Section 2.4 Addition of a System of Coplanar Forces (page 32)

CARTESIAN VECTOR IN TWO DIMENSIONS (page 1)

Section 2.4 Addition of a System of Coplanar Forces (page 32)

CARTESIAN VECTOR IN TWO DIMENSIONS (page 2)

• Rectangular components of a vector

!F =!Fx+!Fy

!Fx

and

!Fy

are the rectangular components of

!F .

• Cartesian unit vectors

!i is a dimensionless vector of length one

which points along the positive x-axis.

!j is a dimensionless vector of length one

which points along the positive y-axis.

!i and

!j designate the directions of the x and y axes.

• Cartesian vector

Write

!Fx= F

x

!i F

x= F cos!

!Fy= F

y

!j F

y= F sin!

Then

!F = F

x

!i + F

y

!j

= F cos!

!i + F sin!

!j

Section 2.4 Addition of a System of Coplanar Forces (page 33)

RESULTANT OF A SYSTEM OF FORCES:

CARTESIAN VECTOR METHOD (page 1)

• We want to determine the resultant F

!"

R of a system of forces

!F1,!F2,!F3.

That is, we want to determine the magnitude and direction of F

!"

RR where

F

!"

R = !F

!"

Section 2.4 Addition of a System of Coplanar Forces (page 33)

RESULTANT OF A SYSTEM OF FORCES:

CARTESIAN VECTOR METHOD (page 2)

• Method: Write

!F1,!F2,!F3 as Cartesian vectors:

!F1= F

1x

!i + F

1y

!j

!F2= F

2x

!i + F

2y

!j

!F3= F

3x

!i + F

3y

!j

Section 2.4 Addition of a System of Coplanar Forces (page 33)

RESULTANT OF A SYSTEM OF FORCES:

CARTESIAN VECTOR METHOD (page 3)

• Resultant F

!"

R = !F

!"

= FRx

!i + F

Ry

!j

FRx

= !Fx= F

1x+ F

2x+ F

3x

FRy= !F

y= F

1y+ F

2y+ F

3y

Magnitude FR= F

2

Rx + F2

Ry

Direction ! = tan"1FRy

FRx

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