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 21

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