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 Method Jerome 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 75° 20°

Analytical vector addition 75° 20°

cosθ = a/h a = h cosθ therefore a = h cosθ h = 3km a = 3 cos20 ° a = 2.82km sinθ = o/h o = h sinθ therefore o = h sinθ o = 3 sin20° o = 1.03km

Analytical vector addition 75° 20° Vector addition table VectormagAngle X Compt Y Compt Rest

Analytical vector addition Vector addition table VectormagAngle X Compt Y Compt Rest R 2 = x 2 + y 2 R 2 = R = 4.46 km 4.46 R

Analytical vector addition Vector addition table VectormagAngle X Compt Y Compt Rest tanθ = opp/adj θ = 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 displacement is 10 meters at 36º south of east = °

Vector Addition