EM Lecture 1,2

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Lecture 1,2
Engineering Mechanics
CE - 101
Lt Col Syed Mohsin Ali
[email protected]
0334-5231553
Introduction
Introduction
 Lt Col Syed Mohsin Ali
 1997 – 2000
BE Mechanical Engineering (EME College)
 Gold Medal in Final Year Project
 2004 – 2006 and 2009 – 2010
OIC Design Centre – Military Vehicles Research &
Development Establishment
 2011 – 2012
MSc in Art & Science of Warfare (Staff Course)
 2013 – 2015
MSc in Mechanized Mining Systems (South Africa)
 2015 – 2016
Instructor Class-B at MCE (EM, FCP, CACE)
Class Introduction
Course Outline
Course Outline
 Credit Hours
Total = 3
Theory = 2.5
Practical = 0.5
 Number of Contact hours
Total = 64
Theory = 40
Practical = 24
Course Learning Outcomes
• Understand the basic terms used throughout
the course, geometrical properties of plane
areas and basic concepts about virtual work
and dynamics.
• Resolution of forces, moments, couples, two
dimensional force system and frictional forces;
and finding reaction and member forces in
simple beams and plane trusses.
• Verify some of the concepts through practical
in the laboratory.
Course Plan
Do’s and Don'ts
Introduction to Engineering
Mechanics
-What is Mechanics?
Mechanics is the science which describes and predicts
the conditions of rest or motion of bodies under the
action of forces
-Categories of Mechanics?
- Rigid bodies  A Rigid Body does not deform under load!
- Statics
- Dynamics
- Deformable bodies
- Fluids
Branches of Engineering Mechanics
Introduction to Engineering
Mechanics
Mechanics is the foundation of most engineering
sciences and is an indispensable prerequisite to
their study
Introduction to Engineering
Mechanics
- Rigid Body Mechanics
• Statics: deals with equilibrium of bodies under action
of forces (bodies may be either at rest or move with a
constant velocity).
Designing structures (Mechanical & Civil).
Introduction to Engineering
Mechanics
- Rigid Body Mechanics
• Dynamics: deals with motion of bodies (accelerated
motion).
Analyze responses of buildings to earthquakes (Civil)
& determine trajectories of satellites (Aerospace).
Introduction to Engineering
Mechanics
• Engineering Applications
– Describes how mechanics is applied in various
fields of engineering
– Emphasis on 2 essential aspects of engineering:
• Design – to choose parameters values to satisfy
stated design criteria
• Safety – to evaluate the safety of devices and
choose parameter values to satisfy stated safety
requirements
Fundamental Concepts
• Space & Time
– Space:
• 3-dimensional space & locations/positions of
points in space
• Distance between 2 points in space = length of
the straight line joining them
• SI unit of length: meter (m)
• U.S. Customary unit: foot (ft)
Fundamental Concepts
• Space & Time
– Time:
• Measured by the intervals between the events
• SI unit & U.S. Customary unit of time: second (s)
Fundamental Concepts
• Position of a point in space relative to some
reference point changes with time:
– Rate of change of position = velocity
• SI unit: meters per second (m/s)
• U.S. Customary unit: feet per second (ft/s)
– Rate of change of velocity = acceleration
• SI unit: meters per second squared (m/s2)
• U.S. Customary unit: feet per second squared
(ft/s2)
Fundamental Concepts
• Mass:
Quantity of matter in a body  measure of inertia of
a body (its resistance to change in velocity)
Fundamental Concepts
• Force:
The ‘push’ or ‘pull’ exerted by one body on another
 Characterized by its magnitude, direction of its
action, and its point of application.
 Force is a Vector quantity.
Fundamental Concepts
• Force:
Force acting on a body is related to the mass of the
body and the variation of its velocity with time.
Force can also occur between bodies that are
physically separated (Examples: gravitational,
electrical, and magnetic forces)
Fundamental Concepts
• Remember:
- Mass is a property of matter that does not change
from one location to another
- Weight refers to the gravitational attraction of the
earth on a body or quantity of mass. Its magnitude
depends upon the elevation at which the mass is
located
- Weight of a body is the gravitational force acting on it
Units and Dimensions
Quantity
Unit
Area
m2
Volume
m3
Velocity
m/s
Acceleration
m/s2
Mechanics - Idealization
• Particle:
A body with mass but with dimensions that can be
neglected
Mechanics - Idealization
• Particle:
A body with mass but with dimensions that can be
neglected
Three forces act on the hook at A.
All forces met at point A.
→ Hook can be assumed as a Particle
A
Mechanics - Idealization
• Rigid Body:
- A combination of large number of particles in which all
particles remain at a fixed distance (practically) from one
another before and after applying a load
- Material properties of rigid body are not required to be
considered when analyzing the forces acting on the body
- In most cases, actual deformations occurring in
structures, machines, mechanisms, etc. are relatively
small, and rigid body assumption is suitable for analysis
Newton’s Three Laws of Motion

