# ME102: Mechanics I

Unit 1: Statics   *The first unit of this course covers static analysis.  You will briefly review vectors (graphical elements allowing you to visualize the direction and magnitude of a physical quantity, like velocity), forces (influences that cause unrestrained objects to accelerate), and moments (forces that cause free bodies to rotate) in two dimensions and three dimensions.  You will then turn your attention to “static” objects—that is, objects in equilibrium, or objects that are either motionless or moving at a constant speed but not accelerating.

Once you have a solid grasp on how to effectively examine what happens when static structures are subjected to forces, you will learn how friction (a force resisting the lateral movement of an object) will affect a situation.  These concepts are basic, but you must know how to locate and use them when physically analyzing a structure.  You will learn to compute moments and resultants of force systems and study internal forces exerted on members. You will analyze trusses, machines, and frames, as well as study the effects of friction on belts and wedges.

The material in this unit should be understood at a level sufficient for application to and analysis of new situations; sample questions at this level are included at the end of the unit.*

Unit 1 Time Advisory
This unit will take you approximately 40 hours to complete.

☐    Subunit 1.1: 12 hours ☐    Subunit 1.1.1: 7 hours

☐    Subunit 1.1.2: 2 hours

☐    Subunit 1.1.3: 2 hours

☐    Subunit 1.1.4: 1 hour

☐    Subunit 1.2: 10 hours

☐    Subunit 1.2.1: 1 hour

☐    Subunit 1.2.2: 2 hours

☐    Subunit 1.2.3: 2 hours

☐    Subunit 1.2.4: 2 hours

☐    Subunit 1.2.5: 2 hours

☐    Subunit 1.2.6: 1 hour

☐    Subunit 1.3: 14 hours ☐    Subunit 1.3.1: 2 hours

☐    Subunit 1.3.2: 3 hours

☐    Subunit 1.3.3: 1 hour

☐    Subunit 1.3.4: 2 hours

☐    Subunit 1.3.5: 2 hours

☐    Subunit 1.3.6: 1 hour

☐    Subunit 1.3.7: 1 hour

☐    Subunit 1.3.8: 2 hours

☐    Assessment: 4 hours

Unit1 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Identify, explain, and perform calculations using units and notations common in mechanics; convert between unit systems. - Perform vector calculations including dot products, cross products, and magnitude calculations. - Identify, explain, and perform calculations involving forces, couples, and moments. - Use the concepts of forces and moments to compute resultants and equivalents in mechanics. - Analyze and perform calculations concerning static, rigid bodies including trusses, frames, and machines. - Identify and analyze problems involving friction, tension, and compression. - Perform calculations involving friction; analyze belts and pulleys.

1.1 Introduction   1.1.1 Motivation   - Activity: The Saylor Foundation's “Introduction and Motivation: Bridge Design” Link: The Saylor Foundation’s “Introduction and Motivation: Bridge Design” (PDF)

Instructions: Please read click on the link above and perform the activities described in the resource.  You may collaborate with peers to perform this exercise.  This activity will take you about five hours to complete.

`````` Terms of Use: This resource is licensed under a [Creative Commons
``````

1.1.2 Units, Dimensions, and Notations   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Notation and Units” Link: University of Nebraska-Lincoln: Dr. M. Negahban’s “Notation and Units” Lecture (PDF)

Instructions: Please click on the link above and read the lecture notes on notation and units.  This review is intended to refresh your memory of units from previous courses.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Reading: Units, Dimensions, and Scaling Arguments The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

1.1.3 Vectors   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Scalars and Vectors” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Scalars and Vectors” (PDF)

Instructions: Please click on the link above and read the entire article, which provides a concise reference for vector addition and resolution.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here(HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Lecture: Vectors The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

1.1.4 2D Vectors   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Vector Components 2-D” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Vector Components 2-D” (PDF)

Instructions: Please click on the link above and read the entire article, which provides a reference for the representation of vectors in an orthogonal basis.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.1.5 3D Vectors   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Vector Components 3-D” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Vector Components 3-D” (PDF)

Instructions: Please click on the link above and read the entire article, which provides a reference for representation of vectors in three dimensions.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Activity: The Saylor Foundation’s “Vectors: Review and Self Study” Link: The Saylor Foundation’s “Vectors: Review and Self Study” (PDF)

Instructions: Please read the linked document in its entirety. Follow along with the example problems in detail.  You may need to refer back to these examples later in your study.

