Chapter 2: Forces in a Plane, Vectors, resultants, equilibrium, FBD's, Newton's 1st law

Flipped Classroom

What's harder -
Watching someone else do something?
Or doing it yourself?
.

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Which part would you rather do in class 
- the watching part (lecture)?
- or the doing part (solving problems)?



Homework:
We'll be using the lectures by Yiheng Wang, now teaching ENGR at LSC Cy-Fair, throughout the semester.  These are a great resource, are very clear and concise, so bookmark her page!  Through watching lectures at home, we will have more time to work through examples problems and do HW in class.    

Lec 4: Vector operation 3:38
Lec 5: Cartesian vectors and operations

Lec 6: Position and Force vector
Lec 7: Dot Product

Lec 8: FBD's
Lec 9: Particle Equilibrium

Another statics resource:
https://ecourses.ou.edu/cgi-bin/display_lectures.cgi?course=st&status=disp_ch

Read Chapter 2 in book

To motivate you to do your homework...

• Beginning of class 10 minute study comprehension quiz.

Come to class prepared to work through example problems!  Don't forget to bring your calculator and your textbook!

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2.1-2.3: Vocabulary~~~~~~~~~~~~~~~~~~~~~~~

 

resultant force

•  replacing multiple forces acting on a particle with a single equivalent force
• Make a parallelogram, 
• resultant = diagonal of parallelogram

note: the magnitude of the vector
P + Q is NOT equal to the sum of the magnitudes o P+Q. 

equilibrium

Summation of forces acting on a particle is 0.  State of rest.

particle

Size & shape insignificant, all forces assumed to be applied at a single point.



force

Vector quantity
action of one body on another; characterized by:

• point of application
• magnitude 
• SI units: 1,000N = 1 kN
• U.S. customary: 1,000 lb = 1 kip
  
• Direction of Force
• line of action  - line force acts along
•  sense: arrow pointing which way it is acting; ↑? ↓?

Scalar 

• has magnitude but not direction.   
• Examples:  
• mass, 
• volume, 
• temperature

Vector 

• has magnitude and direction
• add according to the parallelogram law.
• Examples:   
• displacements
• velocities
• accelerations

Vector classifications

• Fixed or bound vectors 

 well defined points of application that cannot be changed without affecting an  analysis.

• Free vectors 

may be freely moved in space without changing their effect on an analysis.

• Sliding vectors 

may be applied anywhere along their line of action without affecting an analysis.

2.4 Addition of vectors~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Trapezoid rule for vector addition

Triangle rule for vector addition
 - Just draw half of the parallelogram
- arrange vectors head to tail

Vector addition is commutative
 

Vector subtraction 

     → Just change which way the arrow points ←

 

Sum of three or more vectors


Add two together, and then add on the third etc.
 
P + Q + S = (P + Q) + S


 

It doesn't matter what order you add them

 
Product of a Scalar and a Vector

•  Keep the same line of action

• Change the magnitude

concurrent forces
all forces pass through a common point

Resultant of concurrent forces:

Replace multiple forces with single force,
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R → same effect as S+P+Q on "A"

Resolution of a force into components

Describe force in terms of x, y, z

Trig Review~~~~~~~~~~~~~~~~~~~~~~~~~~.
 Law of cosines

Law of sines

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Group Exercise:

2.16 hint - do not assume that R is perfectly horizontal!!

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2.7
Rectangular Components of a Force: Unit Vectors
rectangular vector components

 



..
unit vectors

scalar components Fx and Fy

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2.8 Addition of Forces by Summing Components

Trig Review

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Class Exercise

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HW2:
2.6, 2.15, 2.30, 2.33,

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2.9 Equilibrium of a Particle
equilibrium
resultant of all forces acting on a particle is zero
Newton’s First Law
If the resultant force on a particle is zero, the particle will remain at rest or will continue at constant speed in a straight line

2.11
Free-Body Diagrams

Space Diagram

 A sketch or picture of the problem



Free Body Diagram FBD
sketch showing the forces on a selected particle

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class exercise:

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2.12 Expressing a Vector in 3-D Space

 Draw a box to better visualize forces

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see pg 47 in your book

See example problem 2.7 in your book - pg51

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HW#3:
2.46, 2.51, 2.72, 2.89  

2.15 Equilibrium of a Particle in Space

ΣFx = 0  
ΣFy = 0
ΣFz = 0

Study sample problem 2.9 in book

Class Problems:
2.103
2.108

HW: 2.104, 2.107