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