Lect-2-Intro to Basic Physical Quatities & Unit

8/2/2019 Lect-2-Intro to Basic Physical Quatities & Unit

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Basic Mechanical Engineering

Course CodeME-113

Course TeacherEngr. N.A. ANJUM

Text Book:Engineering Mechanics Dynamics

ByMeriam, J.L., Kraige, L.G., John Wiley


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Fundamental Principles

Basic concepts used in mechanics:

space, time, mass, force, particle, rigid body


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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.


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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


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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


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Space, time, mass, force, particle, rigid bodymass of a body [kg, to] action of weight, behavior under the

action of an external force


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magnitude, direction, point of applicatione.g. action on a rigid body, action of one body onto another


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infinitesimal small piece of a body, single point in space


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Space, time, mass, force, particle, rigid bodybody consisting of a non-deformable material (no

displacement under the action of forces)


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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.


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Vectors and Scalars


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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


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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

.


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Graphical representation of a Vector

- line segment of certain length (magnitude) and orientation ()- arrowhead indicating direction


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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


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Symbolic representation of a Vector


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Representation of VectorsAlgebraically a vector is represented by its components

along the three dimensions.


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Representation of Vectors


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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.


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1. Free Vector action in space not associated with a

unique linee.g. uniform displacement of a body


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2. Sliding Vector action in space described by a

unique linee.g. action of force on rigid body


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3. Fixed Vector action in space described by a

unique pointe.g. action of force on non rigid

body


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Vector

A vector has a length A and a direction (unit vector)

A

Ae

AA =v

Ae


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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+


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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.


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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


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3-D Cartesian coordination system

zAyAxA

zAyAxAeAA

zyx

zyxA

coscoscos

++=

++==

v

22222 :Note AAAAAzyx

r

==++

z

A

v

x

e

y

AyAx

Az


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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


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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


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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:


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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


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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 ( )


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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)


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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 ?


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What is a Force ?

Force is simply:

A PUSH A PULLor

Forces have both magnitude

and directionForces have both magnitude

and direction


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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


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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)


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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)


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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


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Energy

What is Energy


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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


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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


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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


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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


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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

Lect-2-Intro to Basic Physical Quatities & Unit

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