Transcript pp01

Engineering Mechanics:
Statics in SI Units, 12e
1
General Principles
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
Copyright © 2010 Pearson Education South Asia Pte Ltd
Chapter Outline
1.
2.
3.
4.
5.
6.
Mechanics
Fundamental Concepts
Units of Measurement
The International System of Units
Numerical Calculations
General Procedure for Analysis
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.1 Mechanics
• Mechanics can be divided into 3 branches:
- Rigid-body Mechanics
- Deformable-body Mechanics
- Fluid Mechanics
• Rigid-body Mechanics deals with
- Statics
- Dynamics
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.1 Mechanics
• Statics – Equilibrium of bodies
 At rest
 Move with constant velocity
• Dynamics – Accelerated motion of bodies
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.2 Fundamentals Concepts
Idealizations
1. Particles
- has a mass and size can be neglected
2. Rigid Body
- a combination of a large number of particles
3. Concentrated Force
- the effect of a loading
Copyright © 2010 Pearson Education South Asia Pte Ltd
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”
Copyright © 2010 Pearson Education South Asia Pte Ltd
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”
F  ma
Copyright © 2010 Pearson Education South Asia Pte Ltd
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”
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.2 Fundamentals Concepts
Newton’s Law of Gravitational Attraction
F G
m1 m 2
r2
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
mM e
Weight: W  G 2
r
2
Letting g  GM e / r yields W  mg
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.3 Units of Measurement
Name
Length
Time
Mass
International
Systems of Units
(SI)
Meter (m) Second (s) Kilogram (kg) Newton (N)
Copyright © 2010 Pearson Education South Asia Pte Ltd
Force
 kg .m 
 2 
 s 
1.3 Units of Measurement
•
•
•
At the standard location,
g = 9.806 65 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
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Eg: 4,000,000 N = 4000 kN (kilo-newton)
= 4 MN (mega- newton)
0.005m = 5 mm (milli-meter)
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.4 The International System of Units
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.5 Numerical Calculations
Dimensional Homogeneity
•
•
•
Each term must be expressed in the same units
Regardless of how the equation is evaluated, it
maintains its dimensional homogeneity
All terms can be replaced by a consistent set of units
Copyright © 2010 Pearson Education South Asia Pte Ltd
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)
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.5 Numerical Calculations
Calculations
•
•
•
Retain a greater number of digits for accuracy
Work out computations so that numbers that are
approximately equal
Round off final answers to three significant figures
Copyright © 2010 Pearson Education South Asia Pte Ltd
1.6 General Procedure for Analysis
•
1.
2.
3.
4.
5.
6.
To solve problems, it is important to present work in a
logical and orderly way as suggested:
Correlate actual physical situation with theory
Draw any diagrams and tabulate the problem data
Apply principles in mathematics forms
Solve equations which are
dimensionally homogenous
Report the answer with
significance figures
Technical judgment
and common sense
Copyright © 2010 Pearson Education South Asia Pte Ltd
Example
Convert to 2 km/h to m/s.
Solution
2 km  1000 m  1 h 
2 km/h 


  0.556 m/s
h  km  3600 s 
Remember to round off the final answer to three significant figures.
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Copyright © 2010 Pearson Education South Asia Pte Ltd
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.
Copyright © 2010 Pearson Education South Asia Pte Ltd
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.
Copyright © 2010 Pearson Education South Asia Pte Ltd
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
Copyright © 2010 Pearson Education South Asia Pte Ltd