Introduction to Engineering Mechanics

• Students should be able to define mechanics, engineering mechanics, and statics of rigid bodies, and grasp their significance in engineering
• Students should be able to differentiate between scalar and vector quantities and give real-world examples
• Students should be able to recognize and categorize different types of units, understanding the SI system
• Students should be able to apply dimensional homogeneity to ensure equations and physical formulas are correct
• Students should be able to use significant figures and rounding techniques in numerical calculations for accurate results
• Students should be able to describe force, including its definition and classification based on application and direction
• Students should be able to identify and analyze different force systems in static situations
• Students should be able to explain laws of mechanics (motion, gravitation, transmissibility) and their implications in engineering analysis
• Students should be able to explain the laws of mechanics and force principles
• Students should be able to describe a general procedure for analyzing engineering problems

Mechanics

• Mechanics is a branch that deals with the state of bodies, whether at rest, in motion, or deforming under a force system
• Applying a force system results in:
  • Body movement if unrestrained
  • No movement but noticeable deformation
• Noticeable deformation falls under deformable-body mechanics, otherwise known as strength/mechanics of materials
• Negligible deformation or no movement falls under rigid-body mechanics
• Mechanics is divided into statics and dynamics, and statics studies bodies at rest
• Dynamics studies bodies in motion
• Fluid mechanics focuses on liquids

Engineering Mechanics

• Engineering Mechanics is a branch associated with the effect of forces on rigid bodies
• Forces can maintain a body's state of rest or motion
  • A body at rest means the net force is zero, known as static or equilibrium
  • A moving body indicates an unbalanced force, leading to dynamics
• Engineering mechanics focuses on forces affecting rigid bodies, but mechanics is classified by the nature of bodies influenced (solid/rigid, deformable, or fluid)

Fundamental Concepts

• Mechanics involves studying forces on solids and fluids
• Solid Mechanics branches into Rigid Body and Deformable Body mechanics
  • Rigid Body mechanics includes Engineering Mechanics
    • Engineering Mechanics branches into Statics and Dynamics -Dynamics further splits into Kinematics and Kinetics -Deformable Body mechanics focuses on Strength of Materials
• Fluid Mechanics covers Incompressible and Compressible Fluids
  • Incompressible fluids are Hydraulics
  • Compressible fluids are Gasses

Engineering Mechanics Applications

• Mechanics aims to explain and predict physical events, providing foundations for engineering applications
• Statics helps determine the forces on bridge designs and structural resistance
• Statics helps determine the necessary force a dam needs to endure from water in the river.
• Statics calculate crane lifting capacity, locomotive pulling force, and circuit board resistance

Fundamental Quantities

• Space describes geometric regions occupied by bodies, defined by linear/angular measurements relative to a coordinate system
  • 3D problems need three independent coordinates
  • 2D problems need only two
• Time measures event succession, a core aspect of dynamics, but is not directly involved in the realm of statics
• Mass is inertia, or a body's resistance to velocity change
  • Mass is the quantity of matter, influencing gravitational attraction and impacting statics
• Force is the action of one body on another, moving the body in direction of the force
  • Force is specified by magnitude, direction, and application point

Particles and Rigid Bodies

• A particle is a body with negligible dimensions, a point mass in mathematical terms
  • Particles are used as differential elements or when dimensions do not matter
• A rigid body has negligible distance changes between any two points

Length and Concentrated Forces

• Length locates points and describes physical systems
  • Standard units of length define distances and geometric attributes as multiples
• A concentrated force models a loading acting at a point
  • Loads are represented as concentrated forces if the application area is small relative to the body

Types of Units

• Fundamental or Base units are unalterable, separate entities
  • Length, time, and mass are fundamental quantities
  • Meter, second, and kilogram are their respective base units, used extensively in mechanics
• Derived Units depend on fundamental units
  • Force, work, power, density, area, volume, velocity, and acceleration use derived units

System of Units

• Common systems of units:
  • M.K.S (Meter-Kilogram-Second) system
  • C.G.S (Centimeter-Gram-Second) system
  • F.P.S (Foot-Pound-Second) system often called USCS (US Customary system)
  • S.I (International System) system

SI Units

• Base Units
  • Amount of substance - mole
  • Current - ampere
  • Length - meter
  • Luminous intensity - candela
  • Mass - kilogram
  • Temperature - kelvin
  • Time - second
• Supplementary Units
  • Plane angle - radian
  • Solid angle - steradian
• Derived units with distinct names
  • Force - newton
  • Frequency - hertz
  • Power - watt
  • Pressure, stress - pascal
  • Work, heat, energy - joule
• Derived units with base units -Acceleration - meter/sec/sec -Activity (radioactive) - 1/sec -Area - square meter -Concentration - mole/cubic meter -Luminance - candela/square meter -Mass density - kilogram/cubic meter -Specific volume - cubic meter/kilogram -Velocity, speed - meter/sec -Volume - cubic meter

Prefixes

• Prefixes modify SI units for very large/small quantities -Tera = 1 000 000 000 000 -Giga = 1 000 000 000 -Mega = 1 000 000 -Kilo = 1 000 -Milli = 0.001 -Micro = 0.000 001 -Nano = 0.000 000 001 -Pico = 0.000 000 000 001

