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Understanding Vector Components and Calculation Practice

Learn about vertical and horizontal components of vectors and practice calculating them for different forces. Illustrated examples provided.

robertjford
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Understanding Vector Components and Calculation Practice

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  1. Physics Review Vectors

  2. Component Vectors The word “component” means a “part” of a system. When dealing with vectors, the word “components” refersto the vector parts that “add up” or constitute a vector. Note well that while any vector may have many component vectors, there are two “special” vectors that that when addedtogether result in the given vector. Horizontal Component The horizontal component of a given vector is that part which acts along the horizontal axis (x-axis). FH FH Vertical ComponentThe vertical component of a given vector is that part which acts along the vertical axis (y-axis). FV FV Click

  3. Together, the horizontal and vertical components make up a vector. REMEMBERAll vectors can berepresented by theirHorizontal and Verticalcomponents. Vertical axis Vector Vertical component Horizontal axis Horizontal component Vector = Horizontal component + Vertical component Click

  4. Remember “North” is “Up” “South” is “Down” “East” is “Right” “West” is “Left” N(Up) (Left)W E(Right) S(Down) Next

  5. PRACTICE

  6. 2.1 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor each of the given forces: 200 N [West] N (or Up) W (or Left) E (or Right) S (or Down) 200 N [West] 0 FH = ____________________ FV = ____________________ Click

  7. N W E S 2.2 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor each of the given forces: 500 N [North] 0 500 N [North] FH = ____________________ FV = ____________________ Click

  8. FH = 500 N Cos 45o = 354 N FV = 500 N Sin 45o = 354 N 2.3 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: REMINDER Southeast means at 45o between South and East. 500 N [Southeast] NOTERound off your answers to the nearest whole number. 45o 354 N [East] 354 N [South] FH = ____________________ FV = ____________________ Click

  9. FV = 400 N Sin 25o =169 N FH = 400 N Cos 25o = 363 N 2.4 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: 400 N [25o from the horizontal] 400 N 25o 363 N [East] 169 N [North] FH = ____________________ FV = ____________________ Click

  10. This means “from the South , 60o East” FH = 290 N Sin 60o = 251 N FV = 290 N Cos 60o = 145 N 2.5 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: 290 N [S 60o E] 290 N 60o 251 N [East] 145 N [South] FH = ____________________ FV = ____________________ Click

  11. This means “from the West , 60o South” FH = 600 N Cos 60o = 300 N FV = 600 N Sin 60o = 520 N 2.6 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: 600 N [W 60o S] 60o 600 N 300 N [West] 520 N [South] FH = ____________________ FV = ____________________ Click

  12. FV = 400 N Sin 35o = 229 N This means “from the East , 35o North” FH = 400 N Cos 35o = 328 N 2.7 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: 400 N [E 35o N] 400 N 35o 328 N [East] 229 N [North] FH = ____________________ FV = ____________________ Click

  13. This means “from the South , 20o West” FH = 500 N Sin 20o = 171 N FV = 500 N Cos 20o = 470 N 2.8 Vectors Slide: Calculate and sketch the horizontal and vertical componentsfor the following force: 500 N [S 20o W] 500 N 20o 171 N [West] 470 N [South] FH = ____________________ FV = ____________________ Click

  14. 2.9 Vectors Slide: The diagram on the right illustrates fourforces acting on a cart that is free tomove in any direction. Which of the following forces willplace the system in equilibrium? A) 3.00 N at 0o from horizontal B) 12.2 N at 180o from horizontal C) 12.2 N at 0o from horizontal D) 3.00 N at 180o from horizontal E) 22.4 N at 0o from horizontal 180o FE FR Click Click

  15. 2.10 Vectors Slide: Click

  16. 2.11 Vectors Slide: An electron is subjected to a magnetic force of 2.6 x 10‑24 N actinghorizontally and an electric force of 3.0 x 10‑24 N acting vertically. Determine the equilibrant force. Click

  17. 2.12 Vectors Slide: An object is suspended by a cord which is 5.2 m long. As shown in the diagram, the horizontal force, F, is 75 N East. Calculatethe mass of the object. A) 18 kg B) 1.8 kg C) 39 kg D) 28 kg E) 46.5 kg Finally we find the mass Next we find the weight First we find the angle A 11o FH = 75 N 11o 386 N w Click Click Click Click Click

  18. 2.13 Vectors Slide: When a weight is hung in the middle of a 20 m long wire, the wire sags 3 m. If the tension in the wire is 270 N, determine the weight. A) 155 N B) 102 N C) 78 N D) 48 N E) 26 N T = 270 N w/2 w/2 73.3o 10 m T = 270 N 3 m 73.3o Step-3 Find the weight. w With reference to the shaded triangle: Step-1 Draw all the forces acting on the system. Step-2 Find the angle. Click Click Click Click

  19. The End … and good luck!

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