Physics Study guide PDF

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University of Alberta PHYS114 Physics: The Big Picture Fall 2017 Final Professor: Joy Stacey

Exam Guide

Table of content: - Waves, Light and The Electromagnetic Spectrum and more - Special Relativity Introduction - Proof of Special Relativity - Twin Paradox - Time Dilation - The Equivalence Principle (Not in the final exam)

Waves, Light and The Electromagnetic Spectrum and more Hans Christian Oersted •

Made a big discovery (mid-1800s) o

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Serendipitous discovery

In the past, scientists had "celebrity status", many people would pay money to listen to lectures and presentations done by these scientists

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Oersted was delivering such a lecture in Denmark o

During this time, we had just discovered electricity

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Volta had made the first battery

Oersted was making a presentation on these batteries (voltaic piles) o

Had the intention of connecting the batteries so it would produce large, visible sparks in the air

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As he was setting up, the table had a mass of different metals

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From a previous demonstration, a compass was left on the table

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As Oersted is presenting the lecture and connecting the battery, he sees out of the corner of his eye, the needle of the compass moving

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He disconnects the battery, and the needle moves back (he repeats connecting and disconnecting the battery, and the same thing occurs each time: the compass needle is deflected) 

Appeared that this happens as long as an electrical current/field is involved

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Suggests a relationship between magnetism and electricity

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Continued his presentation, but took note of this

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Remember that Oersted was the one of the first to observe the connection between electricity and magnetism 

If you get an electric current flowing through a wire, it induces a magnetic effect on the compass needle that caused deflection

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Wrote it up, and the news set off a flurry of activity, especially in Paris

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Many French physicists, embarked on developing more understanding on the relationship between electricity and magnetism 

All because of Oersted's serendipitous discover

Michael Faraday o

Debatably one of the top ten physicists of our time

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Made incredibly important discoveries that shape our understandings of the world

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Discovery he is most famous for: Faraday's Law of Induction

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Observed that if you make a complete circuit out of aluminum and move a magnet over it, a current is formed •

Current is measured using an ammeter

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Somehow a moving magnet, can create an electrical force and a current to form

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Strengthens the connection between electricity and magnetism-- they should no longer be treated as isolated concepts

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This discovery is also significant because this property is what is used to generate electricity in powerplants, natural gas plants, hydro-plants, etc. (our technical framework is based on Faraday's law 

We turn big loops of wires in a magnetic field (which is essentially the same thing as moving the magnet)

 o

Also explains how motors work

In this lecture, we focus on the fact that Faraday shows that somehow there is a direct connection between electricity and magnetism

Key Observations So Far •

Electric charges produce electric forces

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Magnets always come in dipoles (opposite ends- North and South)

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Moving electric charges (current) produce magnetic forces

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Changing magnetic positions induces an electrical force (Faraday)

We have to go back to a fundamental question: How do these forces propagate through empty space? •

If you take on object like a pen, how does it know to fall down to the Earth?

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How do electrically charged objects know to attract/repel?

James Maxwell and the Field Concept •

Most famed Scottish physicist (people don't really know him though- maybe because his discoveries were too technical)

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One of the first to attempt to answer this fundamental question

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Proposed that all of empty space, despite the fact that it is a vacuum, has properties, and that these properties are defined through fields o

Space is not just nothing, but it has properties that are defined by fields

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The pen knows to fall to the ground, because of the presence of a gravitational field in that empty space

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So if you take two electrical charges, they know that each one is present because their "fields" affect each other

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Had no experimental proof that fields existed, it was more of an idea

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He knew what they would look like though: similar to when iron filings are dropped around a bar magnet o

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Still does not prove that fields exist

Maxwell's proof that showed the existence of fields is slightly weird

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Analogy: (kind of imperfect) -- take a fish-tank full of water and put a goldfish inside (now it can swim around--it is an active goldfish), then put another goldfish (lazier, doesn't move around much). Since the first goldfish is moving, its tail will shake, the other goldfish can feel the oscillations in the water caused by the tail moving and will react accordingly

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Maxwell: replace fish with charges and the water with a field. Believed that if the source of the field is accelerating, the waves can transmit energy, causing a nearby object to feel a force o

If you take a charged object and shake it, waves will be produced in the electromagnetic field

o

Note that the field must be accelerating, waves will not be transmitting if the speed is constant

Question is: how/when does the second charge react to the first (how long does it take for the field signal to be transmitted): what is the speed of a wave? o

Came up with equations that explain this (complete descriptions of electromagnetic phenomena): we don't need to know this!

