1. 1 Physics 7B - AB Lecture 4 April 24 Chapter 6 Galilean Space-Time Model, lots of Vectors, Intro. to Force, Momentum Lecture slides available at http://physics.ucdavis.edu/physics7 http://physics.ucdavis.edu/physics7

2. 2 Course Website http://physics.ucdavis.edu/physics7 Click on Physics 7B-A/B Today Quiz 2! May is a busy month. There will be four Quizzes.

3. 3 What is Galilean Space-Time model about? The Galilean Space-Time Model In our ordinary experience, three spatial dimensions and one time dimensions are all independent of each other. x y z Ex. You walk on a moving bus, what is your V w.r.t.the ground ? What if the bus was moving really fast? Like close to the speed of light? (i.e., C = 3 x 10 8 m/s)

4. 4 What is Galilean Space-Time model about? The Galilean Space-Time Model In our ordinary experience, three spatial dimensions and one time dimensions are all independent of each other. x y z Ex. You walk on a moving bus, what is your V w.r.t.the ground ? The Special Relativity Model of Space-Time The three spatial dimensions are NOT independent of time. i.e. Someone on the moving bus and someone on the ground will measure different velocity. If the speed of the bus was close to the speed of light…

5. 5 Models in 7B are based on Galilean Space- Time model. Good news is, The predictions of special relativity agree well with Galilean Space- Time model in their common realm of applicability, specifically in experiments in which all velocities are small compared to the speed of light. x y z Why does she start spinning much faster when she pulls her arms and legs in? What are the forces exerted on the airplane for it to accelerate?

6. 6 To describe the motion of objects, we use several vector quantities such as… Position vector R e.g. R initial, R final Displacement vector ∆R = R final – R initial Velocity vector v = dr/dt Acceleration vector a = dv/dt Force vector F Ok… What were vectors again?? New physical quantities! Linear momentum vector p = mv Angular momentum vector L = rp tangential

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19. 19 Example #1 I take four steps right and three steps up, what is my displacement?

20. 20 If I take a different path from point A to point B, would my displacement be different as well? A B ∆R AB A completely different path Example #2

21. 21 v ave = ∆R/ ∆t, v = dR/ dt Therefore, velocity (vector) points in the same direction as the displacement (vector) The magnitude of velocity is a positive number called speed 21

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41. 41 Introduction to Conservation of Momentum Momentum is another (vector) quantity Nature chooses to conserve (for a closed system).

42. 42 Momentum For a particle: Defined by p = mv Is a vector, points in the same direction as v (see above equation) For a system: Defined by adding together the momentum vectors of everything that makes up the system, I.e. p total = ∑p i = p 1 + p 2 + p 3 +… Is conserved for a system if nothing external pushes or pulls on it Has units of kg m/s

43. 43 Conservation of Momentum Example Rifle recoil Before shooting (at rest)

44. 44 Conservation of Momentum Example Rifle recoil Before shooting (at rest) v bullet p bullet After shooting

45. 45 Conservation of Momentum Example Rifle recoil After shooting v bullet p bullet v Rifle p Rifle Before shooting (at rest)

46. 46 Conservation of Momentum Railroad cars collide A 10,000kg railroad car A, traveling at a speed of 24m/s strikes an identical car B, at rest. If the car lock together as a result of the collision, what is their common speed afterward? Before collision vAivAi pAipAi After collision v B i =0 At rest v A+B f AB A+B

47. 47 Conservation of Momentum Railroad cars collide A 10,000kg railroad car A, traveling at a speed of 24m/s strikes an identical car B, at rest. If the car lock together as a result of the collision, what is their common speed afterward? Before collision vAivAi pAipAi After collision v B i =0 At rest v A+B f p A+B f AB A+B

48. 48 When does momentum of something change?? … when a force F acts on the something during a time interval e.g. A bat hits a baseball change in momentum is called: Impulse Impulse Is related to the net external force in the following way: Net Impulse ext = ∆ p = ∫ ∑ F ext (t)dt Approximate a varying force as an average force acting during a time interval ∆t Net Impulse ext = ∆ p = ∑ F ave.ext x ∆ t

49. 49 Next week May1 Quiz3(20min) will cover: Today’s lecture (exclude momentum, force, Impulse) Activities and FNTs from DLM7 and Activities from DLM8 Bring Calculator! Closed-book, formulas will be provided. DLM8&9 : Use of vectors, Force Model, Some new ideas: Force diagram, Momentum chart

50. 50 Be sure to write your name, ID number & DL section!!!!! 1MR 10:30-12:50 Dan Phillips 2TR 2:10-4:30Abby Shockley 3TR 4:40-7:00John Mahoney 4TR 7:10-9:30Ryan James 5TF 8:00-10:20Ryan James 6TF 10:30-12:50John Mahoney 7W 10:30-12:50Brandon Bozek 7F 2:10-4:30Brandon Bozek 8MW 8:00-10:20Brandon Bozek 9MW 2:10-4:30Chris Miller 10MW 4:40-7:00Marshall Van Zijll 11MW 7:10-9:30Marshall Van Zijll