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Lecture Notes for Chapter 1
- Introduction (Reference: The Feynman Lectures, Vol. 1, p. 37-3) -- REPLACE WITH JUST THE The Examined Life VIDEO
- Imagine a pond in which we start a water wave ripple. The ripple starts out near the center and spreads radially outward -- Water Ripples Movie and also video from The Examined Life
- Very far away, the water wave ripple will look like a straight line. Something interesting happens to these plane waves (in this case, water waves) when they hit two slits.
- The water wave ripple will divide up into two new ripples when it hits the slits and, if the slits are spaced just right, the two new water wave ripples will experience something called interference -- Double Slit Movie and Great Java Applet.
- This is just adding up the parts of a wave; where two crests (or troughs) meet, they add; where a crest and trough meet, they cancel.
- This property, interference, only happens for waves! We can represent it graphically by plotting the big and small parts as a graph:
- Particles behave completely differently when they encounter slits...
- E.g., suppose you fired bullets at two slits? What does that look like? Just two separate curves...
- Light was, at this time, thought to be a particle (e.g., look at sharp shadows, photoelectric effect, etc. -- also, Newton endorsed the view that light was made up of particles)
- Now what happens when you fire light at it? Interference like water waves
- So okay, light is a wave since it exhibits wave behaviour. But we also know light is made up of particles (photons). So light is nutty... light, like all matter, is actually a quantum particle, which exhibits both wave AND particle aspects (wave-particle duality)
- But that's not all there is to the quantum strangeness... what happens when you fire electron (quantum) particles? Same interference pattern even though you detect individual electron "particles" at the other end!
- Well, then electrons are also waves and that's the end, right? No! Reduce flow to a single electron (or photon) at a time and you still get the same pattern build up over time!
- And we definitely pick up particles at the other end (particle detectors)
- Each particle somehow knows where it should go... welcome to the quantum reality, welcome to the real nature of existence itself, which will (hopefully) reveal itself through this course...
- Summary of Important Equations to understand for the HW:
- Δ → means Change in
- v = Δd/Δt = df - di/tf - ti
- a = v/t
- ac = v2/r
- d = ½at2
- vavg=(vf + vi)/2
- REMEMBER, v is always equal to the slope of the x vs. t graph
- Basic Skills Review: http://www.easyphysics.net/ch1/ch1.htm
- Tips for Students:
- Keep up with the reading!
- Lots of reading, lots of homework, lots of quizzes... in short, this class, like learning physics in general, will require a LOT of work!
- But if you keep up with the work, you're guaranteed to do well.
- Don't worry about taking copious notes as the lecture notes will always be available online. But, make sure your notes contain the main points and important terms.
- Learning Physics is like learning a new language. And, just as every new language has a new vocabulary, you should pay careful attention to new, or frequently used, terms. Don't assume that because you use a word every day you know it's scientific definition. Often, a word will be used in a much more restricted, more precise, and unambiguous manner in science and its meaning will be very different from its common definition.
- What is science?
- Process of seeking and applying knowledge about the universe
- Body of knowledge we've amassed about the universe
- Pursuit of knowledge for its own sake & applications
- Why study Physics
- Learn how world around you works
- Learn how to think critically (like a scientist)
- Insight into nature of existence
- Ancient man lived in a mysterious & magickal world but with little certainty or predictability (or, for that matter, control)
- Technology gives us all of the latter but physics gives us back the magick.
- Those who held specialized knowledge of the magickal incantations were
priests. Modern-day priests are, no doubt, the scientists who truly
understand the basis of the technologies that define and govern our
everyday world. So the irony is that our world truly is more magickal
than anyone suspected but only the priests are truly aware of it.
- Long ago, the world was filled with more magick... but it was a magick that arose from ignorance and not some secret knowledge of the universe or existence. The amount of magick being inversely proportional to the amount of technology.
- Those who held specialized knowledge of the magickal incantations were
priests. Modern-day priests are, no doubt, the scientists who truly
understand the basis of the technologies that define and govern our
everyday world. So the irony is that our world truly is more magickal
than anyone suspected but only the priests are truly aware of it.
- This class isn't just about equations, calculations, etc. That is a vital part of physics, no doubt. But true physics, or for that matter, any true science, is about the wonder & mystery of nature!