1.2 Force, Moments, and Couples   Note: Now that you understand vectors and forces, you are ready for moment analysis.  Moments, also known as “couples” in some situations, are force systems that cause an object to rotate.  For example, consider the way in which you use a wrench to loosen a nut.  The force you exert on the end of a wrench creates a moment.  When performing structural analysis, we will look at the sums of both the forces and the moments acting on an object.

1.2.1 Force   - Reading: The Saylor Foundation's “Forces and Moments” Link: The Saylor Foundation's “Forces and Movements” (PDF)

Instructions: Please click on the link above and read the entire article.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````

1.2.2 Equilibrium   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Static Equilibrium for a Particle” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Static Equilibrium for a Particle” (PDF)

Instructions: Please read the entire webpage which introduces the equations for  static equilibrium.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder.

• Lecture: Static Equilibrium, Stability, Rope Walker The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

1.2.3 Moment of a Force and Torque   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Moment of a Force: Part 1” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Moment of a Force: Part 1”  (PDF)

Instructions: Please click on the link above and read the entire webpage.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Lecture: Torque The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

1.2.4 Moment of a Force-Cross Product   - Activity: The Saylor Foundation’s “Moments and Cross Products: Practice Calculations” Link: The Saylor Foundation’s “Moments and Cross Products: Practice Calculations” (PDF)

Instructions:  Please click on the link above and work through all problems in the document and compare your solutions with those provided in the document. You may wish to review basic vector operations first.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````
• Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Moment of a Force: Part 2”

Link: University of Nebraska atLincoln: Mehrdad Negahban’s “Moment of a Force: Part 2”  (PDF)

Instructions: Please click on the link above and read the entire article.  You may wish to practice computing the moments of forces.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban, and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.2.5 Equivalent of Force-Couple System   - Reading: The Saylor Foundation’s “Resultant of Systems” Link: The Saylor Foundation’s “Resultant of Systems” (PDF)

Instructions:  Please click on the link above and read the entire article. You may wish to review basic vector operations first.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````
• Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equivalent of Force-Couple System: Part 1” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equivalent of Force-Couple System: Part 1” (PDF)

Instructions: Please click on the link above and read the entire article. It introduces the calculations of reducing mulitiple forces to equivalents for ease of further calculation.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban, and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.2.6 Equivalent of Force-Couple System with Distributed Loads   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equivalent of Force-Couple System: Distributed Loads” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equivalent of Force-Couple System: Distributed Loads” (PDF)

`````` Instructions: Please click on the link above and read the entire
article.  The reading introduces how equivalent of multiple force
couple systems are computed for distributed loads.

Terms of Use: This resource has been reposted by the kind
permission of Dr. Mehrdad Negahban, and can be viewed in its
original
form [here](http://emweb.unl.edu/negahban/em223/note10/note10.htm) (HTML).  Please
note that this material is under copyright and may not be reproduced
in any capacity without the explicit permission of the copyright
holder.
``````

1.3 Analysis of Rigid Bodies   1.3.1 Equilibrium for Rigid Bodies   - Reading: The Saylor Foundation’s “Equilibrium Conditions” Link: The Saylor Foundation’s “Equilibrium Conditions” (PDF)

Instructions:  Please click on the link above and read the entire article.

`````` <span
style="color: rgb(51, 51, 51); font-family: sans-serif; line-height: 16.787878036499023px; ">Terms
style="color: rgb(51, 51, 51); font-family: sans-serif; line-height: 16.787878036499023px; ">.
It is attributed to The Saylor Foundation.</span>
``````
• Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equilibrium for Rigid Bodies” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Equilibrium for Rigid Bodies” (PDF)

Instructions: Please click on the link above and read the entire article.  This reading introduces the equations involved in the equilibrium of rigid bodies in mechanics.

