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Exam & Labs Due Tomorrow! Study Guide Available.

Don't forget! The labs are due tomorrow and Exam 3 starts tomorrow as well. Need help studying? Check out our study guide for tips and hints!

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Exam & Labs Due Tomorrow! Study Guide Available.

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  1. Announcements 4/1/11 • Prayer • Labs 9, 10 due tomorrow • Exam 3 starts tomorrow • “So, Dr. Colton, what’s on the exam?”

  2. Reading Quiz • From my point of view, objects which experience no force don’t accelerate. What type of reference frame am I in? • An “Einsteinian” reference frame • An “enlightened” reference frame • An “inertial” reference frame • A “null” reference frame • A “typical” reference frame

  3. Fictitious forces • Toss a ball straight up, in car. Slam on the brakes. What happens? • Throw a ball to a friend on a merry-go-round (as it’s spinning). What path does the ball take? • Reference frames where Newton’s Laws apply: “inertial frames”

  4. Galilean Relativity v2 = 100 mph v1 = 80 mph Credit: this slide and next one from Dr. Durfee

  5. Galilean Relativity Reference frame moving with car 1 v2 = 20 mph v1 = 0 mph

  6. HW 37-3 • A 1 kg object (m1) collides with a 2 kg object (m2) on a frictionless surface. Before the collision, m1 is traveling at 9 m/s to the right and m2 is at rest with respect to the ground. The collision is elastic and m1 bounces straight back to the left. • Figure out the final velocities of both masses after the collision. [Hint given.] • A bicycle rider moving at 5 m/s to the right (relative to the ground) observes the collision. Show that both kinetic energy and momentum are also conserved in her frame of reference.

  7. Bike lights • I’m riding my bike at 1108 m/s. I turn on my front bike light (c=3108 m/s). • How fast does someone on the ground see the light waves go away? • How fast do I see the light waves go away? http://stokes.byu.edu/emwave_flash.html Changing magnetic field  electric field Changing electric field  magnetic field Nothing in equations says anything about the flashlight!!! (the source of waves)

  8. Compare to Sound • Source stationary: sound waves travel at 343 m/s (as measured by both source and observer) • Source moving at 100 m/s: ?  sound waves still travel at 343 m/s (as measured by both source and observer). Only frequency will be changed. Why is it a Big Deal that light waves do the same thing?

  9. Einstein: There is no problem • Postulate 1: The laws of physics apply in all inertial reference frames. • Postulate 2: The speed of light is the same for all inertial observers, regardless of motion of the light source. Michelson-Morley experiment The “Big Deal”: these two simple statements have some crazy implications, as we shall see.

  10. Example: Light Ray on a Train • If height of train car inside is h, how long did that take (to me, inside the train)? Answer: t = 2h/c Credit: animations from Dr. Durfee

  11. As seen from ground • If height of train car inside is h, how long did that take (to you, on the ground)? • Train is traveling at speed v How long did it take, really? Why doesn’t this “problem” exist with sound waves? Answer: t = 2h/c  (1-v2/c2)-1/2

  12. g v/c Notation • Time measured by me, on train: Dt • Time measured by you, on ground: Dt Answer 1 (measured on train): t = 2h/c Answer 2 (measured on ground): t = 2h/c  (1-v2/c2)-1/2 For v = 0.9c: b = 0.9 g = 2.3

  13. Think about this… • Suppose I, Dr. Colton (in the train), measure a time interval to be 1 second, presumably through lots and lots of light bounces or something along those lines. If the train is moving at 0.9c, you, the class (on the ground) measure that time interval to be 2.3 s. To you, it looks like things in the train are running in slow motion. However, what if you on the ground are the one that is bouncing light rays back and forth. If you measure a time interval to be 1 s, how long will that interval look like, to me on the train? • 1 s. That is, to Dr. Colton, it looks like things on the ground are running normally • (1/2.3) s. That is, to Dr. Colton, it looks like things on the ground are sped up • 2.3 s. That is, to Dr. Colton, it looks like things on the ground are running in slow motion. To you, my time appears to be slowed. To me, your time appears to be slowed. Who is right?

  14. A different effect Light from which lightning bolt will reach Jim first? Jim Slide credit: Dr Durfee, again

  15. This is a classical effect It has nothing to do with Special Relativity Now for something completely different . . . Jim

  16. An “array” of observers • Jim’s friends all record the actual times in Jim’s reference frame • Or equivalently, Jim is just smart enough to factor out the time the light took while traveling. Jim Jim’s friends

  17. Twin “Paradox” • Speedo & Goslo…which twin is older?

  18. Simultaneity • Dr. Colton on train, again Turn the flashlights on at the same time, the photons reach the walls simultaneously. OK?

  19. Simultaneity • Viewed from the ground; train moving to right. Events which happen simultaneously in one “reference frame” do NOT happen simultaneously in any other reference frame Which light ray travels farther? Which light ray hits the wall first?

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