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Physics 214: General Physics
Professor: Ricky J. Sethi Instructor Info

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Lecture Notes for Chapter 4

  • Reading Memo Insights:
    • Why can gases be compressed much more readily than solids or liquids?
    • On the subject of matter, what is electricity? Is it only electrons or is it a charged particle?
    • How can gases be considered fluids?
  • Summary of Important Equations to understand for the HW:
    1. p = F/A (Force density)
    2. D = m/V
    3. w = mg
    4. Dw = w/V
    5. FB = weightdisplaced fluid
  • So far, we've dealt with the consequences of the first two fundamental aspects of physical existence/reality: space and time...
    • We first studied how space and time are related to each other → this led us to the idea of velocity, or motion, which is the essence of everything that happens.
    • We then moved from kinematics, or the study of motion, to the causes of motion: Forces (or dynamics).
    • Forces were "paid" for with Energy and we found out that this strange, abstract concept underlies all of existence and, in a very real sense, everything is a form of energy (e.g., even a vacuum has energy)
  • Now we turn our attention to the 3rd, and final, fundamental quantity of nature/existence: matter
    • Matter is anything that has mass and occupies space
    • Alchemists
      • Silly quest changing Pb ⇒ Au?
      • Many famous people (including Newton) were alchemists
        • A lot of his hidden (and destroyed) notes dealt with alchemy
      • Al-chemy is the Arabic source of the word (and field) of chemistry
        • Radioactivity changes one element to another
    • What are elements?
      • Fundamental form of matter (sorta) is the atom -- there are actually many different kinds of atoms
      • Atoms are made up of protons, neutrons, and electrons
        • Turn-of-century model: Plum-pudding
        • Replaced by: Solar System Model
        • Current QM model: energy levels
          • The different models of the atom are all valid within the limits of their applicability, just like Newton's laws are perfectly reasonable as long as your speed is nowhere near the speed of light.
          • Also, there are many different models for things depending on current technology (e.g., brain was modeled after drainage system in Roman times, automatons moved by water by Descartes (pineal gland), telephone switchboard at turn of last century, computer in more recent times, etc.).
          • Everything you've learned in school as "obvious" becomes less and less obvious as you begin to study the universe. For example, there are no solids in the universe. There's not even a suggestion of a solid. There are no absolute continuums. There are no surfaces. There are no straight lines. -- R. Buckminster Fuller
      • The number of protons in an atom determine its identity
        • Rutherford scattering gave proof of a massive nucleus
        • Protons are 1000 times more massive than electrons
        • Simple realization of Alchemy -- change # of protons ⇒ change element!
    • Compounds are combinations of molecules or atoms
      • Molecules are 2 or more atoms bonded together with electrical forces (Coulombic attraction and also QM)
      • The properties of the compound are different from the properties of its elements
        • NaCl -- Na+ deadly, NaCl not
      • Organic compounds/molecules form the basis of life
        • Organic chemistry is the chemistry of carbon compounds
    • Mixtures and solutions are made up of atoms & molecules that are mixed but still separate!
      • The key is that they're not bonded together (at least not to any significant degree)
    • Atoms are about 2x10-10 m (H atoms are on the order of 1 Angstrom)
      • If you expand a golf-ball to the size of the Earth, each atom would be the size of a golf-ball
      • Smallest visible particle contains more atoms than all the people on Earth
      • About 100,000 Billion Billion atoms in a fingernail
        • You can estimate the size of an atom using a simple experiment (see Colin Bruce's Sherlock Holmes solves The Einstein Paradox):
          1. Measure the volume of some oil in a beaker
          2. Pour the oil over a pan containing water
          3. Divide the volume by the area to get the height of a single atomic layer (the approximate diameter of an atom)
    • Electrons and protons exert electrical forces on each other
      • These forces determine the properties of the atoms (e.g., bonding, etc.)
      • Electricity is the flow of any charged particle (usually, e-, ions, etc.)
