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Addition of Vectors

Addition of Vectors. N. Imagine that you have a map that leads you to a buried treasure. This map has instructions such as 15 paces west northwest of the skull. The 15 paces is a distance and west northwest is a direction.

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Addition of Vectors

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  1. Addition of Vectors

  2. N • Imagine that you have a map that leads you to a buried treasure. • This map has instructions such as 15 paces west northwest of the skull. • The 15 paces is a distance and west northwest is a direction.

  3. Quantities that are described by a magnitude (such as the distance on the previous slide) and a direction are called vectors. • Those quantities that have no direction are called scalars.

  4. Examples of scalars in physics are mass time distance speed work energy • Examples of vectors in physics are displacement velocity acceleration force momentum angular momentum

  5. The math associated with scalars is familiar to everyone. • The math associated with vectors is more involved. • Today you will explore the graphical addition of vectors.

  6. Let’s use a treasure map again as an example of the addition of vectors. • Let’s imagine the instructions tell you to go 4 miles east then 3 miles north.

  7. 5 miles 3 miles 36.90 4 miles

  8. In this case you could have gone 3 miles north first and then 4 miles east next and still end up at the same location. • Your final position is 5 miles at 36.90 north of east. • It would have saved time if that had been the one distance and one direction traveled in the first place.

  9. We say that the 5 miles at 36.90 north of east is the vector sum of the 4 miles east vector and the 3 miles north vector. • The order of the addition does not matter. • Examples of addition of vectors follows. The method used is the head-to-tail method. • You must know how to do these for your lab exams.

  10. Head-to-Tail Method of Addition of Two Vectors

  11. Head-to-Tail Method of Addition of Three Vectors

  12. You will need to use a scale when you graph your vectors. For example, you might set 10 cm to represent 100 grams.

  13. How to ConstructTwo Perpendicular Lines(With a Protractor)to form aSet of Coordinate Axes

  14. N E W S

  15. How to Constructa Second Set of Coordinate Axes Parallel toan Initial Set of Coordinate Axes

  16. Mark the angle for the vector.

  17. Remember the angle marked.

  18. N E W S Resultant

  19. N 900 1800 00 E W 2700 S Resultant Equilibrant

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