Download - 1.2 Vectors in Two Dimensions Defining Vector Components Any vector can be resolved into endless number of components vectors. p. 11 DRDR DRDR D1D1 D2D2.

1.2 Vectors in Two Dimensions

Defining Vector Components

Any vector can be resolved into endless number of components vectors.

p. 11

DR DR

D1

D2

D3

D4

The ability to add components vectors is key to solving all sorts of Physics problems.


p. 12

Trigonometric Rations Used in Vector Problems:

CB

A

ѳ

adjacent side

opposite sidehypotenuse Sin ѳ =

Opposite side

hypotenuse=

o

h

Cos ѳ =adjacent side

hypotenuse=

a

h

Tan ѳ =Opposite side

Adjacent side=

o

a

Trigonometric ratios can help you solve vector problems. The rules for adding velocity vectors are the same as those for displacement and force vectors.


p. 13

Resolving Vectors into Vertical and Horizontal Components

FR = 60.0 N

A force of 60.0 N is applied downwards at an angle of 53o below the horizontal.

This vector can be show as the addition of two perpendicular component vectors.

Vertical Component

Horizontal Component

Vertical Component is directed downwards into the ground:

Horizontal Component is directed horizontally to the ground (may be used to move the object along the ground)

Ѳ = 53o


p. 12

Method 1: Solving by Scale Diagram

FR = 60.0 N Ѳ = 53o

A scale is used (1.0 cm = 10.0 N) is drawn over the vectors.

By using this scale the vertical component can be determined to be 36.0 N and the horizontal component is 48.0 N.

Fy= 36.0 N

Fx = 48.0 N

Length = 4.8 cm

Length = 3.6 cm


p. 13 - 14

Method 2: Resolve into Components

FR = 60.0 N Ѳ = 53o

Fy = cos 53o x 60

Cos Ѳ =

adjHyp

Cos 53o = Fy

FR

Fy = 36 N

Fx = sin 53o x 60

Sin Ѳ = Hyp

Sin 53o = Fx

FR

Fx = 48 N

Opp

By using the correct trigonometric functions both the vertical and horizontal components can be determined.


p. 13 - 14

Method 2: Resolve into Components (con’t)

FR = 60.0 N Ѳ = 53o

Fy = 36 N

Fx = 48 N

To check to see if you have the right answer use Pythagorean theorem as follows:

FR2 = Fx

2 + Fy2

FR2 = 482 + 362

FR = 60 N

1.2 Vectors in Two DimensionsMore than One Vector: Using a Vector Diagram

30o

Force of gravity Fg = 36.0 N

String #2

String #1Two strings support an object.

To determine tension in each string a force triangle is made from the three forces.

Fg = 36 N

Tension #2

Tension #130o

p. 14

1.2 Vectors in Two DimensionsMore than One Vector: Using a Vector Diagram

Fg = 36 N

F2 = Tension #2

F1 = Tension #130o

Tan 30o = Fg

F2

F2 = 36.0

Tan 30o

F2 = 20.8 N

Cos 30o = F1

F1 = 36.0

Sin 30o

F1 = 41.6 N

Fg

Each tension can be found by using the correct trigonometric function.

p. 15


A Velocity Vector Problem – Vectors in ActionBoats crossing rivers and Planes travelling against wind are all ideal vector problems.

v r

v b

v p

v p

v w v w

v r

v b

v R

vR 2 = vr2 + vb

2 vR = vp + vw vR = vp - vw

ѳ

tail wind head wind

v Rv R

p. 17 - 20


Key Questions

In this section, you should understand how to solve the following key questions.

Page 16 – 17 – Practice Problem 1.2.1 #1 - 3Page 20 – Practice Problem 1.2.2 #1 – 3P. 21 – 22 1.2 Review Questions # 1 - 9