-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
1/48
1
Basic Mechanical Engineering
Course CodeME-113
Course TeacherEngr. N.A. ANJUM
Text Book:Engineering Mechanics Dynamics
ByMeriam, J.L., Kraige, L.G., John Wiley
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
2/48
2
Fundamental Principles
Basic concepts used in mechanics:
space, time, mass, force, particle, rigid body
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
3/48
3
Chapter 1 Introduction to Mechanics
Give the meanings and qualitative explanation of the following
specific terms, i.e. space, time, mass, and force.
Space is the region occupied by the bodies. We set up an
coordinate system to specify where the object is by the positionand its posture by the orientation.
Time is the measure of the succession of events. Often, we are
more interested in the change of physical quantities with respect
to time, e.g. v = dr/dt, instead of time variable itself.
Mass is the measure of the inertia of a body. The inertia indicates
the resistance to a change in motion.
Force a fixed vector, is the measure of the attempt to move abody.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
4/48
4
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid body
coordinates - position of a point P (x, y, z)
measured from a certain point of reference
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
5/48
5
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid body
time of an event taking place, determination of velocity
and accelerationmass of a body [kg, to] action of weight, behavior under the
action of an external force
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
6/48
6
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid bodymass of a body [kg, to] action of weight, behavior under the
action of an external force
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
7/48
7
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid body
magnitude, direction, point of applicatione.g. action on a rigid body, action of one body onto another
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
8/48
8
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid body
infinitesimal small piece of a body, single point in space
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
9/48
9
Fundamental PrinciplesBasic concepts used in mechanics:
Space, time, mass, force, particle, rigid bodybody consisting of a non-deformable material (no
displacement under the action of forces)
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
10/48
10
Introduction to Mechanics
Give the meanings and qualitative explanation of the following
specific terms, i.e. particle, rigid body, and nonrigid body.
Particle is a body of which its dimension is negligible. The
rotation effect is insignificant because it is just a point. Whetherthe body can be treated as the particle or not depends on the
relative dimensions in the problem and how much detailed of the
solution we are interested in.
Rigid body is a body whose relative movement between its partsare negligible relative to the gross motion of the body. For
example the motion of an ingot can be analyzed by assuming the
object being rigid.
Nonrigid body is a body whose relative movement between its
parts are significant relative to the gross motion of the body.
Knowledge of the mechanics of the deformable material must be
used along with Dynamics in order to determine the absolutemotion of the rigid body.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
11/48
11
Vectors and Scalars
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
12/48
12
ScalarsScalar quantities are those which are described solelyby their magnitude
Some examples are:
Mass e.g. 14 [kg], 36 [lbs], Time e.g. 10 seconds, 40 minutes,
Volume e.g. 1000 cm3, 4 litres, 12 gallons
Temperature e.g 14o
F , 25o
C, Voltage e.g. 9 Volts, etc
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
13/48
13
VectorsVector quantities are those which need to be described by BOTH
magnitude and direction
Some of the most common examples which we will encounter are:
Velocity e.g. 100 [mi/hr] NORTH
Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST
Force e.g. 980 [Newtons] straight down (270o)
Momentum .g. 200 [kg m/sec] at 90o
.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
14/48
14
Graphical representation of a Vector
- line segment of certain length (magnitude) and orientation ()- arrowhead indicating direction
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
15/48
15
Symbolic representation of a Vector
- magnitude, length of vector: V, |V| orV, e.g. in scalar equations- vector quantities respecting the orientation: V, V
e.g. mathematical vector operations
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
16/48
16
Symbolic representation of a Vector
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
17/48
17
Representation of VectorsAlgebraically a vector is represented by its components
along the three dimensions.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
18/48
18
Representation of Vectors
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
19/48
19
Representation of Vectors
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
20/48
20
Representation of Vectors
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
21/48
21
Representation of Vectors
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
22/48
22
Classification of Vectors
Sliding vector is a vector whose line of action must be specified inaddition to its magnitude and direction. External force or moment
acting on the rigid body falls under this category. Therefore sliding
vector has a freedom to slide along the fixed line of action.
Fixed vector is a vector whose magnitude, direction, line of action,and point of application are all important in the analysis. External
force or moment acting onto the nonrigid body must be dealt with as
the fixed vector due to the deformable effect of the object.
Free vector is a vector whose action is not confined with a uniqueline in space. That is, only its magnitude and direction do matter.
