Module 1 - Fundamentals
Chapter 2: Force Vectors
Chapter 2 Overview
In Chapter 2, we will explore force vectors with the following objectives:
- Demonstrate how to add forces and break them into components using the Parallelogram Law.
- Represent force and position in Cartesian vector form, and explain how to calculate a vector's magnitude and direction.
- Introduce the dot product and use it to determine the angle between two vectors or the projection of one vector onto another.
Lecture 3 Tasks
Today, we’ll explore the differences between scalars and vectors, emphasizing how vectors include both magnitude and direction, which scalars only have magnitude. We will also cover vector representation in 1D, 2D, and 3D using Cartesian coordinates and unit vectors to simplify analysis and computation.
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Read
- Sections 2.1, 2.4-2.5, and 2.7-2.8 of Engineering Mechanics: Statics by R.C. Hibbeler to learn more about vectors in 1, 2, and 3 dimensions.
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Watch
- What is a vector? - David Huynh: Watch this TedEd video to learn more about why vectors are so useful. (We won't discuss tensors in this class, which are mentioned towards the end of the video.)
- Unit vectors | Vectors | Precalculus | Khan Academy: Watch for a review of unit vectors.
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Practice
- Try the Practice In-Class Quiz 1
- Afterwards, see how you did by reviewing the Practice In-Class Quiz 1 Solutions
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Complete
- Lecture 3 Quiz: due Thursday, January 16 at 11:59 PM on D2L.
Lecture 3 Resources
Lecture 4 Tasks
In class, we'll discuss vector addition and dot products. Then, we'll take our first in-class quiz. Here are some things you can do to prepare:
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Read
- Section 2.2-2.3, 2.6 and 2.9 of Engineering Mechanics: Statics by R.C. Hibbeler to learn more about adding vectors and dot products.
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Watch
- How Do You Draw a Force Diagram? - Watch this animated video to learn about combining force vectors in 1 and 2 dimensions to find resultant forces.
- Vectors [Science of NFL Football] - To prepare for the upcoming Super Bowl, learn about how vector addition helps quarterbacks complete passes.
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Practice
- See the homework problems for week 2 posted under Discussions in D2L (Problems 2-3, 2-7, 2-18, 2-22, 2-31, 2-32, 2-37, 2-42, 2-43, 2-52, 2-53, 2-54, 2-80, 2-96, 2-97, 2-98, 2-106, 2-113, 2-115, 2-129, and 2-130 in Engineering Mechanics: Statics by R.C. Hibbeler). Remember that if you ask/answer enough questions in the Discussion forums you can get two in-class quiz grades dropped!
Lecture 4 Notes
- Lecture 4 Notes[pdf]