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Physics Chapter 6A Vector Addition: Graphical Method

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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

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Vector Addition: Parallelogram Method Jerome walks 4 km north, and 8 km east. What is his displacement? science.andersonscience.net/notes/

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Graphical: Tip to Tail Method Jerome walks 4 km north, and 8 km east. What is his displacement?

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Graphical Vector Addition: Parallelogram Method

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Tip to Tail Method

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Analytical vector addition 2km @ 75° 3km @ 20°

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Analytical vector addition 2km @ 75° 3km @ 20°

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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

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Analytical vector addition 2km @ 75° 3km @ 20° Vector addition table VectormagAngle X Compt Y Compt 13202.821.03 2275 Rest.521.93 3.342.96

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Analytical vector addition Vector addition table VectormagAngle X Compt Y Compt 13202.821.03 2275 Rest.521.93 3.342.96 R 2 = x 2 + y 2 R 2 = 3.34 2 + 2.96 2 R = 4.46 km 4.46 R

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Analytical vector addition Vector addition table VectormagAngle X Compt Y Compt 13202.821.03 2275 Rest.521.93 3.342.96 tanθ = opp/adj θ = tan -1 (y/x) θ = tan -1 (2.96/3.34) θ = 41.5˚ 4.46 R 41.5˚

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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

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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. 6 2 +8 2 =10 2 36 °

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Vector Addition

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