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

Reading Quiz From my point of view, objects which

experience no force don’t accelerate. What type of reference frame am I in?

a. An “Einsteinian” reference frameb. An “enlightened” reference framec. An “inertial” reference framed. A “null” reference framee. A “typical” reference frame

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”

Galilean RelativityGalilean Relativity

Credit: this slide and next one from Dr. Durfee

v1 = 80 mph

v2 = 100 mph

Galilean RelativityGalilean Relativity

v1 = 0 mph

v2 = 20 mph

Reference frame moving with car 1

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.

a. Figure out the final velocities of both masses after the collision. [Hint given.]

b. 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.

Bike lights

I’m riding my bike at 1108 m/s. I turn on my front bike light (c=3108 m/s).

a. How fast does someone on the ground see the light waves go away?

b. How fast do I see the light waves go away?

http://stokes.byu.edu/emwave_flash.htmlChanging magnetic field electric fieldChanging electric field magnetic field

Nothing in equations says anything about the flashlight!!! (the source of waves)

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?

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.

The “Big Deal”: these two simple statements have some crazy implications,

as we shall see.

Michelson-Morley experiment

Example: Light Ray on a Train

If height of train car inside is h, how long did that take (to me, inside the train)?

Credit: animations from Dr. Durfee Answer: t = 2h/c

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 vAnswer: t = 2h/c (1-v2/c2)-1/2

How long did it take, really?

Why doesn’t this “problem” exist with sound waves?

Notation

Time measured by me, on train: t Time measured by you, on ground: t

Answer 2 (measured on ground): t = 2h/c (1-v2/c2)-1/2

Answer 1 (measured on train): t = 2h/c

2

1

1

v

c

For v = 0.9c: = 0.9 = 2.3

t t

v/c

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?

a. 1 s. That is, to Dr. Colton, it looks like things on the ground are running normally

b. (1/2.3) s. That is, to Dr. Colton, it looks like things on the ground are sped up

c. 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?

A different effect

Light from which lightning bolt will reach Jim first?

JimSlide credit: Dr Durfee, again

Jim

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.

An “array” of observers

Jim Jim’s friends

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

Simultaneity Dr. Colton on train, again

Turn the flashlights on at the same time, the photons reach the walls

simultaneously. OK?

Simultaneity Viewed from the ground; train moving to

right.

Which light ray travels farther?

Which light ray hits the wall first?

Events which happen simultaneously in one “reference frame” do NOT happen

simultaneously in any other reference frame