Announcements 11/20/12
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Prayer
Lab 10, HW 36 due
tonight
Exam 3 starts Monday
after break
Exam 3 review: Monday,
4:30 – 6 pm, this room
Close to Home
From warmup
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Extra time on?
Other comments?
a. You might know this already, but the Mythbusters did an
experiment where they shot a soccer ball out of a cannon
positioned at the back of a truck to illustrate the effects of the
Galilean velocity transformation equation, and they succeeded
in canceling out the two velocities. Here's a link to the video
http://www.youtube.com/watch?v=BLuI118nhzc
About the Exam…
Clicker question:
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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 frame
b. An “enlightened” reference frame
c. An “inertial” reference frame
d. A “null” reference frame
e. A “unique” reference frame
Fictitious forces
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Toss a ball straight up, in car. Slam on the
brakes. What happens?
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Throw a ball to a friend on a merry-go-round
(as it’s spinning). What path does the ball
take?
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Reference frames where Newton’s Laws
apply: “inertial frames”
Galilean Relativity
v2 = 100 mph
v1 = 80 mph
Credit: this slide and next one from Dr. Durfee
Galilean Relativity
Reference frame moving with car 1
v2 = 20 mph
v1 = 0 mph
HW 37-3
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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.
All valid physical laws are true in all inertial reference frames
Bike lights
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I’m riding my bike at 1108 m/s. I turn on my front
bike light (c=3108 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.html
Changing magnetic field  electric field
Changing electric field  magnetic field
Maxwell Eqns: speed of waves is
1
 0 0
 3  108 m/s
Nothing in equations says anything about the flashlight!!!
(the source of waves)
Compare to Sound
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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
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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 or observer.
Michelson-Morley experiment
The “Big Deal”: these two
simple statements have
some crazy implications,
as we shall see.
From warmup
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The Galilean velocity transformation equation, Eqn 39.2
(8th edition), is simple--much simpler than its name
implies. It's also sometimes called the "classical velocity
addition" formula. It's "obviously" true. Use it to answer
this question: A pickup truck is traveling at 5 m/s. A
man standing in the back of the truck throws a ball
forward at 10 m/s (relative to himself). How fast will
someone on the ground measure the ball to be
traveling? What is the faulty assumption on which the
equation relies?
a. The person on the ground would measure the speed
to be 15 m/s (speed of frame + speed of ball). I
believe that the faulty assumption in this equation is
that time is the same in each frame, not dependent
on their velocity.
From warmup
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Explain in your own words (in language that your nonphysics-major roommates could understand) how the Galilean
velocity transformation equation and the 2nd postulate of
special relativity are at odds with each another.
a. The Galilean velocity transformation equation assumes
that speed will always add up, so if you switched on a
flashlight while on a pickup truck moving forward with
speed v, you would get c + v as the speed of the light.
However, the second postulate states that nothing can
move faster than the speed of light...unless you have a
Lorentzian manifold which allows you to warp space-time
to create a warp bubble (Go Dr. White!).
Example: Light Ray on a Train
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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
How long did it take, really?
Why doesn’t this “problem”
exist with sound waves?
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If height of train car inside is h, how long did
that take (to you, on the ground)?
Train is traveling at speed v
Answer: t = 2h/c  (1-v2/c2)-1/2
Notation
Answer 1 (measured on train): t = 2h/c
Answer 2 (measured on ground): t = 2h/c  (1-v2/c2)-1/2
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Timemeasured by me, on train: Dt
Time measured by you, on ground: Dt
v

c

v/c
1
1 
2
Dt   Dt
For v = 0.9c:
 = 0.9
 = 2.3
Think about this…
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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
raysmy
back
andappears
forth. If to
you
To you,
time
bemeasure
slowed.a time
interval toTo
beme,
1 s,your
how time
long will
that interval
look like, to me on
appears
to be slowed.
the train?
Who is right?
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.
Twin “Paradox”
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Speedo & Goslo…which twin is older?
Simultaneity
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Dr. Colton on train, again
Turn the flashlights on at the same
time, the photons reach the walls
simultaneously. OK?
Simultaneity
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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?
A different effect
Light from which lightning
bolt will reach Jim first?
Jim
Slide credit: Dr Durfee, again
Jim
An “array” of observers
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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.
Jim’s friends