1. Physics 215 – Fall 2014Lecture 04-11 Welcome back to Physics 215 Today’s agenda: Relative motion

2. Physics 215 – Fall 2014Lecture 04-12 Current homework assignment HW3: –Exam-style problem (print out from course website) –Ch.4 (Knight textbook): 52, 62, 80, 84 –due Wednesday, Sept 17 th in recitation

3. Physics 215 – Fall 2014Lecture 04-13 Exam 1: Thursday (9/18/14) In room 208 (here!) at the usual lecture time Material covered: –Textbook chapters 1 - 4 –Lectures up through 9/16 (slides online) –Wed/Fri Workshop activities –Homework assignments Work through practice exam problems (posted on website) Work on more practice exam problems on Wednesday in recitation workshop

4. Physics 215 – Fall 2014Lecture 04-14 Kinematics Consider 1D motion of some object Observer at origin of coordinate system measures pair of numbers (x, t) – (observer) + coordinate system + clock called frame of reference (x, t) not unique – different choice of origin changes x (no unique clock...)

5. Physics 215 – Fall 2014Lecture 04-15 Change origin? Physical laws involve velocities and accelerations which only depend on  x Clearly any frame of reference (FOR) with different origin will measure same  x, v, a, etc.

6. Physics 215 – Fall 2014Lecture 04-16 Inertial Frames of Reference Actually can widen definition of FOR to include coordinate systems moving at constant velocity Now different frames will perceive velocities differently... Accelerations?

7. Physics 215 – Fall 2014Lecture 04-17 Moving Observer Often convenient to associate a frame of reference with a moving object. Can then talk about how some physical event would be viewed by an observer associated with the moving object.

8. Physics 215 – Fall 2014Lecture 04-18 Reference frame (clock, meterstick) carried along by moving object A B

9. Physics 215 – Fall 2014Lecture 04-19 A B A B A B

10. Physics 215 – Fall 2014Lecture 04-110 A B A B A B

11. Physics 215 – Fall 2014Lecture 04-111 A B A B A B

12. Physics 215 – Fall 2014Lecture 04-112 Discussion From point of view of A, car B moves to right. We say the velocity of B relative to A is v BA. Here v BA > 0 But from point of view of B, car A moves to left. In fact, v AB < 0 In general, can see that v AB = -v BA

13. Physics 215 – Fall 2014Lecture 04-113 Galilean transformation xAxA xBxB v BA P v BA t x PA = x PB + v BA t -- transformation of coordinates   x PA  t  x PB /  t + v BA  v PA = v PB + v BA -- transformation of velocities yByB yAyA

14. Physics 215 – Fall 2014Lecture 04-114 Discussion Notice: –It follows that v AB = -v BA –Two objects a and b moving with respect to, say, Earth then find (P  a, B  b, A  E) v ab = v aE - v bE

15. Physics 215 – Fall 2014Lecture 04-115 You are driving East on I-90 at a constant 65 miles per hour. You are passing another car that is going at a constant 60 miles per hour. In your frame of reference (i.e., as measured relative to your car), is the other car 1.going East at constant speed 2.going West at constant speed, 3.going East and slowing down, 4.going West and speeding up.

16. Physics 215 – Fall 2014Lecture 04-116 Conclusion If we want to use (inertial) moving FOR, then velocities are not the same in different frames However constant velocity motions are always seen as constant velocity There is a simple way to relate velocities measured by different frames.

17. Physics 215 – Fall 2014Lecture 04-117 Why bother? (1) Why would we want to use moving frames? Answer: can simplify our analysis of the motion

18. Physics 215 – Fall 2014Lecture 04-118 Relative Motion in 2D Motion may look quite different in different FOR, e.g., ejecting ball from moving cart Cart frame Earth frame Motion of cart = simple! = complicated!

19. Physics 215 – Fall 2014Lecture 04-119 Relative Motion in 2D Consider airplane flying in a crosswind –velocity of plane relative to air, v PA = 240 km/h N –wind velocity, air relative to earth, v AE = 100 km/h E –what is velocity of plane relative to earth, v PE ? v AE v PA v PE v PE = v PA + v AE

20. Physics 215 – Fall 2014Lecture 04-120 Why bother? (2) Have no way in principle of knowing whether any given frame is at rest –Room 208 is NOT at rest (as we have been assuming!)

21. Physics 215 – Fall 2014Lecture 04-121 What’s more … Better hope that the laws of physics don’t depend on the velocity of my FOR (as long as it is inertial …) Einstein developed Special theory of relativity to cover situations when velocities approach the speed of light

22. Physics 215 – Fall 2014Lecture 04-122 Is the average velocity vector of cart J relative to cart I (or, in the reference frame of cart I ) in the time interval from 1 to 2…? 1.to the right 2.to the left 3.zero 4.unable to decide The diagram shows the positions of two carts on parallel tracks at successive instants in time. Cart I Cart J

23. Physics 215 – Fall 2014Lecture 04-123 Is the instantaneous velocity vector of cart J relative to cart I (or, in the reference frame of cart I ) at instant 3…? 1.to the right 2.to the left 3.zero 4.unable to decide Cart I Cart J

24. Physics 215 – Fall 2014Lecture 04-124 Is the average acceleration vector of cart J relative to cart I (or, in the reference frame of cart I ) in the time interval from 1 to 5: 1.to the right 2.to the left 3.zero 4.unable to decide Cart I Cart J

25. Physics 215 – Fall 2014Lecture 04-125 Accelerations? We have seen that observers in different FORs perceive different velocities Is there something that they do agree on? –Demo with ball ejected from cart: cart and Earth observer agree on acceleration (time to fall)

26. Physics 215 – Fall 2014Lecture 04-126 If car I moves with constant velocity relative to the road, Then the acceleration of any other object (e.g., car J) measured relative to car I is the same as the acceleration measured relative to the road. Acceleration

27. Physics 215 – Fall 2014Lecture 04-127 Acceleration is same for all inertial FOR! We have: v PA = v PB + v BA For velocity of P measured in frame A in terms of velocity measured in B   v PA /  t =  v PB /  t since v BA is constant  Thus acceleration measured in frame A or frame B is same!

28. Physics 215 – Fall 2014Lecture 04-128 Reading assignment Forces, Newton’s Laws of Motion Ch.5 in textbook Review for Exam 1 !