1. FACULTY OF SCIENCE Physics Bridging Course Chapter 3 VECTORS AND MOTION IN 2 & 3 DIMENSIONS School of Physics

2. Questions from last lecture/tutorial?

3. Welcome to the 2nd dimension! ›So far one dimension only -Straight lines! ›The real world has 3 dimensions. ›This slide has 2 : -up/down -left/right

4. 2 Dimensions To describe something in 2 dimensions You need 2 quantities

5. Vectors and Scalars Vectors have ›Magnitude ›Direction

6. Examples: Vectors & Scalars Vectors ›Displacement ›Velocity ›Acceleration ›Force ›Electric field ›Magnetic fields ›Gravity Scalars ›Distance ›Speed ›Energy ›Temperature ›Mass ›time Q: What do you get when you cross a mosquito with a climber?

7. Working with Vectors Vectors are tricky to add up: Sydney Uni Central Fish & Chips Pub A: Nothing, you can’t cross a vector with a scalar

8. Working with Vectors “Resolve them into their components”: 3 3 + = 6 Horizontal Component

9. Working with Vectors “Resolve them into their components”: 24 - = 2 Vertical Component

10. TRIG is your friend! a x y  ayay axax Horizontal cos  = a x / a a x = a cos 

11. TRIG is your friend! a x y  ayay axax Vertical sin  = a y / a a y = a sin 

12. Unit vectors a x y  ayay axax

13. a + b = easy! a b a + b a b b

14. a - b = ?! a b a - b a b b -b

15. Working backwards… a x y  ayay axax Magnitude a 2 = a x 2 + a y 2 Direction tan  = a y /a x

16. Vectors are everywhere Vector addition works well for displacement and: ›Velocity ›Acceleration ›Forces Or any other vector quantity…

17. Worked Example ›I drive to Newcastle, (200 km north and 15 km east of Sydney). ›Then I drive to Mudgee, (130km west and 50 km north of Newcastle). How far am I from Sydney?

18. Questions?

19. Chapter 3 continued: Projectiles

20. Questions from last lecture/tutorial?

21. Projectiles Any object travelling in free-fall is called a projectile. The physics is quite simple (if you neglect air resistance etc)

23. “Free fall” does NOT mean falling downwards Free fall means accelerating downwards with a = g, i.e. at the acceleration due to gravity i.e. under the influence of gravity only

25. Path of a projectile ›The path of a projectile is parabolic -Or rather, the path of its centre of mass is parabolic ›The projectile moves in two dimensions, horizontally and vertically -That’s why we learnt all about vectors…

26. Question One egg is thrown off a cliff. Another egg is dropped at the same time. Which hits the ground first ? Bullet fired vs dropped http://www.youtube.com/watch?v=D9wQVI EdKh8

27. Hint Horizontal and Vertical components are independent. ›What is the vertical acceleration in each case? ›What is the horizontal acceleration in each case?

28. Let’s do an experiment!

29. Answer ›The two objects take exactly the same time to fall. ›The vertical and horizontal components of the motion are independent.  Horiz motion: a = 0  Vert motion: a = -9.8 m/s 2 Bullet fired vs dropped http://www.youtube.com/watch?v=D9wQVI EdKh8

30. Velocity of a projectile v x y  vyvy vxvx V y is affected by gravity V x is not

31. Q: Dropping a package ›A rescue plane flying at 1200 m elevation at 430 km/h approaches a person struggling in the water. At what distance should the pilot release a rescue capsule if it is to strike the water close to the person?

32. Conditions Apply ›Air resistance ›Spin/slice/swing ›These apply additional forces which we don’t take into account at this stage (too complicated).

33. Ski Jump on Moon ›Worked example

34. Questions?