
units – the Foot, Pound and the Second for length, mass and
time respectively.
The M.K.S. system of units (Metre, Kilogram, Second system)
was set up by France. This system also deals with three
fundamental units – the Metre, kilogram and the Second for
length, mass and time respectively. This system is also called
the metric system of units and is closely related to C.G.S
system of units. E.M - B.K.P
7. System of Units
The measurement system which is internationally accepted
now is the one suggested by the Eleventh general conference
of weights and Measures held in 1960 in France, and is known
as Systeme Internationale d’ Unites or International System of
Units abbreviated as SI units of measurement.
According to this system, there are seven basic or fundamental
units and three supplementary units.
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12. Examples of SI Units in Everyday Use
Examples of SI Unit Usage SI Units Used
Medication dose such as pills 100 mg, 250 mg, or 500 mg Hi
Height 170 cm
Sports - running 100 m, 200 m, 400 m, 5000 m, and so
on
Light bulbs 60 W, 100 W, or 150 W
Electric consumption kWh (killo-Watt-hour)
Radio broadcasting signal frequencies 88–108 MHz (FM broadcast band)
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17. Newton`s First Law
It states that every body continues in its state of
rest or of uniform motion in a straight line unless it is
compelled by an external agency acting on it.
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Laws of Mechanics
18. Newton`s Second Law
It states that the rate of change of momentum of a
body is directly proportional to the impressed force
and it takes place in the direction of the force acting
on it.
Newton`s Third Law
It states that for every action there is an equal and
opposite reaction.
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Laws of Mechanics
F m × a
19. Lami`s theorem
• Lami`s theorem states that, “If three forces acting on
a particle are in equilibrium then, each force acting on
the particle is proportional to the sine of the angle
between the other two forces”.
• Lami’s theorem is also known as law of sines.
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20. Exercise 1
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Determine the force required the hold the 4kg lamp in
position.
21. Exercise 2
A barge is pulled by two tugboats. If the resultant of
the forces exerted by the tugboats is a 25 kN directed
along the axis of the barge, determine
a)the tension in each of the ropes for α= 45o,
b)the value of α for which the tension in rope 2 is
minimum and the tension in each rope.
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Hint:
The minimum tension in rope 2
occurs when T1 and T2 are
perpendicular.
22. Parallelogram Law
If two vectors acting at a point be represented in
magnitude and direction by the adjacent sides of a
parallelogram, then their resultant is represented in
magnitude and direction by the diagonal of the
parallelogram passing through that point.
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23. Triangle Law
If two forces acting on a body are represented one
after another by the sides of a triangle, their resultant
is represented by the closing side of the triangle taken
from first point to the last point.
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24. Exercise 3
A disabled automobile is pulled by means of two
ropes as shown in figure. Determine the Magnitude
and direction of Resultant by (a) parallelogram law
and (b)Triangle law.
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25. Exercise 4 (2.4)
If two concurrent, coplanar forces F1 and F2 act at a
point as shown in figure, find the magnitude and
direction of the resultant by using parallelogram law.
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26. Exercise 5 (2.7)
Find the resultant of F1 = 100 kN and F2 = 200 kN,
which are acting on a particle as shown in figure using
triangle law.
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27. Vector representation of forces
Vectors is a quantity that has both magnitude and
direction. It is typically represented by an arrow
whose direction is the same as that of the quantity and
whose length is proportional to the quantity's
magnitude. There are four operations in vectors -
1. Vector addition,
2. Vector subtraction,
3. Vector dot product and
4. Vector cross product.
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28. Vector addition
Two force vectors A and B may be added by using
(i) Parallelogram law of addition
(ii) Triangle law of addition
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29. Parallelogram law of addition :
If two forces A and B are represented by the
adjacent sides of the parallelogram then their resultant
is represented by the diagonal of parallelogram drawn
from the same point.
R = A + B
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Vector addition
30. Vector addition
Triangular law of addition :
If two forces A and B are acting in a same
direction then its resultant R will the sum of two
vectors.
R = A + B
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31. Vector subtraction
If two forces A and B are acting in the
direction opposite to each other then their
resultant R is represented by the difference between
the two vectors.