Newton’s 1st Law of Motion

A particle originally at rest, or moving in a straight
line with constant velocity will remain in this state
provided particle is not subjected to an
unbalanced force
Newton’s Three Laws of Motion

Newton’s 1st Law of Motion

First Law contains the principle of the equilibrium
of forces  main topic of concern in Statics
Newton’s Three Laws of Motion

Newton’s 2nd Law of Motion

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=m.a
Newton’s Three Laws of Motion

Newton’s 3rd Law of Motion

The mutual forces exerted by 2 particles on each
other are equal in magnitude & opposite in
direction. The particles remains in state of
equilibrium only if exerted forces on them are
collinear
Newtonian Gravitation
• Gravitational force between 2
particles of mass m1 & m2 that
are separated by a distance ‘r’
is:
Gm1m2
F
2
r
where
G = universal gravitational constant
G = 6.673 × 10–11 Nm2/kg2
D
Newtonian Gravitation
• Weight of an object of mass m due to the gravitational
attraction of the earth is approximated by:
GmmE
W
2
r
where
mE = mass of earth,
r = distance from the center of earth to
the object
Newtonian Gravitation
• Weight of an object at sea level (r = RE):
W  mg
• The value of g varies from location to location on the
surface of the earth.
– g = 9.81 m/s2 (SI units)
– g= 32.2 ft/s²
Newtonian Gravitation
Systems of units
- Very important for Engineers
- SI (System international) is used in Europe
- FPS ( Foot pound System) is used In USA
- Be careful when switching from one system to
the other
Units
• U.S. Customary Units:
– Base units:
• Length: feet (ft)
• Force: pounds (lb)
• Time: second (s)
– Derived Unit:
• Mass: slug (the mass of material accelerated at
1 ft/s2 by a force of 1 lb)
• Newton’s 2nd law:
1 lb  1 slug  1 ft/s 2

1 slug  1 lb  s 2 /ft

C
Systems of units
– Force & mass are defined by the 2nd law
1 slug = Amount of matter accelerated at 1 ft/s2 when acted upon by
a force of 1 lb (slug = lb· s2/ft).
1 Newton = Force required to give 1 kg of mass an acceleration 1
m/s2 (N= 1kg· m/s2)
Systems of units
Newton
1 Newton is the force required to give a mass
of 1 kg an acceleration of 1 m/ s².
Weight is a force.
The weight of 1 kg Mass is:
W = mg
W = (1 kg)(9.81 m/ s²)
W = 9.81 N
Conversion of Units
Values must be expressed in terms of one system of
units before they are substituted into the equation
Conversion of Units
Example:
To express 1 mi/h in terms of ft/s:
 5280 ft 
1 mi/h  
  1.47 ft/s
 3600 s 
Conversion of Units
Convert:
(a) 60 miles/h to ft/sec
(b) 100 lb.ft/s2 to kg.m/s2
2
2
(c) 20 slug/ft to kg/m
Units - Prefixes
• E.g. 1 kg = 1000 g, 1 Mg = 106 g = 1000 kg
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