practice final exams are on the physics 214 web page in class help / review session

1. Practice final exams are on the physics 214 web page

2. In Class HELP / REVIEW Session

Wednesday and Friday

Help Center Open all day, every day RMs 235,237

3. Final Exam

Saturday, May 8, Rm 112 Physics

10:20am - 12:30 pm

4. Exam III Lunch right after the final exam!

Reading QuizAlthough many aspects of Einstein’s theory of special

relativity are confusing, at least the behavior of clocks (and time) behaves the way we always thought.

1.False2.True

Reading Quiz

• Black holes can never really be detected, because they do not emit any light.

• False• True

A BC

v

What if Observer A aims a light beam in the forward direction? Will observers B and C see different speeds of light, or the same?

Einstein’s postulates of special relativity•The laws of physics are the same in any inertial frame of reference•The speed of light is the same in any inertial frame of reference.

Luminiferous EtherJust as air is the medium which allows sounds wave to exist. The ether allows electromagnetic wave to exist.

Why is the speed of light

299,792,458 m/sand not some other value?

There must be a media controlling it’s valueMaxwell used the concept of this media to predict the existence of electromagnetic wave and their speed.

Observers B and C will measure the same speed of light, no matter what the speed the truck travels.

Instead, Observers B and C will find that time itself, and distances, will be different!

Michelson-Morley Experiment

Is the speed of light the same in all directions in a moving reference frame?

Simplisity

We have a choice:Assume speed of light is constantOr Space and time are altered in the direction of the motionAs with Newton we could refer everything to the universe’s

In contrast to sound waves or a ball, the velocity of the airplane does not add to the velocity of a flashlight beam to yield the velocity of light relative to the earth. The speed of light is the same for all observers. (Velocity vectors are not drawn to scale.)

Special Relativity: The speed of light looks the same to all observers! (Light does not act like a wave in a medium, unlike sound traveling through air.)

It doesn’t matter if…

•The source of light is moving.

•The source is at rest.

•You are moving.

•You are at rest.

This must be true for the laws of physics to be the same for everybody.

In a light clock, the time taken for light to travel the distance 2d to the overhead mirror and back becomes the basic measure of time to.

To an observer standing on earth, the light takes a diagonal path to the mirror and back to the source. This yields a

longer time interval as measured by the light clock.

With the help of assistants, the observer on earth can mark the position of the spaceship when the

light pulse is emitted and when it returns. The distance between these positions L0 can be easily measured.

Consequences:

Time Dilation

Length Contraction

E=mc2

€

γ= 1

1−v2

c2

Note: is larger than 1.

If v=0.6c, then =1.25.

€

t = γ toL = γ Lo

Mass is not constant

The mass of a moving object

€

m = γ mop = γ mo

r v

F = Δr p

ΔtK.E . = γ moc

2 −moc2

A. curved up

B. straightC. levelD. straight

E. curved down

Top

Bottom

A gun fires a bullet horizontally in an elevator. For an observer inside the elevator, which curve best describes the shape of the path taken by the bullet? (Curves are exaggerated.)1. The elevator is at rest, on the Earth.

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

A gun fires a bullet horizontally in an elevator. For an observer inside the elevator, which curve best describes the shape of the path taken by the bullet?2. The elevator is in free fall. (The cable broke!)

A. curved up

B. straightC. levelD. straight

E. curved down

Top

Bottom

A gun fires a bullet horizontally in an elevator. For an observer inside the elevator, which curve best describes the shape of the path taken by the bullet?3. The elevator is floating in intergalactic space.

A. curved up

B. straightC. levelD. straight

E. curved down

Top

Bottom

A gun fires a bullet horizontally in an elevator. For an observer inside the elevator, which curve best describes the shape of the path taken by the bullet?4. It is still in outer space, but a rocket engine pushes up on the bottom, causing it to accelerate.

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

Principle of Equivalence:

It is impossible to distinguish an acceleration of a frame of reference from the effects of gravity.

Instead of a gun, now consider a laser which fires a beam of light in the horizontal direction. For an observer inside the elevator, which curve best describes the shape of the path taken by the beam of light?

5. When the elevator is floating in intergalactic space?

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

Instead of a gun, now consider a laser which fires a beam of light in the horizontal direction. For an observer inside the elevator, which curve best describes the shape of the path taken by the beam of light?6. Still in outer space, but accelerated upwards by a rocket engine.

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

Instead of a gun, now consider a laser which fires a beam of light in the horizontal direction. For an observer inside the elevator, which curve best describes the shape of the path taken by the beam of light?

7. At rest on the surface of the Earth.

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

Instead of a gun, now consider a laser which fires a beam of light in the horizontal direction. For an observer inside the elevator, which curve best describes the shape of the path taken by the beam of light?

8. On the Earth, in free fall.

A. curved up

B. straightC. levelD. straightE. curved down

Top

Bottom

Conclusions:

Light is bent by gravity!

This effect is observable!!

It leads to black holes!!!

Time dilation: Time slows down for moving objects. In principle, the half-life of Radon would be greater than 3.8 days in our frame of reference if it were moving. This effect is actually measurable for particles called muons.

Time dilation is an experimental FACT, in agreement with the theory of relativity.