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Vectors: Resolution and Addition

Vectors: Resolution and Addition. Vectors: The Basics. Vector: has both magnitude and direction Examples: displacement, velocity, acceleration Scalar: has magnitude but no direction Examples: distance, speed, time, mass Drawing Vectors represented by arrows length represents magnitude

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Vectors: Resolution and Addition

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  1. Vectors:Resolution and Addition

  2. Vectors: The Basics • Vector: has both magnitude and direction • Examples: displacement, velocity, acceleration • Scalar: has magnitude but no direction • Examples: distance, speed, time, mass • Drawing Vectors • represented by arrows • length represents magnitude • angle and head of arrow shows direction (angle) • labeled with quantity and/or value v1 = 3 m/s 30

  3. Vector Components • Some vectors point directly along x or y axes, but most do not. • Components • how much in x & y directions • components are still vectors  have direction • 2 component vectors represent original vector Henderson, Tom (n.d.) Vector Components. The Physics Classroom. Retrieved from http://www.physicsclassroom.com/class/vectors/u3l1d.cfm

  4. Vector Resolution: Graphical Method • Sketch projection lines to x & y axis • Draw component vectors along axes Hepburn, Carl Jason. (n.d.) Scalars and Vectors. Splung.com. Retrieved from http://www.splung.com/content/sid/1/page/vectors

  5. Vector Resolution: Algebraic Method • Visualize vector and its components as a right triangle. • Use SOH CAH TOA to calculate components Fullerton, Daniel B. (n.d.) Regents Physics Math Review. APlusPhysics.com. Retrieved from http://www.aplusphysics.com/courses/regents/mathreview/regents_math_review.html#

  6. Vector Resolution: An Example • You might want to click here for a video review of trigonometry and listen to this song about SOH CAH TOA. If you feel comfortable with trigonometry, just click on the link below.If the links do not work, copy & paste into your browser. • Watch this video demonstration of vector resolution done graphically and algebraically. Khan, Salman. (n.d.) Basic Trigonometry. Video posted to http://www.khanacademy.org/math/trigonometry/v/basic-trigonometry KDogde314. (2010, March 25). SOH CAH TOA Song. Video posted to http://www.youtube.com/watch?v=8xwA4DHWLk0 dejongescience. (2010, July 11). Basic vector resolution. Video posted to http://www.youtube.com/watch?v=T4tqR4aUh90

  7. Vector Addition • Add vectors to find the net (overall) magnitude and quantity of what is being measured (i.e. displacement, velocity, force). • Resultant: the one vector that represents the sum of two or more vectors • Only vectors of the same quantity and units may be added or subtracted • You can’t add a velocity vector and a displacement vector • You can’t add a velocity in m/s with a velocity in mph

  8. Vector Addition: Graphical Method • Draw 1st vector • Begin tail of 2nd vector at head of 1st vector • Begin tail of 3rd vector at head of 2nd vector • Continue until there are no more vectors • Draw resultant vector from tail of 1st vector to head of last vector. Label resultant. Appendix: Simple Vectors for Preliminary High School Physics. (2007, April 26) Retrieved from the Bored of Studies wiki: http://www.boredofstudies.org/wiki/Appendix_-_Simple_Vectors_for_Preliminary_High_School_Physics

  9. Vectors Can Be Added In Any Order • Vectors can be moved parallel to themselves in a diagram. • Vectors can be added in any order. • Resultant will always be the same. Henderson, Tom (n.d.) Vector Addition: The Order Does NOT Matter. The Physics Classroom. Retrieved from http://www.physicsclassroom.com/mmedia/vectors/ao.cfm

  10. Resultant of Collinear Vectors Same direction: add Opposite directions: subtract

  11. Resultant of Perpendicular Vectors What is the turtle’s resultant displacement from Po to Pf? Vectors: sides of a right triangle Resultant: hypotenuse How to solve?: Pythagorean theorem Inverse tangent to find angle Resultant: 5 cm @ 53.1 N of E

  12. Vector Addition: Examples • Let’s make sure you get it.Watch this video demonstration of the addition of 2 perpendicular vectors. • But, wait!!!What do we do when our vectors are not perpendicular or there are 3 or more vectors? • Watch this video demonstration to find out! dejongescience. (2010, July 11). Vector addition at right angles. Video posted to http://www.youtube.com/watch?feature=endscreen&v=i2S9iRLXVqw&NR=1 PhunScience. (2011, August 1). Adding Vectors: How to Find the Resultant of Three or More Vectors. Video posted to http://www.youtube.com/watch?v=g_TnqKX5ybY&feature=related

  13. Use the “vector components” method by first resolving all vectors into their components. Magnitude: Find the sum of all x-components and all y-components. These are the component s of the resultant vector. Use Pythagorean Theorem to find resultant from components. Use Inverse tangent to find precise direction of resultant. Summary: Vector Addition of Non-Perpendicular Vectors (or 3 or more vectors)

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