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CHAPTER 2 FORCE VECTORS (Parallelogram Law (Application in finding…
CHAPTER 2
FORCE VECTORS
Parallelogram Law
Vector addition
Vector substraction
Application in finding
Components of a Force
law of sines
: magnitudes of 2 force components
Addition of a system of coplanar forces
A force is resolved into 2 components along x and y axes =
rectagular components
= scalar notation
:
cos = ke/huyen
sin = doi/huyen :!:
= Cartesian vector notation
Cartesian unit vector i and vector j
Coplanar Force Resultants
1 more item...
:
components of resultant force
2 more items...
Cartesian Vectors with Right-Handed Coordinate System
Rectangular Components of a Vector
5 more items...
Cartesian Unit Vectors :
to solve problems in three
dimensions :red_flag:
Resultant force
law of cosines: magnitude
law of sines: direction
Addition of Several Forces
vector
scalar: a positive or negative number
Multiplication or division of a vector by a scalar will change the
magnitude of the vector
negative scalar = change the sense of vector
Position Vector r
is fixed by 2 points
r
=
r AB
(but NOT rA or rB)
Force Vector Directed Along a Line
:
F
= F.
u
= F (
r
/r) :red_flag:
F (unit of force)
r (unit of length)
FIND THE ANGLE B/W 2 LINES/VECTORS
DOT PRODUCT = multiplying two vectors
A. B
= A.B cosθ :red_flag:** :<3:
IF 0° <= θ<= 180°
:<3:
Laws of Operation
Communicative
Multiplication by a scalar
Distributive law
Cartesian Vector Formulation
OR
therefore
:<3:
