Engineering Mechanics: Statics in SI Units, 12e [Compatibility... · Title: Microsoft PowerPoint -...
Transcript of Engineering Mechanics: Statics in SI Units, 12e [Compatibility... · Title: Microsoft PowerPoint -...
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General Principles11
Engineering Mechanics:
Statics in SI Units, 12e
Copyright © 2010 Pearson Education South Asia Pte Ltd
Copyright © 2010 Pearson Education South Asia Pte Ltd
Chapter Objectives
• Basic quantities and idealizations of mechanics
• Newton’s Laws of Motion and Gravitation
• Principles for applying the SI system of units
• Standard procedures for performing numerical
calculations
• General guide for solving problems
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Chapter Outline
1. Mechanics
2. Fundamental Concepts
3. Units of Measurement
4. The International System of Units
5. Numerical Calculations
6. General Procedure for Analysis
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1.1 Mechanics
• Mechanics can be divided into 3 branches:
- Rigid-body Mechanics
- Deformable-body Mechanics
- Fluid Mechanics
• Rigid-body Mechanics is divided into two areas:
- Statics
- Dynamics
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1.1 Mechanics
• Statics – Equilibrium of bodies
� At rest
� Move with constant velocity
• Dynamics – Accelerated motion of bodies
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1.2 Fundamentals Concepts
Basic Quantities
1. Length
- locate the position of a point in space
2. Mass
- measure of a quantity of matter
3. Time
- succession of events
4. Force
- a “push” or “pull” exerted by one body on another
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1.2 Fundamentals Concepts
Models or Idealizations
1. Particles
- has a mass, but a size that can be neglected
2. Rigid Body
- a combination of a large number of particles
3. Concentrated Force
- the effect of a loading
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Isaac Newton
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1.2 Fundamentals Concepts
Newton’s Three 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”
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1.2 Fundamentals Concepts
Newton’s Three 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”
maF =
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1.2 Fundamentals Concepts
Newton’s Three Laws of Motion
• Third Law
“The mutual forces of action and reaction between two
particles are equal and, opposite and collinear”
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1.2 Fundamentals Concepts
Newton’s Law of Gravitational Attraction
Weight:
Letting yields
2
21
r
mmGF =
F = force of gravitation between two particles
G = universal constant of gravitation
m1,m2 = mass of each of the two particles
r = distance between the two particles
2r
mMGW e=
2/ rGMg e= mgW =
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1.3 Units of Measurement
SI Units
• Stands for Système International d’Unités
• F = ma is maintained only if
– 3 of the units, called base units, are defined
– 4th unit is derived from the equation
• SI system specifies length in meters (m), time in
seconds (s) and mass in kilograms (kg)
• Force unit, Newton (N), is derived from F = ma
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1.3 Units of Measurement
Name Length Time Mass Force
International
Systems of Units
(SI)
Meter (m) Second (s) Kilogram (kg) Newton (N)
2
.
s
mkg
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1.3 Units of Measurement
• At the standard location,
g = 9.80665 m/s2
• For calculations, we use
g = 9.81 m/s2
• Thus,
W = mg (g = 9.81m/s2)
• Hence, a body of mass 1 kg has a weight of 9.81 N, a
2 kg body weighs 19.62 N
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1.4 The International System of Units
Prefixes
• For a very large or small numerical quantity, units can
be modified by using a prefix
• Each represent a multiple or sub-multiple of a unit
for example: 4,000,000 N = 4000 kN (kilo-newton)
= 4 MN (mega- newton)
0.005m = 5 mm (milli-meter)
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1.4 The International System of Units
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1.5 Numerical Calculations
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1.5 Numerical Calculations
Significant Figures• Accuracy of a number is specified by the number of
significant figures it contains
• A significant figure is any digit including zero
e.g. 5604 and 34.52 have four significant numbers
• When numbers begin or end with zero, we make use
of prefixes to clarify the number of significant figures
e.g. 400 as one significant figure would be 0.4(103)
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1.5 Numerical Calculations
Rounding Off Numbers
• Accuracy obtained would never be better than the
accuracy of the problem data
• Calculators or computers involve more figures in the
answer than the number of significant figures in the
data
• Calculated results should always be “rounded off” to
an appropriate number of significant figures
As a general rule, any numerical figure ending in five or
greater is rounded up and a number less than five is
rounded down.
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1.5 Numerical Calculations
Calculations• Retain a greater number of digits for accuracy (do not
round off calculations until expressing the final result)
• Work out computations so that numbers that are
approximately equal
• Round off final answers to three significant figures
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1.6 General Procedure for Analysis
• To solve problems, it is important to present work in a
logical and orderly way as suggested:
1. Correlate actual physical situation with theory
2. Draw any diagrams and tabulate the problem data
3. Apply principles in mathematics forms
4. Solve equations which are
dimensionally homogenous
5. Report the answer with
significance figures
6. Technical judgment
and common sense
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Example
Convert 2 km/h to m/s.
Solution
m/s 556.0s 3600
h 1
km
m 1000
h
km 2 km/h 2 =
=
Remember to round off the final answer to three significant figures.
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QUIZ
1. The subject of mechanics deals with what happens to
a body when ______ is / are applied to it.
A) magnetic field B) heat C) forces
D) neutrons E) lasers
2. ________________ still remains the basis of most of
today’s engineering sciences.
A) Newtonian Mechanics B) Relativistic Mechanics
C) Greek Mechanics C) Euclidean Mechanics
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QUIZ
3. Evaluate the situation, in which mass (kg), force (N),
and length (m) are the base units and recommend a
solution.
A) A new system of units will have to be formulated.
B) Only the unit of time have to be changed from second to
something else.
C) No changes are required.
D) The above situation is not feasible.
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QUIZ
4. Give the most appropriate reason for using three
significant figures in reporting results of typical
engineering calculations.
A) Historically slide rules could not handle more than three
significant figures.
B) Three significant figures gives better than one-percent
accuracy.
C) Telephone systems designed by engineers have area
codes consisting of three figures.
D) Most of the original data used in engineering
calculations do not have accuracy better than one percent.
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QUIZ
5. For a static’s problem your calculations show the final
answer as 12345.6 N. What will you write as your final
answer?
A) 12345.6 N B) 12.3456 kN C) 12 kN
D) 12.3 kN E) 123 kN
6. In three step IPE approach to problem solving, what
does P stand for?
A) Position B) Plan C) Problem
D) Practical E) Possible
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Thank you for your patience
and attention.
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Homework
• Chapter One: 1-1, 1-6, 1-7, 1-14. Page # 15
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