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Resolving A Vector Into Its Components

Resolving A Vector Into Its Components. Created by Dick Heckathorn 26 June 2K+1 for C.V.C.A. Honors Physics. Introduction.

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Resolving A Vector Into Its Components

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  1. Resolving A Vector Into Its Components Created by Dick Heckathorn 26 June 2K+1 for C.V.C.A. Honors Physics

  2. Introduction We have learned how to add vectors. In so doing we have taken two or more vectors and found their resultant, which is a vector that can take the place of the other vectors.

  3. Introduction 2 Now, we will learn how to, given a vector, resolve it into two component vectors which will be equivalent to the vector from which the components were determined.

  4. What we will need We will need to be given a vector. The vector we will use as an example will be:

  5. Drawing the vector 39o E

  6. What we will need? We will need to be given the direction of the two components which we will be asked to find. In this situation, we will find the horizontal and the vertical components.

  7. Drawing the Component Directions Vertical 39o Horizontal

  8. Next We will find the magnitude in each direction. How? We will construct a parallelogram with the diagonal being the vector to be resolved into its components.

  9. Completing the Parallelogram Vertical 39o Horizontal

  10. Continuing Next we will draw in the component vectors which we have been asked to find.

  11. Drawing the Components Vertical 39o Horizontal

  12. Identifying the Sides Vertical hyp opp 39o Horizontal adj

  13. What Trig Function will give the Horizontal Component? Vertical hyp opp 39o Horizontal adj

  14. Finding The Horizontal Component

  15. Finding The Vertical Component Vertical hyp opp 39o Horizontal adj

  16. Finding The Vertical Component

  17. Here Is Another Vector Block on Frictionless Incline Gravity Is Acting 22o

  18. Identify Component Directions 22o

  19. Vectors at Right Angles Means? This means that each component vector will be independent of the other.

  20. Completing the Parallelogram 22o

  21. Draw Component Vectors Component along plane of ramp 22o Component Perpendicular to ramp

  22. All that is left to do is to find the length of the two components by whatever method you choose. 22o

  23. Find the Angle   22o The correct answer is 22 degrees?

  24. Next Find the Magnitude of the Two Components Component along plane of ramp 22o Component Perpendicular to ramp

  25. Here Is an Acceleration Vector

  26. With Components Directions Identified 85o 29o

  27. With Parallelogram Completed 85o 29o

  28. With Component Vectors Drawn 85o 29o

  29. All that is left to do is to find the length of the two components. 85o 29o

  30. Determine the Angles in the Lower Triangle A 85o C 66o 85o 29o

  31. Determine Magnitude of ‘a’ and ‘b’ A 85o b c 66o 85o C 29o a B

  32. A b 85o c 66o 85o 29o C a B

  33. And Now…... Download program ‘vcomp’ to your TI-83+ and resolve any vector into their right-angle components.

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