Vector Addition Through Analytic Method.
- 1. General Physics 1/2 Science, Technology, Engineering, and Mathematics General Physics 1 Science, Technology, Engineering, and Mathematics Lesson 2.2 Vector Addition Through Analytic Method
- 2. 2 Have you ever played a treasure hunting game? Most of the time, people looking for these supposedly “treasures” use a map.
- 3. 3 In literature and film, a common treasure map is tattered and has a signature “x” in the middle to identify the location of the treasure.
- 4. 4 Each individual path can be combined and added to specifically identify how far and in what direction you should go to reach it.
- 5. 5 How are two or more vectors added?
- 6. Learning Competency At the end of the lesson, you should be able to do the following: 6 Perform addition of vectors (STEM_GP12V-Ia-9).
- 7. Learning Objectives At the end of the lesson, you should be able to do the following: 7 ● Explain the rules of vector addition and subtraction. ● Use the graphical method to add vectors.
- 8. 8 Can you help the monkey get its banana? Recall of Vectors
- 9. 9 In what directions did you go into? Recall of Vectors
- 10. 10 What is the total distance you have travelled in bringing the banana to the monkey? Recall of Vectors
- 11. 11 What is the total displacement you have travelled in bringing the banana to the monkey? Recall of Vectors
- 12. 12 Two vectors are considered equal if their magnitudes and direction are the same. If two or more vectors are pointing in the same direction, it means that they are parallel to each other. Vectors in One Dimension
- 13. 13 When two vectors have opposite directions but have the same magnitude, they are called antiparallel. Vectors in One Dimension
- 14. 14 What is the difference between parallel and antiparallel vectors?
- 15. 15 What are the rules in adding and subtracting vectors?
- 16. 16 Suppose a person has a displacement of A eastward. Addition of Vectors
- 17. 17 Suppose he covered an additional displacement B eastward. Addition of Vectors
- 18. 18 The initial point of the total displacement is the starting point of A while the endpoint is the endpoint of B. Addition of Vectors
- 19. 19 The total displacement is called the resultant, R. Addition of Vectors
- 20. 20 The addition (and subtraction) of vectors can be done using the head to tail method. Addition of Vectors tail head head tail
- 21. 21 Suppose a person has a displacement of A eastward. Subtraction of Vectors
- 22. 22 Suppose he covers another displacement of B westward. Subtraction of Vectors
- 23. 23 The resultant R can be measured using head to tail method. Subtraction of Vectors
- 24. 24 The resultant R can be measured using head to tail method. Subtraction of Vectors
- 25. 25 ● Most of the vectors that you will encounter are not always parallel or antiparallel. ● However, the same rules for the addition of vectors apply even if there are specific angles given. ● Head to tail method can still be used in adding vectors while considering their angles. Graphical Method of Adding Vectors
- 26. 26 We can add vectors by placing them head to tail. Graphical Method of Adding Vectors
- 27. 27 Adding them in reverse gives the same result. This is the commutative law of addition. Graphical Method of Adding Vectors
- 28. Remember 28 When you add two or more vectors, they should contain similar units and should describe the same physical quantity. For example, a displacement vector can only be added to another displacement vector. It does not make sense to add it to a velocity vector, for example.
- 29. 29 How are vectors added graphically?
- 30. 30 ● Vectors can be added graphically (geometrically) or algebraically. ● A graphing paper or a bond paper, a ruler, and a protractor are needed in adding vectors graphically. Graphical Method of Adding Vectors
- 31. Let’s Practice! 31 A car initially traveled 35 km due south and then traveled 65 km to the west. What is the car’s resultant displacement?
- 32. Let’s Practice! 32 A car initially traveled 35 km due south and then traveled 65 km to the west. What is the car’s resultant displacement? The resultant displacement is 74 km, 28°.
- 33. Try It! 33 33 What is the resultant displacement if a man jogs 120 m, east and then walks 50 m due south?
- 34. Try It! 34 34 Philip jogged along the street and covered 110 m north. He stopped for a while and jogged for another 20 m north. What is his total displacement?
- 35. Try It! 35 35 A student walks 10 m east and 6 m north. What is her resultant displacement?
- 36. Remember 36 The vector sum or resultant may vary from one individual to another due to the limitations of our measuring devices such as the ruler and the protractor. However, this deviation should only be by a few millimeters and a few degrees.
- 37. Let’s Sum It Up! 37 ● The sum of the vectors is called the resultant, R. ● Vectors are considered equal only if they have the same magnitude and direction. ● Parallel vectors are those that are pointing in the same direction. On the other hand, antiparallel vectors are those that are in
- 38. Let’s Sum It Up! 38 ● Vector addition follows the commutative and associative laws of addition. ● Vectors can be added graphically using the head to tail method.
- 39. Bibliography 39 Bauer, W., and Gary D. Westfall. University Physics with Modern Physics. New York: McGraw-Hill, 2013. Faughn, Jerry S. and Raymond A. Serway. Serway’s College Physics (7th ed). Singapore: Brooks/Cole, 2006. Knight, Randall Dewey. Physics for Scientists and Engineers: a Strategic Approach with Modern Physics. Pearson, 2017. Serway, Raymond A. and John W. Jewett, Jr. Physics for Scientists and Engineers with Modern Physics (9th ed). USA: Brooks/Cole, 2014. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky’s University Physics with Modern Physics (13th ed). USA: Pearson Education, 2012.