Numerical Calculations

• Answers should be reported with justifiable accuracy using significant figures
• Dimensional Homogeneity requires each term in an equation to have the same units
  • This ensures terms can be combined when substituting values
• Significant figures determine the accuracy of a number
  • 1079 is composed of four significant figures
• If zeros trail a whole number, the number of significant figures is unclea
  • This ambiguity is solved using engineering notation
• Engineering notation rounds numbers to appropriate significant digits in multiples of (103), such as (103), (106), or (10–9)
  • 23 400 with five significant figures becomes 23.400(103), three becomes 23.4(103)

Rounding Off

• Rounding maintains result accuracy relative to problem data, this can be applied in some rules
  • Digits > 5 are rounded up, digits < 5 leave rounded values the same
  • Round numbers ending in 5 based on the prior digit
    • even numbered digits leave rounded values the same
    • odd numbered digits round up
• Store intermediate calculator results and round only the final result to maintain precision

Scalar and Vector Quantities

• Scalar quantities described by magnitude only (mass, length, volume, power, temperature, time)
  • Scalars are specified by magnitude
• Vector quantities need magnitude and direction (force, weight, moment, couple, displacement, velocity, acceleration, momentum)
  • Vectors are forces, positions, and moments shown as arrows
    • Arrow length indicates vector magnitude, and the angle defines the line of action direction
    • Arrowhead shows direction

Force Definition

• Force happens when a body acts upon another, and it may change the rest or motion of the body
• Forces result from object interactions
• Force is a vector quantity that has effects that depend on direction and magnitude
• Forces may change an object's shape/motion (start, stop, accelerate, or decelerate)
• The effect of force is influenced by magnitude, direction, sense, and contact point

Qualities of Force

• Magnitude represents the value of force and is graphically represented for drawing vectors to scale
• Direction is the line of action, and the angle relative to the reference axis
• Sense is the direction specified by an arrowhead and specifying the direction
• Point of application is where force contacts the other body. The graphical representation is the tip of the arrowhead Force Classification
• Contact forces are distributed over the surface area and involve direct contact forces like normal or frictional
• Body force happens with a force field such as gravity or a magnetic or electric field, with the interacting objects not necessarily in contact
• External forces are applied to either applied or as reactions
• Internal forces resist deformation
• A concentrated force occurs at a point
• Distributed force occurs across an area

Types of Forces

• Area over which contact force is applied is very small like a point, the force may be considered
• Force is concentrated if applied to a point
• Force that is distributed if it occurs over an area

Force Systems

• A Force System is a group of various forces acting on a rigid body
• Force system types are classified by the number of forces acting in planes
• Two categories are Coplanar and Non-Coplanar Force systems

###Coplanar and Non-Coplanar Force systems

• A coplanar force is a number of forces working in a single or common plane
• A coplanar force sub-divides into Concurrent, Collinear, Parallel and Non-parallel
• Non-Coplanar Force is where there are a number of forces working in different places which subdivides into Concurrent, Non-parallel and Parallel

Force System Laws

• Concurrent Coplanar, these forces work together at a common point in a common plane
• Collinear Coplanar, a number of forces have a single line of action in a common plane
• Parallel Coplanar, these have a parallel line of action in a common plane
• Non-parallel Coplanar, these do not have Parallel Line of Action in a common plane
• Concurrent Non-coplanar, these forces work together while acting through a common point through different plane
• Non-parallel Non-coplanar, a number of force that are having different line of action in three different places
• Parallel Non-coplanar, a number of forces are having parallel line of action in different planes

Laws of Mechanics

• Mechanics builds upon core laws
• Newton's First Law (Inertia): A body at rest stays at rest, and a body in motion stays in motion with constant/uniform velocity, unless acted upon by unbalanced force
• Newton's Second Law (Acceleration): A Particle is that the accerlation is relative to force and in direction towards it
• Newton's Third Law (Action-Reaction): When bodies interact the action force is equal and opposite to the reaction force

Newton's Law Of Gravitation

• Two particles with mass are mutually attracted with equal and opposite given forces
  • F=G(m1m2/r2) -G is the universal gravitational constant -m1 and m2 are the mass of the two particles and r is the distance between them

Laws of Motion additional points

• Newton's First Law encompasses equilibrium
• Newton's Laws basic to understanding forces, every equal force has an opposite and vice versa

Law Of Transmissibility

• The application point on a force and a line of action can be transmitted to other parts of the body

Force System Laws

• Parallelogram, Forces acting will have a magnitude and direction by the adjacent sides
• Triangle, 2 Forces that act as a point, a magnitude is taken in order than closes off a triangle starting and finish ends with the resultant force
• Polygon,Several forces acting will have a magnitude and direction if it's the right order, last force reps the resultant

General Analysis

• Engineering mechanics can be best learned by attending lessons, doing problems and study
• Most successful is when the one solving is the student
• Work should be laid out in a logical manner in these steps
  • Carefully study and understand
  • Compile a table with diagrams used
  • Apply any appropriate principles such as math
  • Solve the questions with appropriate figures
  • Check the logic and use common sense

The Lesson Ends With Some Problems For The Following.

• Convert Units
• Rounding off digits/figures
• Express results with values
• Density and determine the weight