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Scalar & Vector Quantities

Scalar & Vector Quantities. SCALAR QUANTITIES. •Described by a single number and unit of measurement. •Gives the magnitude (size) Examples Mass = 20 g Time = 20.0 s Temperature = 20 o C Speed = 20 m/s. VECTOR QUANTITIES. •Arrows are used •Described by a single number and a

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Scalar & Vector Quantities

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  1. Scalar & Vector Quantities

  2. SCALAR QUANTITIES •Described by a single number and unit of measurement. •Gives the magnitude (size) Examples Mass = 20 g Time = 20.0 s Temperature = 20oC Speed = 20 m/s

  3. VECTOR QUANTITIES •Arrows are used •Described by a single number and a unit of measurement (scalar) •Indicated direction. (head of arrow) Examples 30 m/s, East 30 m/s, N of E

  4. DETERMINING DIRECTION A B N of E N of W S of E C D S of W

  5. ADDITION OF COLLINEAR VECTORS Resultant vector represent the total of two or more vectors drawn from the tail of the lst vector to the head of the last vector

  6. VECTORS ACTING IN THE SAME DIRECTION Connect them head-to-tail and add Always indicate the direction of the the resultant 10 km 10 km R = 20 km, 0o E

  7. VECTORS ACTING IN OPPOSITE DIRECTIONS Connect them tail to tail Subtract 20 km 10 km R = 10 km, 0o, W

  8. VECTORS ACTING AT ARIGHT ANGLE TO EACH OTHER •Connect head-to-tail •Draw resultant from the tail of the lst vector to the head of the second vector. •Determine resultant using pythagorean theorem •Determine angular direction by using the tan function

  9. Pythagorean Theorem • C2 = a2 + b2 • C = hypotenuse • A & B are sides

  10. 20 km 10 km 10 km or 20 km 20 km 10 km R2 = (10 km)2 + (20 km)2 R = 22 km = 20 km

  11. Determine angle  makes with the X-axis. Use the correct number of significant figures. Tan  = Y X = 20 km 10km = 2  = 63o = 60o

  12. Trig of the Right Triangle hypotenuse Opposite side Ө Adjacent side

  13. SOH Sin Ө = opposite side hypotenuse

  14. CAH Cos Ө = adjacent side hypotenuse

  15. TOA • Tan Ө = opposite side adjacent side

  16. NON-COLLINEAR VECTORS Draw vectors on x-y axis Determine the X & Y components of each vector a. X-component = use Cos function b. Y-component = use Sin function c. Theta is 0o if vector is located on X-axis d. Theta is 90o if vector is located on Y-axis C. Indicate direction of vectors (+) and (-)

  17. Add X-components Add Y-components Draw vectors representing the sum of the components head-to-tail. Signs (+) and (-) represents the direction of vectors. Draw Resultant Calculate R using Pythagorean Theorem Calculate theta  J. Indicate direction relative to N, E, S or W

  18. EXAMPLE Walk due west for 52 paces, then walk 30.0o North of West for 42 paces, and then walk due north for 25 paces.What are the magnitude and direction of the resultant, R

  19. VECTOR DIAGRAM 25 42 52

  20. TABLE

  21. DETERMINING DIRECTION OF RESULTANT DRAW TRIANGLE USING SUMS OF X- AND Y-COMPONENTS R 46 Paces N of W 88 Paces

  22. VALUE OF RESULTANT Use Pythagorean Theorem R2 = (88 paces)2 + (46 paces)2 R = 99 paces

  23. Angular Direction Use tan function tan  = 46 paces 88 paces Ø = 28o

  24. FINAL ANSWER 99 Paces, 28o, N of W

  25. Units of Measurements MKS: meters (m), Kilogram (kg), second (s) kilometer (km), hour (h) CGS: centimeter (cm), gram (g), second (s) FPS: foot (ft.), pound (lb.), second (s) miles (mi.), hour (h)

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