#### Transcript The BIG Picture

Conceptual Physics Lesson 1: The BIG Picture We begin with a little philosophy… There are schools of philosophy that maintain… • The only reality we can be sure of is that within our individual minds (eg. Kant, the Idealists) • The only reality is that which we can observe with our senses or measure with our instruments (eg. Empiricists) • The physical world provides evidence of a non-physical world that exists beyond the measuring capacity of our instruments (eg. Aristotle, Aquinas) Natural Philosophy Known Properties Of Physical World Metaphysics Self Unknown Properties Of Physical World Possible Non-Physical World Our approach: • There is a physical reality exterior to our minds, which can be analyzed and understood by the sciences of nature, particularly, physics • While allowing for possible non-physical reality, we will confine our studies to the physical world • We acknowledge that there are properties of the physical world we do not yet understand, and the near-certainty that there are properties we have not yet discovered. We may speculate on these. Conceptual Physics Did You Know… The Tabloid News of Physics 95% of the Universe is Missing! Adding up all the observable stuff in the cosmos we have •0.03% heavy elements (everything except hydrogen and helium) •0.3% neutrinos (subatomic particles that are a by-product of solar fusion) •0.5% stars (There are about 71022 stars in the universe) •4% free hydrogen and helium We can only account for 5% of what we believe is out there! •We conjecture that 30% of the remainder is dark matter, a form of matter that helps hold galaxies together, and only interacts with normal matter via gravity •The remaining 65% is dark energy, a seeming force which is pushing galaxies apart from one another at an accelerating rate The universe is expanding at an ever increasing pace! Is our end to be a lukewarm muddle of maximum entropy? Time stops at the borders of black holes! Nobody knows what goes on down there! Empty space is a writhing mosh pit of virtual particles! Subatomic particles can interact faster than the speed of light! The ultimate physical reality may consist of vibrating 11dimensional strings! It’s possible that our universe is just one of an infinite number of universes that interact gravitationally! Conceptual Physics Physical Existence String Theory (??) The Stuff of Existence Loose Packaged Energy Matter Relativity (E = mc2) Fields (Stationary) & Waves (Traveling) Subatomic Particles (“Stationary” Or Traveling) Quantum Mechanics, (Wave/Particle Duality) The 4 (5) Forces: Gravity Electromagnetic Strong Nuclear Weak Nuclear (Dark Energy) Atomic Constituents: Protons, Neutrons & Electrons (Attraction/Repulsion) Electromagnetism, Light, Astrophysics, Nuclear Physics Kinetic Energy Atoms Condensed Matter, Planetary Science Thermodynamics, Mechanics, Sound Molecules Chemistry Crystals Electronics, Computers Organic Molecules Life Biology Conceptual Physics Why Math & Calculations Normal Physics Courses are heavy with calculations In Conceptual Physics we minimize the calculations, but some skill in physical calculations is required There are key physical relationships you need to know (eg. force = mass * acceleration, energy = force * distance), as well as key concepts like vectors Energy fields and matter particles do not have little formula rule books that dictate their behavior—they simply act as their nature drives them to act. But we observers have found physical laws that consistently predict energy and particle behavior—to within the accuracy we can measure things Our measurements become increasingly sensitive. If we find discrepancies between observation and behavior, we need to refine—or completely change—our mathematical models to realign to physical measurements For example, Einstein’s Special Theory of Relativity is a refinement of Newton’s Laws of Motion for high speed objects, but it radically altered our understanding of the universe. The discovery of atomic structure forced physics to radically change its approach to very small