      • Nuclear forces come into play under extreme conditions only
    • Atoms are essentially indestructible
      • Only destroyed/changed in nuclear reactions
        • Their nuclear structure, that is... they're ionized and bond with each other all the time
      • Everything on Earth is composed of debris from exploding stars
        • Like the Joni Mitchell ("we are billion year old carbon") or Moby (We are all made of stars) songs
      • Atoms are thus primarily recycled on Earth
        • Our atoms could have been part of a dinosaur or Leonardo DaVinci
  • Different forms and phases of matter
    • Four phases of matter:
      • solid
        • rigid and retains shape (when no external forces) -- atoms are tightly bound (imagine they're connected with stiff springs)
      • liquid
        • Each atom/molecule can move about and vibrate -- imagine they're connected (bonded) with loose springs
          • Flows easily and conforms to the shape of the container
        • Has a well-defined boundary/surface
        • Greater density than gases
      • gas
        • Also flows readily and conforms to the shape of the container
        • Does not have a well-defined surface
        • Can be compressed readily
          • The atoms are spread apart and little interaction between atoms
          • The atoms only interact when they actually collide
          • The attractive forces between the atoms are too weak to bind them together
      • plasma
        • Same as gases but conducts electricity
        • Interacts strongly with magnetic fields
        • Exists only at high temperatures
      • superfluids (possibly)
    • Phases can change with temp and pressure
      • Usually measured at STP
    • Example of water boiling on a mountain
    • Solids can form geometric patterns called crystals
      • C60 forms buckminsterfullerene (soccer ball)
      • Liquid crystals in between solid and liquid (LCD's)
        • Carbon and H2O are unique (and basis for life)
        • Boundaries between the different phases is also strange
          • What is a chair? Well, a chair is a certain thing over there... how certain? The atoms are evaporating from it from time to time -- not many atoms, but a few -- dirt falls on it and gets dissolved in the paint; so to define a chair precisely, to say exactly which atoms are chair, and which atoms are air, or which atoms are dirt, or which atoms are paint that belongs to the chair is impossible. -- Richard P. Feynman, Vol 1, Lec 12
        • Collisions of high-speed atoms or molecules cause gas pressure in tires
          • The weight of the car is supported by the collisions of air molecules with the wall of the tires
    • Pressure
      • Archimedes and King Hiero
        • Crown (never made before) made of pure gold or gold + silver?
      • Pressure is an extension of Force p = F/A -- Force density
        • Forces are usually spread over a surface
        • Force applied perpendicular to a surface gives rise to pressure
        • Pressure is a scalar
          • Same pressure in every direction (like a height)
        • Units of N/m2 = Pa with 1 psi = 6,900 Pa
          • In-Class Exercise 1: Convert 1 lb/in2 = ??? lb/ft2
            Known Unknown
            p = 1lb/in2 p = ?lb/ft2
            12in = 1ft
            • Ans: 144 lb/ft2 ⇒ 1 psi on 1 in2 is caused by 1 lb -- BUT -- 1 psi on 1 ft2 is caused by 144 lb!
        • In-Class Exercise 2: A 160-lb person stands on a floor. If the area of each shoe is 20 in2, what is the pressure on the floor of one shoe (assume weight is divided equally among both feet)? How much is it when all weight on one shoe? Finally, how about if you stand on a heel that's 0.5 in x 0.5 in
          Known Unknown
          Fone foot = 80lb pone foot = ?lb/in2
          Aone shoe = 20in2
        • Pressure is a measure of how "concentrated" a force is
        • Same force causes much higher pressure when it acts over a smaller area
      • Gauge pressure is relative to the outside air (which is at 14.7 psi)
        • Gauge pressure goes to zero when outside pressure = inside pressure (tire deflates)
      • Volume decreased ⇒ more collisions ⇒ more pressure
      • pV = constant
        • volume inversely proportional to pressure ⇒ Volume goes down = Pressure goes up
    • Density
      • Density is an extension of Mass
        • mass density: D = m/V ⇒ measure of concentration of matter
        • Mass density of solids and liquids fairly constant
        • D of gases varies greatly
          • Volume decreased ⇒ increased pressure ⇒ increased mass density
      • Can use D to calculate m = D x V
      • Weight Density = Dw = mg/V = Dg
        • Can be used to calculate weight
        • w = Dw x V
        • In-class Exercise 3: Compute mass of air in a room measuring 12 m x 16 m x 8 m (use table 4.4 on p. 139). Then compute the weight of that air.
