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# Chapter 2

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Scalar and Vector Quantities

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### Chapter 2

1. 1. Chapter 2<br />Vectors<br />
2. 2. In this chapter, we will discuss the following:<br />the difference between scalar and vector quantities;<br />representing vectors graphically;<br />resultant and equilibrant vectors; and,<br />finding resultant vector<br />
3. 3. Vectors and Scalars<br />
4. 4. Vectors and Scalars<br />
5. 5. Representing Vectors<br />A vector is represented by an arrow.<br />The length of the arrow is proportional to the magnitude of the vector.<br />The tail indicates the starting point.<br />The orientation of the arrowhead indicates the direction.<br />Vectors maybe denoted using a boldface type (i.e. A denotes vector A).<br />
6. 6. Representing Vectors<br />
7. 7. Vector Addition<br />Vector addition is different from the usual addition in arithmetic.<br />The magnitude and direction should be taken into consideration.<br />Only vectors of the same kind can be added or combined. <br />
8. 8. Properties of Vector Addition<br />Commutative : The order of addition does not matter.<br />A + B = B + A<br />Associative : The grouping does not matter in adding 2 or more vectors.<br />(A + B) + C = A + (B + C)<br />
9. 9. Resultant and Equilibrant<br />
10. 10. Finding Resultant Vector<br />Graphical Method or Polygon Method<br />Use a ruler and a protractor.<br />Analytical Method<br />Requires some knowledge in trigonometry.<br />
11. 11. Graphical / Polygon Method<br />Draw 1st vector using a convenient scale.<br />From the terminal point (head) of the 1st vector, draw 2nd vector; from the terminal point (head) of the 2nd vector, draw 3rd vector; and so on, until the last vector.<br />Draw the resultant vector (R) from the initial point (tail) of the 1st vector to the terminal point (head) of the last vector.<br />Measure the resultant vector R using a ruler and a protractor to find its magnitude and direction. <br />
12. 12. Analytical / Component Method<br />
13. 13. Analytical / Component Method<br />
14. 14. Finding Resultant Vector<br />Answer: 950m East<br />
15. 15. Finding Resultant Vector<br />Answer: 300m West<br />
16. 16. Finding Resultant Vector<br />Answers : <br />a. 7km<br />b. 5km, 53.13o N of E<br />
17. 17. Finding Resultant Vector<br />Answer : 6.17cm, 45.85o N of E<br />
18. 18. Solution for Example 4<br />0o<br />0<br />2<br />40o<br />1.93<br />2.30<br />90o<br />0<br />2.5<br />4.30<br />4.43<br />Direction:<br />Magnitude:<br />
19. 19. Finding Resultant Vector<br />Answer : 15.80m, 29.71oN of W<br />
20. 20. Solution for Example 5<br />50o<br />3.83<br />3.21<br />150o<br />4<br />-6.93<br />180o<br />-10<br />0<br />-13.72<br />7.83<br />Direction:<br />Magnitude:<br />R = 15.8m<br />θ = 150.290<br />29.71o N of W<br />
21. 21. TRY THIS!!!<br />