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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
Mechanics
Fundamental Concepts
Units of Measurement
The International System of Units
Numerical Calculations
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 deals with
- 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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6. 1.2 Fundamentals Concepts
Basic Quantities
Length - locate the position of a point in space
Mass - measure of a quantity of matter
Time - succession of events
Force - a “push” or “pull” exerted by one body on another
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7. 1.2 Fundamentals Concepts
Idealizations
Particles - has a mass and size can be neglected
Rigid Body - a combination of a large number of particles
Concentrated Force - the effect of a loading
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8. 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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9. 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”
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10. 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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11. 1.2 Fundamentals Concepts
Newton’s Law of Gravitational Attraction
Weight:
Letting yields
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
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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)
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1.3 Units of Measurement
At the standard location,
g = 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 N
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15. 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)
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16. 1.4 The International System of Units
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17. 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
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18. 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 and 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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19. 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
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20. 1.5 Numerical 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
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21. 1.6 General Procedure for Analysis
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
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Example
Convert to 2 km/h to m/s.
Solution
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 N. What will you write as your final answer?
A) N B) 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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