Motion

1. Motion Chapter 1

2. Introduction to Motion (Ch. 1) • (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 • When a scientist says a theory was wrong, they don't mean all the scientists were duped by nature and completely misled; it just means the model or theory was applicable under a certain, limited set of constraints and conditions and a more general description/understanding is needed for broader conditions. • 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...

3. 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://easyphysics.netfirms.com/ch1/ch1.htm

4. 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.

5. 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 • Science is done by EVERY one! • Science is any human enterprise that: • Provides insight into nature and how it works • Makes predictions of what should happen • Uses feedback to improve itself

6. 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. • 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

7. The Scientific Method • Careful observation of a phenomenon • Car won't start • Form a hypothesis • Battery is dead! • Devise an experiment • Turn on radio or lights • Outcome may lead to modification of hypothesis • Maybe it's the distributor? • 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)

8. Language of Physics: • Vocabulary - New terms • Syntax - Mathematical equations • Grammar - Theories or Laws

9. Scientific method rests on testing • A major part of the scientific method is experimentation and testing. In order to test Nature we need to measure, or quantify, Nature. • Measurement of physical quantities must be unambiguous and precise -- i.e., exhibit 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 the standard used in measurement; In the SI or metric system: • Length is measured in meters [m] • Mass is measured in kilograms [kg] • Time is measured in seconds [secs]

10. Physics quantifies three basic things: space, time, and matter • Space, time, and matter make up the very 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

11. Because they’re so basic… • They’re hard to define! • Like Love… everyone knows what love is but can you define it? • More than likely no… but it doesn’t stop us from: • Categorizing it relative to other kinds: love of family, love of spouse, love of kids, etc. • Measuring it relative to others: Love for your family is different from love of a car or a movie, etc. • Quantifying it relative to others in the same category: Do you love your car more than your friend’s? Etc. • We end up doing the exact same classification, measurement, and quantification with the fundamental aspects of Nature • Love is just a human emotion but space, time, and matter are the very basis of existence itself! • So it’s even harder to precisely and exactly define them

12. distance: measure of space in one dimension • Always choose a unit appropriate to the 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

13. Calculate the number of hours in 18,000 seconds Setup Known-Unknown Table: Answer: 3 steps Lookup the appropriate conversion factor (60min = 1hr) 1hour = 60mins and 1min = 60sec Create unitless, dimensionless one (3600secs = 1hr è 1 = 1hr/3600secs) by dividing by the unit you want to eliminate (divide by secs) to create the conversion ratio Now just multiply the number and unitsSEPARATELY and cancel/simplify what you can Differentiate between unit of measure and number of units (unit of measure: hour; number of units: 5) In Class Exercise #1: t = 18,000-secs t = ??? hours 1-hr = 3600-secs

14. Units (continued) • 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 is 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) • Units of secs • Frequency: number of cycles per unit time (f or n) • Units of Hz • Mass = measure of inertia • Also measure of how much matter there is • Mass is different from weight! • Measured in kg or slugs

15. Motion is the key to everything • Relates two of the three fundamental quantities • without motion: electrons stop & we stop, with motion: time dilation, length contraction, etc. • Zeno's Paradox • Motion is impossible; can’t go from point A to point B • Resolution: • Accounts for Fundamental space but forgot Fundamental time is also essential to motion (also, sum of infinite series isn’t always infinite)

16. What is speed? • Suppose you run a race. How do you describe your run to a friend? • Saying that you ran for 20 minutes would not be enough for your friend to tell how fast you went. • What you need to tell how fast you went is your speed. • There are two things you need to describe your speed: • 1. The distance you traveled • 2. The time it took you.

17. Speed = rate of movement (change in distance) • v = Δd/Δt • Greek letter delta (Δ) → means Change in • Δd = df - di • 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 • 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

18. In Class Exercise #2: • Convert 20 m/s to mph v = 20m/s v = ?miles/hour 1m/s = 2.24miles/hour

19. Velocity vs. Speed • When speed is 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

20. 3-m/s 4-m/s Vector Addition Example • Moving vectors & Pythagorean theorem & components • Suppose a man is on a cruise ship that's going East at 4-m/s. • Suppose he gets up and walks North at 3-m/s. • What is the velocity (both speed and direction) of the man relative to an observer on the shore? • Break into components and use Pythagorean:

21. 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 the heart of reality • QM and Relativity describe the very small and very fast and both are very weird (no such thing as a particle or a 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 • These mathematical abstractions (like Copernicus’ HelioCentric theory) sometimes end up actually describing Nature. Mathematical abstractions, when forced into being applied to physical reality, yield uncannily accurate insight into the nature of existence or the physical world

22. What is acceleration? • You speed up • You slow down • You change direction

23. Acceleration = speeding up, slowing down, or turning • Also a vector • Think of a friend that tells you his car goes from 0mph - 60mph in 5sec... that's acceleration! • rate of change of velocity (Δv/Δt) (Accel::Velocity as Velocity::Distance) • Units of m/s2 (dimensional analysis): v → [m/s] and t → [s] • One word, acceleration, for increase, decrease, and change in direction v [m/s] a = --- ==> ------- t [s] [m] ==> ------ [s*s] [m] ==> ------- [s2]

24. 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 v2andr • 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))

25. 2nd transparency: Concept Map 1 • Start from center/beginning • Follow relationships • Many possible representations

26. 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]

27. 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 (this is its speed at the end) • 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)

28. 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.