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These equations helped him figure out how fast these fields can propagate

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First, we should know that if a wave is a wave, it needs to satisfy the universal wave equation

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If the frequency is high, the wavelength must be low to get the same speed c (and vice versa)

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Rearranges his equations to have the same form as the universal wave equation

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The UWE has a term for the speed, when he manipulates his equation, he uses a "similar" term in his equations to determine the speed of a wave (universal for all waves)

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He calculates the wave speed: about 300 000 km/s! (which is extremely close to the known speed of light)

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Proposed that this must mean that light is a wave in the electromagnetic field •

Heinrich Hertz later proved this

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Verified that shaking electric charges will create waves of different frequencies (the frequencies and other properties determine the type of waves produced)

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Shaking with a lower frequency causes a lower frequency wave to be produced, which means a higher wave

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Can oscillate with any frequency, just dependent on the frequency of the oscillator producing the waves

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Possibly shows how light can propagate in a vacuum: it is really oscillating through an electromagnetic field •

Begs the question of whether a field is a real thing, or simply a mathematical construct

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We believe that fields exist

The Electromagnetic Spectrum •

Visible light is only a small part of the electromagnetic spectrum

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Electromagnetic oscillators (ex. Magnet or current) can oscillate with any frequency, so EMR waves can gave any frequency and any wavelength (frequency and wavelength are related through the UWE) (speed= frequency/wavelength, where speed = speed of light)

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Very short wavelengths (high frequency) = gamma rays o

Produced by processes happening in atomic nuclei

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Radioactivity is associated with the production of gamma rays

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Extremely high energy, penetrating and dangerous to living organisms

X-rays are also short wavelengths and high energy o

Not as damaging as gamma rays

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Produced by inner shell electronic processes in atoms

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Ultraviolet radiation o

Higher in frequency than visible light

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Produces sunburns and other negative effects on living organisms

Visible light has a narrow band of wavelength o

From 400-700 nm (know the different wavelengths of the colours)

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The solar spectrum is very strong in emitting wavelengths in the visible light range, visible light is at the peak of the solar spectrum

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Our eyes are specifically sensitive to these wavelengths, over time we have developed sensitivity to the wavelengths that give us the most biological advantage

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Look at the solar spectrum in the slides

Longer waves are infrared, microwaves and radio waves (sound waves)

-cyberphysics.com

The Speed of Light is with Respect to What •

Maxwell calculated the speed of EM waves to be 300 000 km/s, which is the speed of light. So light is an electromagnetic wave

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But what is the speed relative to? o

The emitter? No, although we knew this already from astronomy.

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The observer? No. Inconsistent with astronomical observations from the moving earth. If the moving earth changed the relative speed of light, we would see strange astronomical phenomena, like mistimed orbits

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The medium? Can the field (the vacuum itself) move? Besides, the Earth's motion in though the vacuum of space has no effect

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The crazy thing is that the speed of light is relative to everything, regardless of where you are o

This is weird because the speed of light is constant, and cannot be added. Nothing else acts like this

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This question would be addressed by Einstein, as described in the start of the next section on Special Relativity

Conclusion •

Light is a wave in the electromagnetic field

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The medium is not matter. These waves travel in empty space. The "medium" is the electromagnetic field, a property of space itself

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Electromagnetic disturbances produce waves in the electromagnetic field. We detect these waves as light

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The frequency of light depends on the frequency of the oscillator The human eye can only detect a small part of the electromagnetic spectrum. The dull spectrum of frequencies is much more than the tiny part we an see

Questions: What was the central and critical device in Michelson’s amazing technique for measuring the speed of light to high accuracy? A. a laser B. a rotating 8-sided mirror C. a rotating lens D. an interferometer E. More than one of the above Answer: 8-sided mirror. Concept Question. It is in the notes

What is the frequency of sound with a wavelength of 171.5 m? A. 2 Hz B. 2 kHz C. 171.5 Hz D. 58.8 kHz E. None of the above Answer: A: f = v/λ = 343/171.5 = 2 Hz, Universal Wave Equation

Special Relativity Introduction Where were we? •

We had made many measurements about the speed of light and saw that it was the same for everything it was compared to

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This shouldn't be possible as it makes no sense--no other phenomenon acts like this since it is an apparent violation of simple mathematical rules

Einstein realized the answer in a very weird time •

Difficult position because of the situation he had gotten himself into at school

Went on walks with the "Olympia Academy" and discovered some fundamental truths about the properties of light

Remember that the problem is determining what the speed of light is relative to •

