1.2 Vectors in Two Dimensions Defining Vector Components Any vector can be resolved into endless...
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![Page 1: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/1.jpg)
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.
![Page 2: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/2.jpg)
1.2 Vectors in Two Dimensions
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.
![Page 3: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/3.jpg)
1.2 Vectors in Two Dimensions
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
![Page 4: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/4.jpg)
1.2 Vectors in Two Dimensions
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
![Page 5: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/5.jpg)
1.2 Vectors in Two Dimensions
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.
![Page 6: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/6.jpg)
1.2 Vectors in Two Dimensions
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
![Page 7: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/7.jpg)
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
![Page 8: 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.](https://reader036.fdocuments.in/reader036/viewer/2022082909/5a4d1b6e7f8b9ab0599b4abc/html5/thumbnails/8.jpg)
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
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1.2 Vectors in Two Dimensions
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
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1.2 Vectors in Two Dimensions
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