Lesson 5 scalars and vectors error bars
- 1. Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!
- 2. Which of the following is the odd one out? Mass Speed Force Temperature Distance Elephant DO NOW!
- 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 scalars vectors Magnitude (size) No direction Magnitude and direction temperature mass speed velocity force acceleration
- 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; 6 m/s 4 m/s 2 m/s 4 N 4 N 5.7 N Resultant force Resultant force
- 11. How did we do that?
- 12. How did we do that? 4 N 4 N 5.7 N 4 N 4 N
- 13. Scale drawing You can either do a scale drawing 4 cm 4 cm 1 cm = 1N θ = 45° θ
- 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. 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. Subtracting vectors For example; 4 N 4 N 5.7 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?
- 20. An interesting example velocity? What is its velocity here?
- 21. An interesting example velocity As you can see the velocity has changed as it is now going in another direction.
- 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. 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? 10 000 N ?? 10°
- 28. Vertically 10 000 = 2 X ? X sin10° 10 000 N ?? 10° ? X sin10° ? X sin10°
- 29. Vertically 10 000/2xsin10° = ? 10 000 N ?? 10° ? X sin10° ? X sin10°
- 30. ? = 28 800 N 10 000 N ?? 10° ? X sin10° ? X sin10°
- 31. What happens as the angle deceases? 10 000 N ?? θ ? = 10 000/2xsinθ
- 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! Resultant of forces (addition of vectors) Page 13 Questions 1 to 6
- 40. Sorry, I nearly forgot!
- 42. Resultant force