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Vector Problems in 3- Dimensions

Vector Problems in 3- Dimensions. For example: A statue is being moved to the top of a building. One person is pulling on the statue with a force of 600 N [E]. A second person is pulling on the statue with a force of 500 N [N]. A crane lifts upward with a force of 1500 N.

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Vector Problems in 3- Dimensions

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  1. Vector Problemsin 3- Dimensions

  2. For example:A statue is being moved to the top of a building. One person is pulling on the statue with a force of 600 N [E].

  3. A second person is pulling on the statue with a force of 500 N [N].

  4. A crane lifts upward with a force of 1500 N

  5. We now have three vectors. We must model this type of problem using a box.

  6. The resultant of the North and East vectors lies diagonally across the bottom of the box.

  7. We can calculate the magnitude of this vector using Pythagorean theorem.

  8. The final resultant is then located from the bottom left corner to the top right corner OR diagonally through the center of the box.

  9. We can calculate the magnitude and direction of this final vector.

  10. Magnitude Direction

  11. Example #2 A crate is being lifted onto a cargo ship to be transported to Japan. A crane lifts upward with a force of 2500 N. One worker is pulling on rope with a force of 700 N [N]. A second worker is pulling on a rope with a force of 900 N [E]. Draw a 3-D box to model this problem.

  12. Example #2 Now, draw in the resultant for the North and East vectors.

  13. Example #2 Calculate the magnitude of this resultant.

  14. Calculate the magnitude and direction of the final resultant

  15. Magnitude Direction

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