Terms of Use: The linked material above has been reposted by the kind permission of Dr. M. Negahban, and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.3.2 Trusses   - Reading: The Saylor Foundation’s “Trusses” Link: The Saylor Foundation’s “Trusses” (PDF)

Instructions: Please click on the link above and read the entire article. Follow along with the example problem in detail.  You may need to refer back to this example later in your study.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````
• Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “The Analysis of Trusses” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “The Analysis of Trusses” (PDF)

Instructions: Please click on the link above and read the entire article.  The lecture will introduce you to mechanics involved in the design and analysis of trusses.

Terms of Use: This resource has been reposted by the kind permission of Mehrdad Negahban, and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Mobile App: Autodesk Inc.’s *Autodesk ForceEffect* Link: Autodesk Inc.’s Autodesk ForceEffect (iOS App) or Autodesk Inc.’s Autodesk ForceEffect (Android App)

Instructions: Download the appropriate app for your mobile device. There are four tutorials in the app: “ForceEffect and the free body diagram,” “Why and when to use ForceEffect,” “The ForceEffect User Interface,” and “ForceEffect and how to create a diagram.” View these tutorials, and refer to them as needed as you use the app.

Downloading this app and watching the tutorials will take you approximately 15 minutes to complete.

• Activity: The Saylor Foundation’s “Automated Truss Calculations” Link: The Saylor Foundation’s “Automated Truss Calculations” (PDF)

Instructions: Please click on the link above and work through the three exercises. Compare your work with the example solutions provided here for “Problem 1” and “Problem 2”.

Completing these activites will take you approximately 60 minutes to complete.

Terms of Use: These exercises are licensed under a Creative Commons Attribution 3.0 License. They are attributed to the Saylor Foundation.

1.3.3 Machines and Frames   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Frames and Machines” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Frames and Machines” (PDF)

Instructions: Please read the entire webpage.  The lecture will introduce you to mechanics involved in the design and analysis of frames and machines. You should revisit section 1.3.1 after reading this material.

Terms of Use: This resource has been reposted by the kind permission of Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.3.4 Friction   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Dry Friction” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Dry Friction” (PDF)

Instructions: Please click on the link above and read the entire article.  It will introduce you to mechanics involved in the design and analysis of rigid bodies involving friction.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

• Lecture: Frictional Forces The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

1.3.5 Internal Forces   - Reading: The Saylor Foundation’s “Internal Forces” Link: The Saylor Foundation’s “Internal Forces” (PDF)

Instructions:  Please click on the link above and read the entire article.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````
• Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Internal Forces” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Internal Forces” (PDF)

Instructions: Please click on the link above and read the entire article.  It introduces the role of internal forces in mechanics.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban, and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.3.6 Wedges and Screws   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Wedges and Screws” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Wedges and Screws” (PDF)

Instructions: Please click on the link above and read the entire article, which introduces mechanics involving wedges and screws.

`````` Terms of Use: This resource has been reposted by the kind
permission of Dr. Mehrdad Negahban and can be viewed in its original
form [here](http://emweb.unl.edu/negahban/em223/note16/note16.htm) (HTML).  Please
note that this material is under copyright and may not be reproduced
in any capacity without the explicit permission of the copyright
holder.
``````

1.3.7 Belts   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Belts” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Belts” (HTML)

Instructions: Please click on the link above and read the entire article, which introduces mechanics involving belts.

Terms of Use: This resource has been reposted by the kind permission of Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

1.3.8 Review Activities   - Activity: The Saylor Foundation’s “Subunit 1.3.8 - Review Activities” Link: The Saylor Foundation’s “Subunit 1.3.8 - Review Activities” (PDF)

Instructions: Please click on the link above and complete both assignments listed.  At this stage, feel free to talk with others and consult reference materials earlier in the unit as you work to complete the assignments.  You may also consider discussing these assignments with your classmates on the ME102 Discussion Forum.  You will need to create a free account to access the discussion forum, which you may do here if you do not already have one.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````

The Saylor Foundation’s “Unit 1 Assessment”   - Assessment: The Saylor Foundation’s “Unit 1 Assessment” Link: The Saylor Foundation’s “Unit 1 Assessment”

Instructions: Please click on the link above and complete the assessment.

`````` You must be logged into your Saylor Foundation School account in
order to access this exam.  If you do not yet have an account, you
will be able to create one, free of charge, after clicking the