ME 201 Engineering Mechanics: Statics Unit 1.1 Mechanics Fundamentals Newton s Laws of Motion Units
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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 2 km hr 1000m 1km 1hr 3600sec 0.556m sec
Conversion of Units - Example How many square meters in a sheet of plywood?
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. = =
Conversion of Units - Example Compare the US mile with the metric mile. Metric mile = 1600 meters Find the difference between the two distances in feet.
Video 1a Fundamental 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 2a Units of Measurement, Significant Figures Units of Measurement SI (System International) US Customary ( English) Significant Figures
Video 3a Conversion 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 Question Mechanics 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 Question Fundamental 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 F ma
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 F G Mm r 2 r = distance between the two particles G = universal constant of gravitation
Newton s Law of Gravitational Attraction For most Engineering Calculations Earth is one mass (M) At sea level, 45º latitude let GM g 2 r Substituting into previous equation, F mg W mg F G Mm 2 r
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 Mass Time Force
Units of Measurement SI US, English Length meters m feet ft Time seconds s seconds s Mass kilogram kg slug slug Force newton N pounds lb
SI System International Gravitational Constant Force Newton W mg m 1kg 9.81 2 s kgm 9.81 2 s 9.81N m g 9.81 2 s By definition: 1N kg m 2 s A body of mass of 1 kg has a weight of 9.81 N
SI Prefixes Symbol Prefix Multiplication Factor G giga 1,000,000,000 10 9 M mega 1,000,000 10 6 k kilo 1,000 10 3 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 W m g 32.2lb ft 32.2 2 s lb s 2 1 ft 1Slug By definition: ft g 32.2 s Slug lb s ft A body of weight 32.2 lb has a mass of 1 slug 2 2
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*10 3
Concept Question Significant 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 2 km hr 1000m 1km 1hr 3600sec 0.556m sec
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/ft 3 to kn/m 3
Solution - #2 Convert 350 lb/ft 3 to kn/m 3
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