- And that deepest of insights into the very nature of existence is what this class should give you.
- My job is to tell you about the physics; your job is to always make sure i'm doing that
- Scientific Method
- 1. Careful observation of a phenomenon
- Car won't start
- 2. Form a hypothesis
- Battery is dead!
- 3. Devise an experiment
- Turn on radio or lights
- 4. Outcome may lead to modification of hypothesis
- Maybe it's the distributor?
- 5. Experimentally verified hypothesis becomes theory/law
- You've got a POS car
- Scientific approach, or scientific method, helps standardize and systematize logical reasoning you already do so that you can extend the applicability of that kind of critical thinking to everyday situations and experiences.
- Ability to think critically, systematically, and experimentally (honestly and postjudiciously -- looking at only the data and willing to accept what the data tells you)
- 1. Careful observation of a phenomenon
- Language of Physics:
- Vocabulary - New terms
- Syntax - Mathematical equations
- Grammar - Theories or Laws
- Measurement of Physical Quantities -- Quantifying
Nature. A major part of the scientific method is experimentation
and testing. In order to test Nature we need to measure, or
quantify, Nature.
- Must be unambiguous and precise -- i.e., mathematical rigor
- Measurement yields quantitative information -- i.e., a number and a unit of measure.
- Complete measurement is BOTH a number and a unit of measure
- Unit of measure is standard used in measurement (e.g., meters or kilograms in metric system)
- Physics quantifies three basic things: space,
time, and matter -- these make up the fabric of
physical reality/existence
- distance, time, and mass & charge are fundamental quantities (there are more but we'll only look at these in this course)
- Hard to define them since they're so basic
- E.g., St. Augustine (5th century BCE): "What then, is time? If no one asks me, I know what it is. If I wish to explain it to him who asks me, I do not know."
- "Time and space, succession and extension, are merely accidental conditions of thought. " -- Oscar Wilde
- "Time and space are modes by which we think and not conditions in which we live." -- Albert Einstein
- distance: measure of space in one dimension
- Choose unit appropriate to scale
- Numerical Measurement == Number x Unit of Measure
- 23 meters = 23 x 1 meter
- Unit conversion (from one system of units to another):
- 1 meter = 3.28 feet → 1 = 3.28 feet/1 meter (Conversion FACTOR → Conversion RATIO)
- 23 meters = 23 x 1 meter = 23 x (3.28 feet/1 meter) meter
- 23 meters = 75.4 feet
- In Class Exercise:
- Calculate number of seconds in 5 hours
- Answer: 3 steps
Known Unknown t = 5 hours t = ??? secs 1hour = 60mins 1min = 60sec - Lookup the appropriate conversion factor (60min = 1hr)
- Create unitless, dimensionless one (60min = 1hr ⇒ 1 = 60min/1hr). Now divide by unit you want to eliminate (divide by hr) to create the conversion ratio
- Now just multiply the number and
units SEPARATELY and cancel/simplify
what you can
- Differentiate between unit of measure and number of units (unit of measure: hour; number of units: 5)
- Answer: 3 steps
- Calculate number of seconds in 5 hours
- Derived units
- Area == size of surface of a solid
- Volume == size of solid (space occupied by it)
- All physical quantities will have units derived from fundamental quantities
- The measure of time is based on periodic phenomena -- processes that repeat over and over at a regular rate.
- Nothing absolute; relative to variations of another (we gave up on "knowing" what time is)
- Period: time for 1 complete cycle of a periodic process (T)
- Frequency: number of cycles per unit time (f or n)
- Mass = measure of inertia
- Also measure of how much matter there is
- Different from weight!
- Measured in kg or slugs
- Motion is the key to everything → relates two of the three
fundamental quantities (without motion, electrons stop, we stop,
time dilation, length contraction, etc.)
