Lesson 5 scalars and vectors error bars

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Lesson 5 scalars and vectors error bars

  1. 1. Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!
  2. 2. Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!
  3. 3. Scalars and vectors
  4. 4. Scalars Scalar quantities have a magnitude (size) only. For example: Temperature, mass, distance, speed, energy.
  5. 5. Vectors Vector quantities have a magnitude (size) and direction. For example: Force, acceleration, displacement, velocity, momentum.
  6. 6. Scalars and Vectors scalars vectors Magnitude (size) No direction Magnitude and direction temperature mass speed velocity force acceleration
  7. 7. Representing vectors Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!
  8. 8. Representing velocity Velocity can also be represented by an arrow. The size of the arrow indicates the magnitude of the velocity, and direction the direction! When discussing velocity or answering a question, you must always mention the direction of the velocity (otherwise you are just giving the speed).
  9. 9. Adding vectors When adding vectors (such as force or velocity) , it is important to remember they are vectors and their direction needs to be taken into account. The result of adding two vectors is called the resultant.
  10. 10. Adding vectors For example; 6 m/s 4 m/s 2 m/s 4 N 4 N 5.7 N Resultant force Resultant force
  11. 11. How did we do that?
  12. 12. How did we do that? 4 N 4 N 5.7 N 4 N 4 N
  13. 13. Scale drawing You can either do a scale drawing 4 cm 4 cm 1 cm = 1N θ = 45° θ
  14. 14. Or by using pythagorous and trigonometry 4 N 4 N Length of hypotenuse = √42 + 42 = √32 = 5.7 N Tan θ = 4/4 = 1, θ = 45°
  15. 15. Subtracting vectors For example; 6 m/s 4 m/s 10 m/s 4 N 4 N 5.7 N Resultant velocity Resultant force
  16. 16. Subtracting vectors For example; 4 N 4 N 5.7 N
  17. 17. An interesting example Think of a dog (dead) orbiting the earth with constant speed (in a circle).
  18. 18. An interesting example At this point, what is its velocity? velocity?
  19. 19. An interesting example velocity
  20. 20. An interesting example velocity? What is its velocity here?
  21. 21. An interesting example velocity As you can see the velocity has changed as it is now going in another direction.
  22. 22. An interesting example velocity In uniform circular motion, we have constant speed but changing velocity. Of course a changing velocity means it must be accelerating! We’ll come back to this next year!
  23. 23. Resolving vectors into components
  24. 24. Resolving vectors into components It is sometime useful to split vectors into perpendicular components
  25. 25. Resolving vectors into components
  26. 26. A cable car question
  27. 27. Tension in the cables? 10 000 N ?? 10°
  28. 28. Vertically 10 000 = 2 X ? X sin10° 10 000 N ?? 10° ? X sin10° ? X sin10°
  29. 29. Vertically 10 000/2xsin10° = ? 10 000 N ?? 10° ? X sin10° ? X sin10°
  30. 30. ? = 28 800 N 10 000 N ?? 10° ? X sin10° ? X sin10°
  31. 31. What happens as the angle deceases? 10 000 N ?? θ ? = 10 000/2xsinθ
  32. 32. Error bars • X = 0.6 ± 0.1 • Y = 0.5 ± 0.1
  33. 33. Gradients
  34. 34. Minimum gradient
  35. 35. Maximum gradient
  36. 36. y = mx + c
  37. 37. y = mx + c • Ek = ½mv2
  38. 38. y = mx + c • Ek = ½mv2 Ek (J) V2 (m2 .s-2 )
  39. 39. Let’s try some questions! Resultant of forces (addition of vectors) Page 13 Questions 1 to 6
  40. 40. Sorry, I nearly forgot!
  41. 41. Resultant force

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