2.15

2.15 Equilibrium of a Particle in Space

ΣFx = 0
ΣFy = 0
ΣFz = 0

Study sample problem 2.9 in book

Example youtubes:
https://www.youtube.com/watch?v=vZiCLABe2ok

https://www.youtube.com/watch?v=Li9X2rrWLWU

Consider using Mathematica for this one!

2.12-2.14

3D YouTubes

2.12 Expressing a Vector in 3-D Space

Draw a box to better visualize forces

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2.9-2.11

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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2.7-2.8

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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2.1-2.6

Tip: Open up YouTube, and adjust the speed to get through videos faster!

Homework:

Read Chapter 2 notes:
Watch some youtubes:

Lost of options to choose between:

TxTech:

Randall:

Force vectors 1:

Force Vectors 2:

Force vectors 3:

Particle Equilibrium 1

Particle Equilibrium 2

Particle Equilibrium 3

Yiheng:

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

Lec 6: Position and Force vector
Lec 8: FBD's

Lec 9: Particle Equilibrium

Another statics resource:

Unit-1 Basics & Statics Of Particles (Resolution of Forces) - Engineering Mechanics

https://www.youtube.com/watch?v=4LTXVznGimw

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

If you find a better YouTube, post it in Ch2 for D2L points!

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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 of P+Q, you need to think about directions.

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