Scalar and Vector Quantities

1. Chapter 2 Vectors

2. In this chapter, we will discuss the following: the difference between scalar and vector quantities; representing vectors graphically; resultant and equilibrant vectors; and, finding resultant vector

3. Vectors and Scalars

4. Vectors and Scalars

5. Representing Vectors A vector is represented by an arrow. The length of the arrow is proportional to the magnitude of the vector. The tail indicates the starting point. The orientation of the arrowhead indicates the direction. Vectors maybe denoted using a boldface type (i.e. A denotes vector A).

6. Representing Vectors

7. Vector Addition Vector addition is different from the usual addition in arithmetic. The magnitude and direction should be taken into consideration. Only vectors of the same kind can be added or combined.

8. Properties of Vector Addition Commutative : The order of addition does not matter. A + B = B + A Associative : The grouping does not matter in adding 2 or more vectors. (A + B) + C = A + (B + C)

9. Resultant and Equilibrant

10. Finding Resultant Vector Graphical Method or Polygon Method Use a ruler and a protractor. Analytical Method Requires some knowledge in trigonometry.

11. Graphical / Polygon Method Draw 1st vector using a convenient scale. 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. Draw the resultant vector (R) from the initial point (tail) of the 1st vector to the terminal point (head) of the last vector. Measure the resultant vector R using a ruler and a protractor to find its magnitude and direction.

12. Analytical / Component Method

13. Analytical / Component Method

14. Finding Resultant Vector Answer: 950m East

15. Finding Resultant Vector Answer: 300m West

16. Finding Resultant Vector Answers : a. 7km b. 5km, 53.13o N of E

17. Finding Resultant Vector Answer : 6.17cm, 45.85o N of E

18. Solution for Example 4 0o 0 2 40o 1.93 2.30 90o 0 2.5 4.30 4.43 Direction: Magnitude:

19. Finding Resultant Vector Answer : 15.80m, 29.71oN of W

20. Solution for Example 5 50o 3.83 3.21 150o 4 -6.93 180o -10 0 -13.72 7.83 Direction: Magnitude: R = 15.8m θ = 150.290 29.71o N of W

21. TRY THIS!!!