          Known Unknown
          Vroom = 12m x 16m x 8m mair = ?kg
          Dair = kg/m3
    • Fluid Pressure and Gravity
      • Answer to Reading Memo: A fluid is any substance that flows easily
      • Fluid pressures act in all directions
      • We live in a sea of air: the atmosphere
        • Air exerts pressure on everything
        • Air pressure varies with altitude
        • Pressure caused by force of gravity
      • Force of gravity causes pressure in a fluid to vary with depth only
        • Example of holes poked in a 2-liter bottle of soda
        • Speed of water spout same for all holes at same level
        • pA = F = ma = m dv/dt ⇒ dv = (pA dt)/m
      • Height of column of water determines pressure on area at bottom (see Fig. 4.24 on p. 142)
        • p = F/A = Wcol /A = DwV/A = Dwh = Dgh (gauge pressure in a liquid)
      • Graph of p vs. depth is a straight line
        • Makes sense since increased depth = more mass above you
          • This is why divers get the bends (caisson disease); breathe high-pressure air being pumped in from above or in their tanks; at high pressures, Nitrogen gets dissolved into blood (normally doesn't); when they resurface, Nitrogen then wants to flow back out and if you come up too quickly, it bubbles out instead of coming out nice and slow and back out through lungs. Also, pressure difference between outside air and inside your head causes stuffing of ears in flights (released by rebalancing of pressures via the Eustachian tube which runs from your nasal cavity to inner ear).
      • Transparency 1: Fig. 4.26 on p. 143
        • pressure depends on density and height: p = Dwh
      • Barometers measure pressure
        • Pressure at any elevation depends on weight of all air above it
          • Air gets thinner (pressure lesser) with altitude (Fig. 4.27)
        • Air removed from tube
        • Pressure on mercury in bowl transmitted to mercury in tube
          • Mercury column rises
        • It is NOT a vacuum sucking up the liquid
          • It's the air pressure pushing DOWN on the liquid
        • Walls of grain silos reinforced near bottom because pressure is higher there
          • Force of gravity pulling on all the material above causes this pressure
    • Archimedes' Principle
      • Why does the Queen Mary float? Heavy metal yet still afloat?
      • Pressure at any depth pushes in all directions -- Because p is a scalar!
        • Including upwards
        • This upward pressure has corresponding force (p = F/A)
        • This upward Force exerted by a liquid is called a Buoyant Force
      • Transparency 2: Fig 4.31 on p. 146 -- Consequence of Fb:
        • If Fb > wobject, net force results upward
        • If Fb < wobject, net force results downward
          • But net downward force is still reduced!
            • Scale reading of weight = Actual weight - Fb
        • Fnet causes object to accelerate until Ffr offsets Fb and a terminal speed is reached
      • Transparency 3: Fig 4.32 on p. 147 -- Why is there a Fb?
        • Pressurelower surface > Pressureupper surface
        • Since p=F/A, Fup > Fdown
        • Difference in fluid pressure on surfaces causes a net upward force
      • Archimedes' Principle: Fb = weight of displaced fluid (fluid at rest)
        • Fb doesn't depend on substance; only on how much fluid it displaces
        • Weight of object doesn't determine if it will float -- The density does!
          • If Dobject < Dwater, then weight of displaced water > weight of object
        • Question: does shape matter when displacing water and floating (i.e., in Fb) more than just the volume? Nope, only volume displaced is essential... see also http://www.getsmarter.org/mstv/L3_d.cfm
        • This is why Queen Mary floats: average density is < Dwater
        • In-class Exercise 3: how much volume must a raft with a total weight of 300lbs displace? See Example 4.8 on p. 152
          Known Unknown
          wraft = 300lb Vraft = ?ft3
          Dw of water = lb/ft3
    • Pascal's principle for fluids at rest (not accelerated)
      • Any pressure by a force is transmitted throughout fluid in all directions -- Since p is a scalar!
        • Think of pressing a toothpaste tube
      • Since true, pressure on one piston transmitted to another
      • p1st piston = F1/A1 = p2nd piston = F2/A2 (see Fig. 4.40 on p. 153)
        • p1st piston = p2nd piston since p is a scalar!
          • This is something like a lever (F1d1 = F2d2) -- like our example of 1psi → 1psf
            • A small force over a small area leads to a certain pressure. But, if that same pressure is created over a larger area, you need (or generate) a much larger force!
    • Bernoulli's Principle applies to moving fluids