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Physics Chapter 6A
Vector Addition: Graphical Method
Vectors
• Vectors indicate magnitude and direction• Vectors can be represented by arrow-
tipped line segment– Length of line indicate magnitude– Arrow points in direction of vector
• Sum of any two vectors can be found graphically– Generally, add the vectors tip to tail– Sum is called the resultant
Vector Addition: Parallelogram MethodJerome walks 4 km north, and 8 km east. What is his displacement?
science.andersonscience.net/notes/
Graphical: Tip to Tail Method
Jerome walks 4 km north, and 8 km east. What is his displacement?
Graphical Vector Addition:Parallelogram Method
Tip to Tail Method
Analytical vector addition
2km @ 75°
3km @ 20°
Analytical vector addition
2km @ 75°
3km @ 20°
3km @ 20°
cosθ = a/htherefore a = h cosa = h cosθθ
h = 3km
a = 3 cos20a = 3 cos20°°
a = 2.82kma = 2.82km
sinθ = o/htherefore o = h sino = h sinθθ
o = 3 sin20°o = 3 sin20°
o = 1.03kmo = 1.03km
Analytical vector addition
2km @ 75°
3km @ 20°
Vector addition table Vector mag AngleX
Comp’tY
Comp’t
1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
Analytical vector addition
Vector addition table Vector mag AngleX
Comp’tY
Comp’t
1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
R2 = x2 + y2
R2 = 3.342 + 2.962
R = 4.46 km
4.46
R
Analytical vector addition
Vector addition table Vector mag AngleX
Comp’tY
Comp’t
1 3 20 2.822.82 1.03
2 2 75
Res’t
.52.52 1.93
3.343.34 2.96
tanθ = opp/adjθ = tan-1(y/x)θ = tan-1(2.96/3.34)θ = 41.5˚ 4.46
R
41.5˚
Forces
• Forces are vectors– Because acceleration has direction!
• Concurrent forces act on an object at the same time
• Force in one direction does not affect the force in another
Vector Addition
6 meters
8 meters
10 meters
The distance traveled is 14 meters and the displacementis 10 meters at 36º south of east.
62+82=102
6386
tan1
36°
Vector Addition