Relative to the aether? No, because the existence of aether was disproved by the Michelson-Morley Experiment

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Relative to the emitter? No, this was checked and disproved by studying the orbits of binary stars

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Relative to the observer? No, this has already been checked using astronomical measurements and disproved

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These orbits were totally Newtonian

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The observations showed that the speed of light was not added to the speed of the emitter, but remains constant independent of how fast the emitter moves

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Observations further show that speed is not relate to the speed of the fields or the vacuum, because our motion through space has no effect on the measured speed of light

Special Relativity •

One of the weirdest concepts in physics was the consistency of light

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Galilean motion: All motion is relative o

Therefore, there is no true speed

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Laws of physics are the same in all inertial reference frames

Einstein focused first on the impact of relativity and time •

If time is depending on speed, the n perhaps one could explain the apparent mathematics

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Developed two postulates

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The law of physics are the same in all inertial reference frames

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The speed of light in a vacuum is really the same in every inertial frame

Therefore, if the speed c is always the same then other things must change, such as time and length. o

Every experiment that has ever been done says “Yes”. Time and distance change, depending on relative velocities.

First, we will look at some of the implications and then we will show the proofs. Einstein’s special theory of relativity has been experimentally proven many, many times in a whole range of different experiments.

Simultaneity •

In order to prepare people for the strangeness of his theory, Einstein first created a thought experiment to show that we should maybe not be so surprised at the existence of a “relative time

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Demonstrated that there is no such thing as absolute simultaneity.

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Imagine an outside “observer” standing on the ground as the train passes by o When exactly half the length of the train has passed the observer, two lightning bolts hit, creating flashes of light at both ends of the train. Because the flashes are equidistant from him, the light from both explosions reaches his eyes at the same moment, and the outside observer sees the bolts hit at exactly the same time. But the on-board observer sees something different. 

He would see the bolt on the right (at the front of the train) strike before the one at the back. This is because the train is continuously moving to the right, so the light from the front of the train would have less distance to cover than the light coming from the back. The observers do not agree on which event happened first.

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Furthermore, if there were a 3rd observer in another train going the other way, he would say that the back bolt hit first. Each would swear that he is correct.

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They are all equally correct – simultaneity is relative!

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Which event appears to happen first really truly does depend on the relative motions. Each observer has a slightly different “reality”.

Proof of Special Relativity Time Dilation and Length Contraction •

Observed from the perspective of a moving/stationary with respect to another observer

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Comes from the observation that light moves at the same speed for every observer regardless of the conditions

Thought Experiment: light clock •

Imagine an astronaut in a space vehicle that is passing over the Earth

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Inside is an astronaut that wants to build a clock to keep track inside (remember that all clocks are based on some type of repetitive phenomenon)

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She decides to make a really accurate clock- a light clock o

Needs •

Light pulser - makes a flash when you press the button

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Mirror- placed some distance away, the light will hit the mirror, reflect and come back down to then be detected by a light detector

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Detector- detects light as it reflects off the mirror; tells the astronaut to press the button again to send another light pulse

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Imagine that it takes one second for this to happen o

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Goes up, goes down, light is detected, she presses the button; this is repeated indefinitely

A person on Earth will see something slightly different o

On the space ship the light is going straight up and down •

She can also measure the time that it takes (change in time = (2x distance)/ speed of light

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Proper time- time measured by the person who is stationary with respect to the time measurement system

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Remember that the person on the ground sees the spaceship travelling at some speed overhead •

So, they will see the light going up and down overhead, but will also see the motion of the space craft

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The motion of the space craft causes the mirror overhead to move in the direction the ship is moving-- as a result the light has to catch up before it can be reflected and ends up taking a diagonal path as opposed to the straight-line path that the astronaut is seeing

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This diagonal path is slightly longer than the straight-line path

-esoteric science •

The Earth based observer will see the path "c" going to the mirror and "c" going back to the sensor, but it will take a longer time since the distances are different

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The astronaut is still ticking her clock for every interval of time, but that interval of time is not the same for the Earth observer because it will take longer for light to

make this journey (as a result she appears to e pressing the button much slower than she actually is) •

Note: the astronaut sees that the light takes one second on her own wristwatch to make the round trip. The observer agrees that one tick of the astronaut’s watch has been made (aka she is pressing the button) but to took more than one tick of the observer's watch. All clocks on board the spaceship appear to be slowing down. 

ALL clocks. This includes the biological ones, the astronaut herself will appear to move slowly, age slowly, etc.

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Everything has to happen slowly because of the speed of light

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There is a reason we don...