Some examples are the displacement vector of a pure translational
rigid object, or the couple vector of a rigid body. Free vector is free
to slide and translate as long as its direction and magnitude aremaintained. In other words, its line of action and point of
application do not matter.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
23/48
23
Classification of Vectors
1. Free Vector action in space not associated with a
unique linee.g. uniform displacement of a body
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
24/48
24
Classification of Vectors
2. Sliding Vector action in space described by a
unique linee.g. action of force on rigid body
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
25/48
25
Classification of Vectors
3. Fixed Vector action in space described by a
unique pointe.g. action of force on non rigid
body
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
26/48
26
Vector
A vector has a length A and a direction (unit vector)
A
Ae
AA =v
Ae
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
27/48
27
2-D Rectangular Coordinate Systems
1. Show the relationships between the planar force vector, its
components, and its direction.
If a 2-D rectangular coordinate system has been specified, aplanar force vector, F, can be written as the addition of its
component vectors along the coordinate axes.
F = Fx + Fy = Fxi + Fyj
The components are the orthogonal projection of the vector onto
the respective axes which is determined by the dot product of the
vector and the unit vector along the axes.
Fx = F i = F cos Fy = F j = F sin The magnitude and direction of the force vector F follow
immediately as F =
= arctan2 (Fy, Fx)
22
xF yF+
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
28/48
28
2-D Moment and Couple
Moment is the measure of the attempt to rotate a body, which is
usually induced by force. The moment is always associated with
a specific point, meaning that we must specify the point indetermining the moment about that point.
In 2-D problems, the moment vectors direction is always
perpendicular to the plane established by the point and the line of
action of the force. In this course, the moment can be treated as asliding vector so the problems can make use of the principle of
transmissibility.
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
29/48
29
2D Cartesian coordination system
(one form of presentation)
22
yx
)sinx(cos
yx
A
AAAA
yAxAyAeAA
+==
+=+==
v
v
x
y
Av
YA
XA
Pythagoras theorem
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
30/48
30
3-D Cartesian coordination system
zAyAxA
zAyAxAeAA
zyx
zyxA
coscoscos
++=
++==
v
22222 :Note AAAAAzyx
r
==++
z
A
v
x
e
y
AyAx
Az
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
31/48
31
Addition of vectors y
x
YBv
xBv
Bv
Av
YAv
XAv
Avv
+
O
y)(x)(
yx
yx
yyxx
yx
yx
BABABA
BBB
AAA
+++=+
+=
+=
vv
v
v
Subtraction of vectors
yx yyxx )BA()BA(B-A +=vv
x
y
Bv
Av
BAvv
O
Bv
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
32/48
32
scale)a(cos ABB vv
yyxx BABABA +=
vv
Dot (scalar) product of two vectors
In 2-D Cartesian coordination system
Definition:
Note:
AB cos
=AB cos (B - A)
=AB(cos B cos A +sin B sin A)
= (Acos A)(Bcos B) + (Asin A) (Bsin B)
Av
Bv
A
x
y
B
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
33/48
33BABABABA zzyyxx
vv
=++
y
B
v
Av
BAvv
+
O
From cosine law:
cos2)()(
)()()(
)180cos(2
222222
222
222
ABBBBAAA
BABABA
BABABA
zyxzyx
zzyyxx
++++++=
+++++
+=+vvvvvv
In 3-D Cartesian system:
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
34/48
34
Time
In physics, we are most often less interested in absolute time than
changes in time, or a time interval.
Time can be expressed in several units as well:
seconds [sec]
minutes [min]
hours [hr]
days
yearsetc
Example 1: How much time does it take for the earth to make one
revolution?Example 2: How long did it take for you to drive to the store today?
We usually refer to a time interval as : t
V l i
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
35/48
35
Velocity
Velocity is a measure of the rate of change of the distance withrespect to time.
v = d /t
It will usually be measured in [m/sec].
What does 5 [m/sec] mean?
It means if an object passes by us at 5 [m/sec], it will advance its
position by 5 [m] every second. So after 2 [sec], it will haveadvanced 10 [m], and 20 [m] in 4 [sec] and so on.
If a train moves at 50 [meters/sec], how far will it go in 50 seconds ?
a) 100 miles b) 2.5 [km] c) 250 [m] d) 2500 miles
A l i ( )
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
36/48
36
Acceleration (I)
Acceleration is the rate ofchange of velocity with respect to time
a = v /t [a] = [m/sec] / [sec] = [m/sec2]What does a = 5 [m/sec2] mean?
If an object starts at rest, its velocity increases by 5 [m/sec]
every second.
