Statics (ENGR 2214) Prof. S. Nasseri Statics ENGR 2214 Vectors in three dimensional space.

Slides:

Advertisements

Similar presentations

Chapter 2 STATICS OF PARTICLES

Advertisements

Statics of Particles MET 2214 Ok. Lets get started.

STATICS OF PARTICLES Forces are vector quantities; they add according to the parallelogram law. The magnitude and direction of the resultant R of two forces.

STATICS OF RIGID BODIES

Rigid Bodies: Equivalent Systems of Forces

CE Statics Lecture 4. CARTESIAN VECTORS We knew how to represent vectors in the form of Cartesian vectors in two dimensions. In this section, we.

Equilibrium of a Rigid Body

12 VECTORS AND THE GEOMETRY OF SPACE.

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

Force System in Three Dimension

ME221Lecture 61 ME221 Statics LECTURE # 6 Sections 3.6 – 3.9.

ME 221Lecture 51 ME 221 Statics LECTURE #4 Sections:

VECTORS in 3-D Space Vector Decomposition Addition of Vectors:

ME 221Lecture 21 ME 221 Statics Sections 2.2 – 2.5.

Chapter 2 Statics of Particles

1 Computer Graphics Chapter 5 Vector Based Algorithms.

Shawn Kenny, Ph.D., P.Eng. Assistant Professor Faculty of Engineering and Applied Science Memorial University of Newfoundland ENGI.

Chapter 3: VECTORS 3-2 Vectors and Scalars 3-2 Vectors and Scalars

Example: Determine the angle between the vectors A and B.

Scalar and Vector Fields

FE/Graduate Seminar Review Notes

Mr. Alok Damare Prof. Civil Engg. Dept.. INTRODUCTION  Engineering mechanics is that branch of science which deals with deals with the system of forces,

CHS Physics Multiplying Vectors. Three Possibilities 1. Multiplying a Vector by a Scalar 2. Multiplying Vector by a Vector 1. Scalar Product 2. Vector.

Engineering Mechanics: Statics

February 18, 2011 Cross Product The cross product of two vectors says something about how perpendicular they are. Magnitude: –  is smaller angle between.

7.1 Scalars and vectors Scalar: a quantity specified by its magnitude, for example: temperature, time, mass, and density Chapter 7 Vector algebra Vector:

EE 543 Theory and Principles of Remote Sensing

Copyright © 2010 Pearson Education South Asia Pte Ltd

VECTOR CALCULUS. Vector Multiplication b sin   A = a  b Area of the parallelogram formed by a and b.

Torque and Static Equilibrium Torque: Let F be a force acting on an object, and let r be a position vector from a chosen point O to the point of application.

CHAPTER TWO Force Vectors.

Scalars A scalar is any physical quantity that can be completely characterized by its magnitude (by a number value) A scalar is any physical quantity that.

Vector Addition Cummutative Law A B C B A C A + B = C B + A = C A + B = B + A.

Solving Problems.

Overview of Mechanical Engineering for Non-MEs Part 1: Statics 3 Rigid Bodies I: Equivalent Systems of Forces.

Physics. Session Kinematics - 1 Session Opener You fly from Delhi to Mumbai New Delhi Mumbai Hyderabad Then you fly from Mumbai to Hyderabad Does it.

CE Statics Lecture 5. Contents Position Vectors Force Vector Directed along a Line.

Chapter 2 Statics of Particles. Addition of Forces Parallelogram Rule: The addition of two forces P and Q : A →P→P →Q→Q →P→P →Q→Q += →R→R Draw the diagonal.

Engineering Mechanics: Statics Chapter 2: Force Vectors Chapter 2: Force Vectors.

RIGID BODIES: EQUIVALENT SYSTEM OF FORCES

ENGR Introduction to Engineering1 ENGR 107 – Introduction to Engineering Coordinate Systems, Vectors, and Forces (Lecture #6)

Engineering Mechanics STATIC FORCE VECTORS. 2.5 Cartesian Vectors Right-Handed Coordinate System A rectangular or Cartesian coordinate system is said.

A rule that combines two vectors to produce a scalar.

Concurrent Force Systems ENGR 221 January 15, 2003.

Statics Chapter Two Force Vectors By Laith Batarseh.

Vectors and the Geometry

VECTORS AND THE GEOMETRY OF SPACE. The Cross Product In this section, we will learn about: Cross products of vectors and their applications. VECTORS AND.