R = A - B
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32. Exercise 6
If two forces represented by
A = 5 i +2 j -3 k and
B = 3 i - 2 j +4k are acting in the same direction,
calculate the resultant force.
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33. Exercise 6 - Solution
If two forces represented by
A = 5 i + 2 j - 3 k and B = 3 i - 2 j + 4 k are
acting in the same direction, calculate the resultant
force.
Solution:
Let A = 5i + 2 j - 3 k
B = 3i - 2 j + 4 k
A + B = 5i + 2 j - 3 k + 3 i - 2 j +4 k
= 8i + k .
The Resultant force R = 8i + k .
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34. Exercise 7
If two forces A = 2i -3k and B =-2i +7 j +4k are
acting in the direction opposite to each other.
Calculate the Resultant force.
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35. Exercise 7 - Solution
If two forces A = 2i -3k and B =-2i +7 j +4k are
acting in the direction opposite to each other.
Calculate the Resultant force.
Solution:
Let A =2i -3k ,
B = -2i +7j +4k
A - B = 2i -3k - (-2i +7j +4k )
= 4i -7j -7k
The Resultant force R = 4i -7j -7k .
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36. Vector dot product
The dot (or) scalar product of two vectors a and b is
written as a .b is a scalar quantity and is defined as the
product of the magnitude of the two vectors and cosine of
the their included angle θ.
Thus, a .b = abcosθ
The scalar product of two vectors is a scalar quantity.
Therefore the product is called scalar product.
Note: When two vectors are at right angles to each other,
the dot product of the vectors should be zero.
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37. Vector cross product
The cross (or) vector product of two vectors a and b
is written as a × b and is another
vector c where c = a ×b , whose magnitude is the
product of the magnitude of the two vectors and sine
of the their included angle.
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Note:
For parallel vectors, their
cross product is zero
38. Exercise 8
If P = 6i +12j -5k and Q = -3i +4j -2k find
(i) 4P +3Q (ii) P . 5Q
(iii) 2P x3Q (iv) (3P xQ ).(2P x4Q )
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39. System of forces
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Generally in a body several forces are acting.
When a number of forces of different magnitude and
direction act upon rigid body, then they are form System
of Forces, These are given below
40. Coplanar Force System:
When the system of forces are in a plane, it is
called coplanar system of forces.
Non-Coplanar Force System:
When the system of forces are not lie in a plane,
it is called coplanar system of forces.
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System of forces
41. System of forces - Coplanar Force
System
1. Collinear forces: In this system, line of action of all
the forces act along the same line.
2. Concurrent forces: All forces of this kind, which act
at one point, are known as concurrent forces.
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42. 3. Parallel Forces: If the lines of action of forces are
parallel to each other and they lie in same plane then
the system is known as parallel forces system.
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System of forces - Coplanar Force
System
43. 1. Non-coplanar concurrent forces: In this system, all
forces do not lie in the same plane, but their line of
action passes through a single point.
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System of forces – Non Coplanar
Force System
44. 2. Non coplanar parallel forces: In this case, all the
forces are parallel to each other, but not in the same
plane.
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System of forces – Non Coplanar
Force System
45. 3.Non-concurrent non parallel: This consists of a
number of vectors that do not meet at a single point
and none of them are parallel but all does not lie in a
same plane.
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System of forces – Non Coplanar
Force System
46. Resolution and Composition of Forces
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1. It is convenient to have
Fx= F cos Ө
Fy= F sin Ө
and always measure angle
from horizontal reference
(acute angle).
2. Assume force pointing
right and top as positive
otherwise negative.
47. Equilibrium of a Particle
When the resultant of all forces acting on a
particle is zero, the particle is in equilibrium.
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48. Equilibrium of a particle in space
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When the resultant of all forces and moments
acting on a particle in space is zero, the
particle is in equilibrium.
49. Principle of Transmissibility
• According to this law the state of rest or motion of
the rigid body is unaltered if a force acting on the
body is replaced by another force of the same
magnitude and direction but acting anywhere on the
body along the line of action of the replaced force.
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