20 m/sec5 m/sec24
15 m/sec5 m/sec23
10 m/sec5 m/sec225 m/sec5 m/sec21
0 m/sec5 m/sec20
VelocityAccelerationTime (sec)
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
37/48
37
Acceleration (II)
Acceleration can be negative also! We call this deceleration.
If the acceleration is in the same direction as the velocity,
the object has positive acceleration (it speeds up).
If the acceleration is in the opposite direction as the velocity,
the object has negative acceleration or deceleration (it slows down).
Wh i F ?
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
38/48
38
What is a Force ?
Force is simply:
A PUSH A PULLor
Forces have both magnitude
and directionForces have both magnitude
and direction
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
39/48
39
Force and Acceleration Experimentally, we find that if we apply a force
to an object, it accelerates.
We also find that theacceleration (a) isdirectlyproportionalto theapplied force (F) and inversely
proportional to the mass (m) . That is:
a = F / m
This is Newtons Law, and it is often written:
F = maF = ma
This means:
Increasing the force increases the acceleration;
decreasing the force results in a lower acceleration.
Isaac Newton
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
40/48
40
Force (I) A force is generally a result of an interactionbetween two (or more)
objects
Can you think of some examples of forces?
Gravitational
ElectricMagnetic
Friction
Wind drag
Van der Waals forces
Hydrogen bonds
Forces in a compressed or stretched spring
+
Forces (II)
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
41/48
41
Forces (II)
Since two or more objects must be involved, aforce intimatelytied to the notion of an interaction.
Interactions are now believed to occur through the exchange of
force carriers. This is a very important point, and well come
back to it later
So far, we know only of four types offundamental forces innature:
Gravity, Electromagnetic, Weak, and Strong
We will come back to each of these
All other forces in nature are understood to be the residual effects
of these fundamental forces
M (I)
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
42/48
42
Momentum (I)What is momentum?
Momentum is simply the product of the mass and the velocity.
Denoting momentum asM, it is simply:
The units of momentum are [kg][m/sec] == [kg m/sec]
Momentum is a very important subject in dynamics/physics
because it is what we call aconserved quantity. What does thismean?
M = m*vmv
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
43/48
43
Energy
What is Energy
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
44/48
44
What is Energy
From Merriam Webster:
Energy: The capacity for doing work (or to produce heat)
What are some forms/types of energy?
1. Energy of motion (kinetic energy)
2. Heat
3. Electricity
4. Electromagnetic waves - like visible light, x-rays, UV rays,
microwaves, etc5. Mass
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
45/48
45
Energy
What do you mean mass is a form of energy?
The thing about energy is that it cannot be created or
destroyed, it can only be transformed from one form into
another
Yes, like momentum it is a conserved quantity. We will
learn that conserved quantities are a powerful tool in
predicting the future!
Summary I
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
46/48
46
Summary I
In nature, there are two types of quantities, scalars and vectors
Scalars have only magnitude, whereas vectors have both
magnitude and direction.
The vectors we learned about are distance, velocity, acceleration,
force, and momentum
The scalars we learned about are time, and Energy.
In nature, there are two types of quantities, scalars and vectors
Scalars have only magnitude, whereas vectors have both
magnitude and direction.
The vectors we learned about are distance, velocity, acceleration,
force, and momentum
The scalars we learned about are time, and Energy.
S II
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
47/48
47
Summary II
Forces are the result of interactions between two or more
objects.
If the net force on an object is not zero, it will accelerate. That
is it will either speed up, slow down, or change direction.
Energy and momentum are conserved quantities. This has
far-reaching consequences for predicting whether certain events
or processes can occur.
There are many forms of energy. The topic of energy will
be discussed in greater detail in next lecture.
Forces are the result ofinteractionsbetween two or more
objects.
If the net force on an object is not zero, it will accelerate. That
is it will either speed up, slow down, or change direction.
Energy and momentum are conserved quantities. This has
far-reaching consequences for predicting whether certain events
or processes can occur.
There are many forms of energy. The topic of energy will
be discussed in greater detail in next lecture.
ASSIGNMENT # 1
-
8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit
48/48
48
ASSIGNMENT # 1
1. Explain with examples fundamental and derived units with
symbols, units, & Physical quantities in the form of tables.
2. Explain some common physical quantities with unit and unit
symbols
3. Explain multiples and submultiples .
4. Write down Properties of Water, Mercury, & Water.
5. Give some examples for interchanging between units
1. Explain with examples fundamental and derived units with
symbols, units, & Physical quantities in the form of tables.
2. Explain some common physical quantities with unit and unit
symbols
3. Explain multiples and submultiples .
4. Write down Properties of Water, Mercury, & Water.
5. Give some examples for interchanging between units