- Zeno's Paradox
- Motion is impossible; cannot go from point A to point B
- Accounts for Fundamental space
- But forgot Fundamental time is also essential to motion
- Speed = rate of movement (change of distance)
- Speed is relative
- Person running on ship (see Fig 1.12 on p. 15)
- Average speed
- Over a significant (large) time interval; just how big large is depends on the particular problem at hand
- Instantaneous speed (speedomenter) → need calculus to calculate it
- Greek letter delta (Δ) → means Change in
- Δd = df - di
- v = Δd/Δt
- Notice that, if you're computing the velocity between two points, the line connecting them is a chord, the slope of which is the average velocity (Δx/Δt = rise/run = slope). As you take the limit as Δt → 0, the chord starts to become the tangent at that point and the instantaneous velocity at that point is the slope of that tangent line! When v = constant, the slope of the chord is the slope of the tangent and vavg = vinstantaneous → REMEMBER, v is always equal to the slope of the x vs. t graph
- Speed is relative
- In Class Exercise:
- Convert 20 m/s to mph (1 m/s = 2.24 mph)
Known Unknown v = 20m/s v = ?miles/hour 1m/s = 2.24miles/hour
- Convert 20 m/s to mph (1 m/s = 2.24 mph)
- Speed constant → average velocity = instantaneous velocity
- Constant Velocity: think of cruise control or the bus in speed
- d is proportional to t
- v is constant of proportionality (d = vt)
- Velocity = speed AND direction
- Speedometer + compass
- Vectors vs. scalars (time, mass, volume)
- displacement vs. distance
- Vector Addition
- 1st transparency (Fig. 1.17)
- Moving vectors & Pythagorean theorem & components
- 1st transparency (Fig. 1.17)
- Classical Physics vs. Modern Physics:
- Classical physics is familiar and describes ordinary, macroscopic phenomena
- Modern physics, on the other hand, shows that there's very weird stuff at heart of reality
- QM and Relativity describe the very small and very fast
and both are very weird (no such thing as particle or
wave; no solidity; no definite knowledge, etc.)
- Relativity affects all fundamental quantities of space, time, AND mass -- e.g., time is measured relative to periodic phenomena.
- Relativity therefore affects everything else
- Everything is relative, including speed
- Acceleration = rate of change of velocity (Δv/Δt)
- Also a vector
- Accel::Velocity as Velocity::Distance
- Think of a friend that tells you his car goes from 0mph - 60mph in 5sec... that's acceleration!
- Accel::Velocity as Velocity::Distance
- Units of m/s2 (dimensional analysis):
- v → m/s
- t → s
v m/s m m a = --- ==> ----- ==> ----- ==> ----- t s s*s s2
- One word, acceleration, for increase, decrease, and change in direction
- Also a vector
- Centripetal (center-seeking) Acceleration
- Acceleration (and Δv) towards center (perpendicular to v) -- Fig 1.24 on p. 25
- ac = v2/r
- ac proportional to both v2 and r
- What's important to get from equations is a sense of proportionalities and what it means; i.e., don't memorize it but instead try to get a sense for it (e.g., if p goes up, T has to go up; if p goes down, V has to go up (in pV=nRT))
- Present 2nd transparency: Concept Map 1
- Start from center/beginning
- Follow relationships
- Many possible representations
- Uniform Motion == constant velocity
- Words: distance increases 7m per second (Fig. 1.26 on p. 27)
- Mathematically: d = 7t (d = vt)
- Table: on p. 27
- Graph: 3rd transparency (Fig. 1.27)
- Directly proportional quantities have straight lines
- Slope of d vs. t graph == velocity
- Even when velocity is not constant, slope of d vs. t graph still == velocity
- Dimensional Analysis: E.g., if you forget that, when
there's constant acceleration, the distance gone in a
certain amount of time is d =
½at2 and instead think it's d =
½at, then dimensional analysis will let you
know you were off
- Dimensional Analysis: only look at units. E.g.,
d = ½ at2 → [m/s2][s]2 = [m]
- Dimensional Analysis: only look at units. E.g.,
- Constant acceleration
- slope of v vs. t = a
- v = at -- drop something off Empire State Building and you'll know exactly how fast it's going after a certain amount of time
- d = ½ at2 (parabola: velocity
(slope) increasing with time) -- throw something off
Empire State Building and, if you know how long it took to
fall, you can figure out exactly how high it is
- If you drop something off from rest, you can also determine the distance by using d=vavgt, where vavg=(vf + vi)/2 and vi=0 and vf=at (velocity it's going at the end)
- Tips for using graphs:
- For d vs. t graphs: straight line means velocity is constant
- For v vs. t graphs: straight line means acceleration is constant
- Downward slope = negative velocity or acceleration
- See Fig. 1.35 on p. 31 at 25ms.
- Zeno's Paradox