scale physics—giving rise to quantum mechanics Conceptual Physics Units of Physical Measurement There is a bewildering array of physical units (eg. pascals, amps, newtons, ohms, joules, etc.) we encounter in undergraduate physics that are utilized in specialized sub-disciplines like electronics, fluid dynamics or thermodynamics Almost all of these can be reduced to simpler units involving: length (meters, m), time (seconds, sec), mass (kilograms, kg), charge (Coulombs, C), and Temperature (degrees Kelvin, K) For example: (in the MKS unit system) Force: Energy: Voltage: Resistance: newtons = kg m / sec2 joules = kg m2 / sec2 volts = kg / C*sec2 ohms = kg / C2*sec When making calculations, keeping track of units is important: • You want to know what your answer signifies (is it energy, volts, pressure, etc…) • It helps you check for mistakes in reasoning (eg. if you expect volts and end up with ohms) • It protects your Mars Orbiter from missing the planet (this really happened…) Conceptual Physics Formulae Notation (MKS units): t = time (seconds, sec) d = distance (meters, m); h: height, z: depth m = mass (kilograms, kg) v = speed (meters/second) c = speed of light in a vacuum a = acceleration (meters/second2) g = acceleration due to gravity (earth surface) 2 F = force (newton = kg m/sec ) p = momentum (kg m/sec) E = energy (kg m2/sec2) = work = KE = PE = thermal & chemical energy (calories) P = power (watt = kg m2/sec3) Q = charge (coulombs); R =resistance (W, ohms) I = current (amp = coulombs/sec) V = voltage (volt = watts/amp = kg m2/(amp sec3) l = wavelength (meters/cycle) f = wave frequency (Hertz, Hz = cycles/sec) A = Area (m2) V = volume (m3) r = Density (kg/m3) n = index of refraction (unitless) 2 P = Pressure [ pascal = kg/(m*sec ) ] T = temperature (K, degrees Kelvin) Formulae: Distance Velocity d = vt; v = at Force F = ma; Momentum Impulse p = mv Momentum of a photon: p = h/l = hf/c (h = Planck’s constant) FDt = Dp = D(mv) = total change of momentum due to a given force d = at2/2 For non-zero initial speed v0: d = v0t + at2/2 For non-zero initial speed v0: v = at + v0 No change of motion if: S F = 0 Hooke’s Law (spring restoration): F = -k Dx Gravitational Attraction: F = G m1 m2 / d2 Electrostatic Attraction: F = k q1 q2 / d2 (Not k in Hooke’s Law) Weight at Earth’s surface; weight = F = mg (g = 9.8m/sec2) Energy: Work W = Fd Energy of photon: E = hf (h = Planck’s constant) 2 Kinetic Energy: KE = ½ mv Gravitational Potential Energy: PE = mgh (earth surface, h = height) Heat transfer: Q’ = CSHmDT Einstein’s energy equation: E = mc2 Power P=W/t Electrical Power P = IV (watts = joules/sec) Wave frequency: f = (1 / wave_period) (unit: Hz = sec-1, cycles per second) Relationship between speed (v), frequency (f) and wavelength (l): fl = v (light: fl = c) Wavelength of a particle: l = h/mv = h/p (h = Planck’s constant) Speed of light in a transparent medium with index of refraction n: v = c / n Density Pressure r=m/V Current I=Q/t Engine_efficiency = 100% * (Thigh – Tlow ) / Thigh P=F/A Pressure at depth z: P = r g z n = #gas moles Ideal Gas Law: P V / T = nR = constant for #moles R = Universal Gas Constant (not electric resistance) Resistance (R): V = I R Uncertainty Principle: Dx Dp > h, DE Dt > h (h = Planck’s constant) Special Relativity factor: f = sqrt( 1 – v2/c2 ) < 1, time_obs = f t, mass_obs = m / f Conceptual Physics Web Resources Textbook’s student web site http://bcs.wiley.com/he-bcs/Books?action=index&itemId=0471150584&bcsId=1907 Hyperphysics: Good resource: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html Wikipedia: For anything (trust but verify): http://en.wikipedia.org/wiki/Main_Page Powers of Ten: http://microcosm.web.cern.ch/Microcosm/P10/english/welcome.html http://www.youtube.com/watch?v=s1jd8AgjP9k http://www.powersof10.com/ Atomic Orbitals: http://www.chemguide.co.uk/atoms/properties/atomorbs.html http://www.falstad.com/qmatom/ http://www.chemistry.wustl.edu/~edudev/Orbitals/movie.html Fun Science & Optical Illusions: http://www.skytopia.com/project/illusion/illusion.html http://www.skytopia.com/