Module 5: Particle Equilibrium

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From the course by Georgia Institute of Technology

Introduction to Engineering Mechanics

1122 ratings

Georgia Institute of Technology

Introduction to Engineering Mechanics

1122 ratings

This course is an introduction to learning and applying the principles required to solve engineering mechanics problems. Concepts will be applied in this course from previous courses you have taken in basic math and physics. The course addresses the modeling and analysis of static equilibrium problems with an emphasis on real world engineering applications and problem solving. The copyright of all content and materials in this course are owned by either the Georgia Tech Research Corporation or Dr. Wayne Whiteman. By participating in the course or using the content or materials, whether in whole or in part, you agree that you may download and use any content and/or material in this course for your own personal, non-commercial use only in a manner consistent with a student of any academic course. Any other use of the content and materials, including use by other academic universities or entities, is prohibited without express written permission of the Georgia Tech Research Corporation. Interested parties may contact Dr. Wayne Whiteman directly for information regarding the procedure to obtain a non-exclusive license.

From the lesson

Forces and Particle Equilibrium

In this section, students will learn the definition of a force and how to represent a force as a vector in two (2D) and three (3D) dimensions. Students will learn the concept of particle equilibrium and equilibrium of systems of particles. Concepts will be reinforced with example problems.

Module 1: Course Introduction6:38

Module 2: Definition of a Force4:28

Module 3: Force Representation in 2D and Resultants8:46

Module 4: Force Representation in 3D8:53

Module 5: Particle Equilibrium4:46

Module 6: Systems of Particles Equilibrium11:27

Module 7: Solve a Particle Equilibrium Problem6:54

Meet the Instructors

Dr. Wayne Whiteman, PE
Senior Academic Professional
Woodruff School of Mechanical Engineering

>> Hi and welcome to module five of an introduction to engineering mechanics.

>> Before we start today's module, I just wanted to look at an overview of the

course again. >> We've gone through the first major

topic already, which is forces and expressing the forces of a vector in 2D

and 3-dimensional >> components.

>> The next topic which we'll start with this module is particle equilibrium,

or looking at the balance of forces on a particle.

>> So, the learning outcomes for today are, first, to state Newton's first law

of motion, which you should be able to recall from your, your background in

Physics. >> And then to express the 2D and 3D

equilibrium equations that re-, re-, result from, an application of Newton's

1st Law. >> And finally we're going to learn

about a graphical tool that we're going to use in applying the equations of

equilibrium to real world problems. >> And I'll go through the rules on how

to draw a free body diagram, and sketch that free body diagram.

>> Which is a a very important equilibrium, excuse me, a very important

tool in engineering mechanics. >> Okay, so first of all, what I'd like

you to do is research the, Newton's First Law of Motion, or review Newton's First

Law of Motion, and take a few minutes and write down in your own words what

Newton's first law states. >> Now that you've answered that

question, let's look at a definition of Newton's First Law of Motion.

>> So a particle that's at rest or moving along a straight line with

constant velocity will remain in that state when it's not subjected to an

unbalanced force. >> And we call this static equilibrium.

>> And so, as a result of that statement, of Newton's First Law for a

particle we can come up with this Static Equilibrium Equations.

>> Which state that [COUGH], the forces, the sum of the forces, vectorily

are equal to zero on >> The particle if it's to remain in

this, in this state of rest or constant velocity.

>> And so in two dimensions, we can break that down into scalar equations for

two orthogonal directions. >> We might use x and y coordinates or

we might use parallel and perpendicular componenets.

>> But the only >> we'll only come up with 2

independent equations in that case and 3 dimensions will have 3 independent

equations. >> A balance of forces in the X, and

the Y, and the Z direction. >> So let's now as a last step in this

module look at a , a, a procedures for drawing something that's called a free

body diagram or a graphical tool for applying the equations of equilibrium,

We're going to use this throughout this course.

>> So the first step is apply or identify the particle or body of interest

that we're, we want to apply equilibrium to.

>> and so in this case, we have this point right here.

>> In which we have a tension of the cable that's acting up the left at a, at

a 40 degree angle. >> And we have another tension in this

cable that's acting up to the right at a 50 degree angle.

>> And then we have a. >> Weight down of 10 pounds.

>> So the body or particle of interest that we're interested in, is this point

right here, which is the intersection of these forces.

>> So I'm going to draw that down here. >> I just draw it as a pointer or

particle. >> And once we've done that, we sketch

the particle free of constraints. >> And so we look it as if it's

disconnected from the rest of the world. >> Okay.

>> Standing there by itself as a particle.

>> And then we apply any external forces that are acting on it.

>> and so in this case as I mentioned we have a

>> Tension up and to the left in this cable, which I'll call, tension one.

>> And, we have a tension up and to the right in this cable, which I'll call

tension two. >> And then, we have a weight down,

which is 10 lbs. >> And the last step in our free-body

diagram is to add dimensions. >> And, so in this case the dimensions

we have are these angles, which are 40 degrees, and 50 degrees.

>> And, so that's a, that's a good free body diagram.

>> You'll find the ability to draw this type of diagram will help us tremendously

in applying the equesions, the equations of equilibrium, to find for instance, the

tension in these two cables in future problem.

>> That's it for today's module. >> Thanks.

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