1. Chapter 1 - General Principles
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Chapter 1 General Principles

2. Chapter 1 General Principles
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Chapter 1 General Principles

3. Chapter 1 General Principles
Objectives
To provide an introduction to the basic quantities and idealizations of mechanics.
To give a statement of Newton’s laws of Motion and Gravitation.
To review the principles for applying the SI system of units.
To examine the standard procedures for performing numerical calculations.
To present a general guide for problem solving.
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4. Chapter 1 General Principles
Definition
Mechanics:
Branch of physical sciences concerned with the state of rest or motion of bodies subjected to forces.
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Chapter 1 General Principles

5. Chapter 1 General Principles
Engineering Mechanics
Solid Mechanics
Fluid Mechanics
Rigid Bodies
Deformable Bodies
Statics
Dynamics
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6. Chapter 1 General Principles
Rigid Body Mechanics
Statics – Bodies at rest
Dynamics – Accelerated motion of bodies
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7. Historical Development
Statics
Depends on geometry and forces
Simple machines
levers
pulleys
inclined plane
Archimedes ( B.C.)
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8. Historical Development
Dynamics
Accurate Measurement of time
Galileo ( )
Newton( )
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9. Chapter 1 General Principles
Basic Quantities
Length
meter
foot
Time
second
Mass
kilogram
slug
Force
newton
pound
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10. Chapter 1 General Principles
Length
Needed to locate the position of a point in space and describe the size of a physical system.
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11. Chapter 1 General Principles
Time
Conceived as a succession of events. Concepts of STATICS are time independent.
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12. Chapter 1 General Principles
Mass
A property of matter by which we can compare the action of one body to another. This property manifests itself as a gravitational attraction between two bodies and provide a qualitative measure of the resistance of matter to a change in velocity.
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13. Chapter 1 General Principles
Force
Generally considered as a push of a pull exerted by one body on another. Interaction occurs when there is direct contact between the bodies. Gravitational, electrical and magnetic forces do not require direct contact. Force is characterized by magnitude, direction and point of application.
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14. Chapter 1 General Principles
Idealizations
Particle - an object having mass but the size is neglected.
Rigid Body - a combination of a large number of particles which remain in a fixed position relative to each other, both before and after the application of a force.
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15. 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 the particle is not subjected to unbalanced forces.
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16. 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. If F is applied to a particle of mass m then: F = ma.
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17. Newton’s Three Laws of Motion
Third Law: The mutual forces of action and reaction between two particles are equal, opposite and collinear.
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18. Newton’s Laws of Gravitational Attraction
Where:
F = force of gravitation
G = universal constant of gravitation
m1,m2= mass of two particles
r = distance between two particles
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19. Chapter 1 General Principles
Weight
m = mass of object
m2 = mass of earth
r = distance from center of earth to particle
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20. Chapter 1 General Principles
Units
Basic quantities (force, mass, length, time) are related by Newton’s second law.
Units used to measure quantities are not all independent.
Three of four units, called base units, are arbitrarily defined and the fourth is derived.
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21. Chapter 1 General Principles
SI Units
Modern version of metric system.
Base units are length, time and mass, meter (m), second (s), and kilogram (kg)
Acceleration of gravity:
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22. Chapter 1 General Principles
SI Units
Force is derived quantity measured in unit called a newton
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23. U.S. Customary Units (fps)
Base units are length, time and force.
feet (ft), second (s), and pound (lb)
Acceleration of gravity:
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24. U.S. Customary Units (fps)
Mass is derived quantity measured in a unit called a slug:
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25. Chapter 1 General Principles
Systems of Units
Name
Length
Time
Mass
Force SI
meter
(m)
second
(s)
kilogram
(kg)
newton
(N)
US Customary
foot
(ft)
slug
(lb s2/ft
pound
(lb
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26. Chapter 1 General Principles
Unit Conversions
Unit Conversions
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27. Chapter 1 General Principles
Prefixes for SI units
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28. Chapter 1 General Principles
Concepts to Study
Dimensional Homogeneity
Significant Figures
Rounding Off Numbers
Calculations
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29. Dimensional Homogeneity
Each of the terms of an equation must be expressed in the same units.
s = v t + 1/2 a t2
s is position in meters
v is velocity in m/s
a is acceleration in m/s2
t is time in seconds
m = m/s  s + m/s2  s2 = m
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30. Chapter 1 General Principles
Significant Figures
Accuracy specified by number of significant figures.
Defined as any digit including a zero (provided it is not used to specify the location of a decimal point).
5604 and both have four significant figures
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31. Chapter 1 General Principles
Engineering Notation
Does 40 have one or two significant figures?
Engineering notation uses powers of ten with exponents in multiples of three.
40 written as 0.04 (103) is forty to one significant figure and (103) is forty to two significant figures.
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32. Chapter 1 General Principles
Calculations
When performing calculations retain a greater number of digits than the problem data.
Engineers usually round off final answer to three significant figures. Intermediate calculations are usually done to four significant figures.
Answer can never have more significant figures than given data!
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33. Chapter 1 General Principles
Convert 2 km/h to m/s. How many ft/s is this?
SOLUTION:
Since 1 km = 1000 m and 1 h = 3600 s, the conversion
factors are arranged so that a cancellation of units can be applied.
Recall that 1 ft = m
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34. Procedure for Analysis
Read the problem carefully and correlate the actual physical situation with the theory studied.
Draw necessary diagrams and tables.
Apply relevant principles, generally in mathematical form.
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35. Procedure for Analysis
Solve the equations algebraically (without numbers) as far as possible, then obtain a numerical answer.
Be sure to use a consistent set of units.
Report the answer with no more significant figures than the accuracy of the given data.
Decide if answer seems reasonable.
Think about what the problem taught you!
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36. Chapter 1 General Principles
Important Points
Statics is the study of bodies at rest or moving with constant velocity.
A particle has mass but a size that can be neglected.
A rigid body does not deform under load.
Concentrated forces are assumed to act at a point on a body.
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37. Chapter 1 General Principles
Important Points
Newton’s three laws of motion must be memorized!
Mass is a property of matter that does not change from one location to another.
Weight is the gravitational attraction of the earth on a body or quantity of mass. Its magnitude depends on the location of the mass.
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38. Chapter 1 General Principles
Important Points
In the SI system the unit of force is the newton. It is a derived quantity. Mass, length and time are the base quantities.
In the SI system prefixes are used to denote large or small numerical quantities of a unit.
Perform numerical calculation to several significant figures and report answers to three significant figures.
Be sure that all equations are dimensionally homogeneous.
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39. Chapter 1 General Principles
Objectives - Review
To provide an introduction to the basic quantities and idealizations of mechanics.
To give a statement of Newton’s laws of Motion and Gravitation.
To review the principles for applying the SI system of units.
To examine the standard procedures for performing numerical calculations.
To present a general guide for problem solving.
11/14/2018
Chapter 1 General Principles