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Scalars And Vectors

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Scalars And Vectors

1. 1. Scalars and VectorsScalars and Vectors By: Lee Yi LiangBy: Lee Yi Liang Joshua Foo and Ryan WongJoshua Foo and Ryan Wong
2. 2. What is scalar? • Scalar quantities only takes into account the magnitude of a measurement, but not its direction. This is where it differs from vector quantities.
3. 3. Examples of scalar quantities • Speed: 100km/h; Vector would be velocity: 100km/h heading north • Temperature: 30o C • Time: 10s
4. 4. Vectors • Quantities with magnitude and direction • Have positive and negative quantities
5. 5. Vectors • All vectors can be broken up into 4 parts – North – South – East – West • Magnitudes of vectors can be compared – |A| compared to |B|
6. 6. Vectors • Example: – Displacement – Velocity – Acceleration – Force – Electric field
7. 7. How to represent a vector?How to represent a vector?
8. 8. How? Like This! • Scaled vector diagrams • Depict a vector by use of an arrow drawn to scale in a specific direction
9. 9. Huh but how? • All vector diagrams should contain the following: – Clearly listed scale – Vector arrow in specified direction – Vector arrow must have • a head • a tail – Cleary labeled magnitude and direction of vector – In this case, magnitude is 20m and direction is 30 degrees west of north
10. 10. • Ohh like that ar?
11. 11. SOLVING RESULTANT OF 2 VECTORS Geometrically
12. 12. Things to note • Dot represents the object • Arrows represent the forces. • Length of arrows represent magnitude of forces. • Direction arrows are pointing to represent direction of forces.
13. 13. Scenario • Let’s say, there are two forces acting on an object. One force is acting 100N upwards, the other is 50N to the right.
14. 14. Step 1 – Drawing object and forces . 100N 50N
15. 15. Step 2 – Move one arrow along the other . 100N 50N OR . 100N 50N
16. 16. Step 3 – Draw an arrow from object to point where the moved arrow is touching . 100N 50N OR . 100N 50N
17. 17. Step 4 – Measure length of resultant arrow • After you find out the length of the arrow, find out the ratio of the resultant arrow to the ratio of any of the beginning arrows. • Hence deduce the force.
18. 18. How to determine theHow to determine the resultant of 2 vectorsresultant of 2 vectors mathematically?mathematically?
19. 19. But then but then but then hor • In the diagram, R is the resultant displacement of displacement vectors A, B, and C • A + B + C = R • In all such cases, the resultant vector is the result of adding the individual vectors
20. 20. But then but then but then still got more • Pythagoras Theorem – Can be used to determine the result of adding two (and only two) vectors which make a right angle to each other
21. 21. But then never mind • Trigonometry – Can be used to determine direction of resultant vector
22. 22. Result of more vectors • Forces in a Plane • Forces in 90 degrees • Forces in all directions
23. 23. Result of more vectors • Forces in Plane – Simply add all the forces together
24. 24. Result of more vectors • Forces in 90 degrees – Add up the vector forces in north and south – Add up the vector forces in east and west – Make a right angle triangle – Use trigonometry to find resultant force
25. 25. Result of more vectors • Addition of Vector – Represent the vector forces with arrows • Greater magnitude, longer arrow – Place all the arrows at the same starting point – Choose an arrow – Choose the next arrow • At the end of the 1st arrow, place the start of the 2nd arrow
26. 26. Result of more vectors – Continue until all the arrows are joint together – All the arrows should end at a point • Match this ending point to the starting point – This new arrow is the resultant force
27. 27. Acknowledgements • The Physics Classroom - http://www.physicsclassroom.com/Class/vectors The Electronic Science Tutor - http://www.physchem.co.za/Vectors/index.htm Resultant of Forces - http://www.walter-fendt.de/ph11e/resultant.htm
28. 28. The End • Qs?