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Vectors

Vectors. A. B. Vector Definition. Any measurement which includes both size and direction 10 m/s isn’t a vector 25 m/s [SW] is a vector. Size and Scale. The resultant of a vector addition can be measured or calculated using scale drawings or Pythagorean Theorem.

walter-gallegos
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Vectors

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  1. Vectors A B

  2. Vector Definition • Any measurement which includes both size and direction • 10 m/s isn’t a vector • 25 m/s [SW] is a vector

  3. Size and Scale • The resultant of a vector addition can be measured or calculated using scale drawings or Pythagorean Theorem

  4. Vector Addition [0º 0r 180º] • Two vectors pointing in the same direction are simply added [direction same] • Two vectors pointing in opposite directions are simply subtracted [direction of larger vector] 5 m [E] 3 m [E] + = 8 m [E] 5 m [E] 3 m [W] + = 2 m [E]

  5. Vector Addition [900] • To add vectors at 90º use a drawing or Pythagoras Theorem • c = (a2 +b2) • = (3.02 +4.02) • = 5.0 cm •  = tan-1(E or W vector/N or S vector) • = tan-1(3.0 / 4.0) • =37o b = 3.0 cm [E] a = 4.0 cm [N] r = 5.0 cm [37o]

  6. Directions • Use the compass rose to the left to calculate the direction of a vector. • Find angle and then transform it according to quadrant. N,0º NW quadrant: 360 - angle NE quadrant: just find angle W,270 º E,90 º SE quadrant: 180 - angle SW quadrant: 180 + angle S,180 º

  7. Example Problem • 5 N [S] + 12 N [W] = • 13 N [SW]

  8. Resolving Vectors • A vector may be “resolved” into 2 right –angled ( orthogonal) components. This technique can be used to add vectors at odd angles together.

  9. 12 m/s [W] =550 9 m/s [S] Example: Resolve 15 m/s [235o] into components along compass axes. • 1. Determine the quadrant • SW • 2. Calculate acute angle • 55o • 3. Calculate magnitude of components • 15 sin55o = 12 m/s [W] • 15 cos55o = 9 m/s [S] 15 m/s [235o]

  10. 55o 4o Example 2: Add 15 m/s [235o] + 35 m/s [3560] by resolving into components along compass axes and then adding components. • 15 m/s [235o] • Acute angle = 55o • 15cos55 = 9 ms-1 [S] • 15sin55 = 12ms-1 [W] • 35 m/s [3560] • Acute angle = 4o • 35cos4 = 35 ms-1[N] • 35sin4 = 2 ms-1 [W] • Resultant • =12 ms-1 [W] + 9 ms-1 [S] + 35 ms-1 [N] + 2 ms-1 [W] • = 14 m/s [W] + 26 m/s [N] • = 30 m/s [NW]

  11. Classwork (8 bonus pts): • 25.5 N [129o] +36.7 N [322o] = • 25.5 N [129o] = 19.8 N [E] + 16.0 N [S] • 36.7 N [322o] = 22.6 N [W] + 28.9 N [N] • 28.9 N [N] + 16.0 N [S] = 12.9 N [N] • 19.8 N [E] + 22.6 N [W] = 2.8 N [W] • 12.9 N [N] + 2.8 N [W] = 13.2 N [N]

  12. Lab # 7 • Your mission is to “fly” around the country (minimum 10 trips) to find a possible site for a SCICORP regional office. • Come home when you’re done! • Click on map to retrieve assignment

  13. Scale • On the map, the scale indicates that 2.02 cm = 500 km • This means that 1 cm = _____ km • 250 km

  14. Lab 7 • Log your flights using the lab 7 word document in the physics assignments folder • Compile the itinerary underneath the map

  15. First Trip: DC to Little Rock • Draw vector from DC to Little Rock. Find size by right clicking on it and choosing “format auto-shape” • 2.55 cm [S] + 5.13 cm [W] • = (2.552 +5.132) • = 5.73 cm • Next, convert to km using scale 1 cm = 250 km • = 5.73*250 = 1 430 km • Calculate direction (use notes) • SW • Now make 10 sequential trips around the country. (Bonus points for >20 trips)

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