CH Review -- how electric and magnetic fields are created Any charged particle creates an electric field at all points in space around it. A moving.

12.3 The Dot Product. The dot product of u and v in the plane is The dot product of u and v in space is Two vectors u and v are orthogonal  if they meet.

Objective: Find the dot product of two vectors. Find the angle between two vectors. Dot product definition Example 1 Find the dot product. v = 2i – j w.

Chapter 3 Lecture 5: Vectors HW1 (problems): 1.18, 1.27, 2.11, 2.17, 2.21, 2.35, 2.51, 2.67 Due Thursday, Feb. 11.

Force is a Vector A Force consists of: Magnitude Direction –Line of Action –Sense Point of application –For a particle, all forces act at the same point.

Chapter I Vectors and Scalars AAIT Engineering Mechanics Statics Department of Tewodros N. Civil Engineering.

ME 201 Engineering Mechanics: Statics Chapter 4 – Part A 4.1 Moment of a Force - Scalar 4.2 Cross Product 4.3 Moment of a Force – Vector 4.4 Principle.

2 - 1 Engineering Mechanics Lecture 2 Composition and Resolution of forces

X, Y axis (Horizontal & Vertical)

Introduction Treatment of a body as a single particle is not always possible. In general, the size of the body and the specific points of application.

GOVERNMENT ENGINEERING COLLEGE, DAHOD CIVIL ENGINEERING DEPARTMENT

Rigid Bodies: Equivalent Systems of Forces

Forces Classification of Forces Force System

X, Y axis (Horizontal & Vertical) Triangle Force (Sine Law)

Statics Test 1 Review By Caleb.

We live in a Three Dimensional World

STATICS (ENGINEERING MECHANICS-I)

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

Cartesian Vectors In right-handed Cartesian coordinated system, the right thumb points in the positive z direction when the right hand figures are curled.

Lecture 1 : Introduction to Engineering Mechanics

Presentation transcript:

Statics (ENGR 2214) Prof. S. Nasseri Statics ENGR 2214 Vectors in three dimensional space

Statics (ENGR 2214) Prof. S. Nasseri This figure shows the Right handed system, which is a coordinate system represented by base vectors which follow the right-hand rule (four fingers from x to y, and thumb will be along z direction). Vectors in three dimensional space Base vectors for a rectangular coordinate system: A set of three mutually orthogonal unit vectors Rectangular component of a Vector: The projections of vector F along the x, y, and z directions are F x, F y, and F z, respectively. F FxFx FyFy i j x y k z FzFz

Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space If the angle between F and its components (F x ) on axis x is , then F FxFx i x y z

Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space Also, if the angle between F and its components (F y ) on axis y is , then F FyFy j x y z

Statics (ENGR 2214) Prof. S. Nasseri Vectors in three dimensional space Similarly, if the angle between F and its components (F z ) on axis z is , then F x y k z FzFz 

Statics (ENGR 2214) Prof. S. Nasseri Direction cosines cos , cos  and cos  are called: Direction cosines. F FxFx FyFy i j x y k z FzFz

Statics (ENGR 2214) Prof. S. Nasseri Coordinates of points in space Coordinates of points in space: The triplet (x,y,z) describes the coordinates of a point. The vector connecting two points: The vector connecting point A to point B is given by

Statics (ENGR 2214) Prof. S. Nasseri Unit vector A unit vector along the line A- B: A unit vector along the line A-B is obtained from

Statics (ENGR 2214) Prof. S. Nasseri A vector along A-B A vector F along the line A-B (and of magnitude F) can be obtained from

Statics (ENGR 2214) Prof. S. Nasseri Dot Product Dot Product: The dot product of vectors F and E is given by Projection of a vector by using the dot product: The projection of vector F along the unit vector u is given by  F E  F u F.u

Statics (ENGR 2214) Prof. S. Nasseri Parallelogram Law Copyright of Ohio University Two forces on a body can be replaced by a single force called the resultant by drawing the diagonal of the parallelogram with sides equivalent to the two forces.

Statics (ENGR 2214) Prof. S. Nasseri Principal of Transmissibility The conditions of equilibrium or motion of a body remain unchanged if a force on the body is replaced by a force of the same magnitude and direction along the line of action of the original force. Copyright of Ohio University