Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant

1. DO NOW! Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant

2. DO NOW! Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant

3. Scalars and vectors

4. Scalars Scalar quantities have a magnitude (size) only. For example: Temperature, mass, distance, speed, energy.

5. Vectors Vector quantities have a magnitude (size) and direction. For example: Force, acceleration, displacement, velocity, momentum.

6. Scalars and Vectors No direction vectors scalars Magnitude (size) Magnitude and direction temperature mass velocity force acceleration speed

7. Representing vectors Vectors can be represented by arrows. The length of the arrow indicates the magnitude, and the direction the direction!

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. 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. Adding vectors For example; Resultant force 2 m/s 6 m/s 4 m/s 4 N 5.7 N 4 N Resultant force

11. How did we do that?

12. How did we do that? 4 N 4 N 4 N 4 N 5.7 N

13. 4 cm 4 cm Scale drawing You can either do a scale drawing θ 1 cm = 1N θ = 45°

14. 4 N 4 N Or by using pythagorous and trigonometry Length of hypotenuse = √42 + 42 = √32 = 5.7 N Tan θ = 4/4 = 1, θ = 45°

15. Subtracting vectors For example; Resultant velocity 10 m/s 6 m/s 4 m/s 4 N 5.7 N 4 N Resultant force

16. Subtracting vectors For example; 5.7 N 4 N 4 N

17. An interesting example Think of a dog (dead) orbiting the earth with constant speed (in a circle).

18. An interesting example At this point, what is its velocity? velocity?

19. An interesting example velocity

20. An interesting example What is its velocity here? velocity?

21. An interesting example As you can see the velocity has changed as it is now going in another direction. velocity

22. An interesting example 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! velocity

23. Resolving vectors into components

24. Resolving vectors into components It is sometime useful to split vectors into perpendicular components

25. Resolving vectors into components

26. A cable car question

27. Tension in the cables? ? 10° ? 10 000 N

28. Vertically 10 000 = 2 X ? X sin10° ? 10° ? ? X sin10° ? X sin10° 10 000 N

29. Vertically 10 000/2xsin10° = ? ? 10° ? ? X sin10° ? X sin10° 10 000 N

30. ? = 28 800 N ? 10° ? ? X sin10° ? X sin10° 10 000 N

31. What happens as the angle deceases? ? = 10 000/2xsinθ ? θ ? 10 000 N

32. Error bars • X = 0.6 ± 0.1 • Y = 0.5 ± 0.1

33. Gradients

34. Minimum gradient

35. Maximum gradient

36. y = mx + c

37. y = mx + c • Ek = ½mv2

38. y = mx + c • Ek = ½mv2 Ek (J) V2 (m2.s-2)

39. Let’s try some questions! Page 13 Questions 1 to 6 Resultant of forces (addition of vectors)

40. Sorry, I nearly forgot!

42. Resultant force