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ME 201Engineering Mechanics: Statics
Unit 1.1
Mechanics Fundamentals
Newton’s Laws of Motion
Units
Mathematica
E-Text
Supplemental Materials
Homework Submission
Unit 1.1 – Getting Started
Unit 1.1 – Getting Started
Maple TA
Conversion of Units
SI to English, English to SI, etc.
Key: Multiply by 1
Force: 1 lb = 4.4482 N
Length: 1 ft = .3048 m
Conversion of Units - Example
Convert 2 km/h to m/s
Conversion of Units - Example
Convert 2 km/h to m/s
hr
km2
km
m
1
1000
sec3600
1hr
sec556.0
m
Conversion of Units - Example
How many square meters in a sheet of plywood?
Conversion of Units - Example
How many square meters in a sheet of plywood?
ft4 ft8
2
1
3048.
ft
m 2973.2 m
Group Exercise
Compare the US mile with the metric mile.
Metric mile = 1600 meters
US Mile = 5280 ft
Find the difference between the two distances
in feet.
=
=
Compare the US mile with the metric mile.
Metric mile = 1600 meters
Find the difference between the two
distances in feet.
Conversion of Units - Example
Video 1aFundamental Concepts
Intro to Statics
3 Branches of Mechanics
Statics is part of Rigid Body Mechanics
4 Basic Quantities: Length, Time, Mass, Force
3 Fundamental Modeling Assumptions
Particle
Rigid Body
Concentrated Force
Newton’s 3 Laws of Motion
Newton’s Law of Gravitational Attraction
Video 2aUnits of Measurement, Significant Figures
Units of Measurement
SI (System International)
US Customary ( English)
Significant Figures
Video 3aConversion of Units
SI to English
English to SI
Multiply by “1”
Conversion of Units Example
Intro to Statics
Mechanics – Branch of physical science concerned with the state of rest or motion of bodies subjected to a force
3 Branches:
Rigid Body Mechanics
Deformable-Body Mechanics
Fluid Mechanics
Which of branch of Mechanics contains Statics?
Intro to Statics
Rigid Body Mechanics consists of 2 areas:
Statics
Equilibrium of bodies at rest / constant motion
Dynamics
Bodies in motion, accelerating, etc.
Concept QuestionMechanics
What are the 4 basic quantities used in
Mechanics?
Basic Quantities Used in Mechanics
Length
Time
Dynamics only
Mass
Related to weight by gravitational constant
Force
Push or pull,
has magnitude, direction, and point of application
3 Fundamental Modeling Definitions/Assumptions
Particle
Has mass but no size
Allows problems to be reduced to simpler form
Rigid Body
Combination of large number of particles which remain fixed after load is applied
Allows us to ignore material properties and small deformations that may occur during our analysis
Concentrated Force
Force assumed to act entirely at a point
Concept QuestionFundamental Modeling
Why are the Fundamental Modeling
assumptions for Particle, Rigid Body, and
Concentrated Force important?
Newton’s 3 Laws of Motion
Form the entire basis for rigid body mechanics
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 the particle is
not subjected to an unbalanced force.
Examples
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 & a
magnitude that is directly proportional to the
force.
Examples
maF
Newton’s 3rd Law of Motion
The mutual forces of action and reaction
between two particles are equal, opposite,
and collinear.
Examples
Newton’s Law of Gravitational Attraction
Two particles of mass (M, m) are mutually
attracted with equal and opposite forces (F
and –F) of magnitude F:
Where
r = distance between the two particles
G = universal constant of gravitation
2r
MmGF
Newton’s Law of Gravitational Attraction
For most Engineering Calculations
Earth is one mass (M)
At sea level, 45º latitude
let
Substituting into previous equation,2r
MmGF
2r
GMg
mgF mgW
Units of Measurement
Engineering commonly uses 2 different
systems of units
SI (System Internation) or Metric
US Customary or English
Commonly used Units of Measurement
Length
Time
Mass
Force
Units of Measurement
SI US, English
Length
Time
Mass
Force
meters
seconds
kilogram
newton
m
s
kg
N
feet
seconds
slug
pounds
ft
s
slug
lb
SI – System International
Gravitational Constant
Force – Newton
A body of mass of 1 kg has a weight of 9.81 N
mgW
281.91
s
mkg
281.9
s
mkg
N81.92
1s
mkgN
281.9
s
mg
By definition:
SI Prefixes
Symbol Prefix Multiplication Factor
G giga 1,000,000,000 109
M mega 1,000,000 106
k kilo 1,000 103
m milli 0.001 10-3
µ micro 0.000001 10-6
n nano 0.000000001 10-9
US Customary - English
Gravitational Constant
Mass – Slug
A body of weight 32.2 lb has a mass of 1 slug
g
Wm
22.32
2.32
s
ft
lb
ft
slbSlug
2
22.32
s
ftg
ft
slb 2
1
By definition:
Slug1
Significant Figures
Generally 3 or 4 appropriate on final answer
Keep intermediate calculations in calculator
Round final answer
Examples:
4.78 47.8 0.478
4780 4.78*103
Concept QuestionSignificant Digits
What is the difference between Scientific
notation and Engineering notation?
Conversion of Units
SI to English, English to SI, etc.
Key: Multiply by 1
Force: 1 lb = 4.4482 N
Length: 1 ft = .3048 m
Conversion of Units - Example
Convert 2 km/h to m/s
Conversion of Units - Example
Convert 2 km/h to m/s
hr
km2
km
m
1
1000
sec3600
1hr
sec
556.0 m
Conversion of Units - Example
Convert 300 lb*sec to SI
Example Problems
Class Exercise - #1
Compare the US mile with the metric mile.
Metric mile = 1600 meters
Find the difference between the two
distances in feet.
Solution - #1
Compare the US mile with the metric mile.
Metric mile = 1600 meters
Find the difference between the two
distances in feet.
Class Exercise - #2
Convert 350 lb/ft3 to kN/m3
Solution - #2
Convert 350 lb/ft3 to kN/m3
Class Exercise - #3
Evaluate (35 mm)2 (48 kg)3 to 3 significant
digits and express in SI units using an
appropriate prefix
Solution - #3
Evaluate (35 mm)2 (48 kg)3 to 3 significant
digits and express in SI units using an
appropriate prefix