Matter

1
Matter

• Chapter 4

2
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?

3
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

4
The story so far

• 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)

5
Now we turn our attention to the 3rd, and final,
fundamental aspect 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

6
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

7
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!

8
Compounds are combinations of molecules or atoms

• Compounds like 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) like they
  are in compounds

9
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)
• Measure the volume of some oil in a beaker
• Pour the oil over a pan containing water
• Divide the volume by the area to get the height
  of a single atomic layer (the approximate
  diameter of an atom)

10
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

11
Atoms are essentially indestructible

• Only destroyed/changed in nuclear reactions
• Changes in 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

12
Different forms 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

13
Four phases contd.

• 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
• Exists only at high temperatures
• Interacts strongly with magnetic fields
• superfluids (possibly)

14
Examples

• 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)

15
Continued

• 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

16
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

Same pressure in every direction
SCALAR
VECTOR 60mph North
17
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 Therefore, 1psi on 1 in2
is caused by 1 lb -- BUT -- 1 psi on 1 ft2 is
caused by 144 lb!
144 lb
1 lb
Pressure on BOTH is 1 psi! (stilletos are lethal!)
1 ft2
1 in2
18
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 from one shoe (assume the weight is divided
  equally among both feet)? How much is it when all
  the weight is on one shoe? Finally, how about if
  you stand on a heel that's 0.5 in x 0.5 in

Known Unknown


pone foot ? lb/in2
Fone foot 80lb
Aone shoe 20in2

• P F/A 80lb/20in2 4psi

19
Pressure Force / Area

• 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)
• Decreased Volume ? more collisions ? more
  pressure since pV constant
• Volume is inversely proportional to
  pressureVolume goes down ? Pressure goes up

20
Density

• Density is an extension of Mass
• mass density mass per unit Volume ? D m/V ?
  measure of concentration of matter
• Mass density of solids and liquids fairly
  constant
• D of gases varies greatly
• Decreased Volume ? increased pressure ? increased
  mass density
• Can use D to calculate mass m D x V
• Weight Density Dw weight/Vol mg/V Dg
• Can be used to calculate weight
• w Dw x V

21
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


mair ? kg
Vroom 12m x 16m x 8m
Dair kg/m3

• D m/V
• ? m DV
• w mg

22
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 on the mass
  of ALL the fluid above it
• 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)

23
Examples

• 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

24
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

25
Contd.
Weight of displaced water FB
Weight of object w mg

• Transparency 2 Fig 4.31 on p. 146 -- Consequence
  of Fb
• If Fb gt wobject, net force results upward
• If Fb lt 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

26
FB

• Transparency 3 Fig 4.32 on p. 147 -- Why is
  there a Fb?
• Pressurelower surface gt Pressureupper surface
• Since pF/A, Fup gt 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 lt Dwater, then weight of displaced
  water gt 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/ms
  tv/L3_d.cfm
• This is why Queen Mary floats average density is
  lt Dwater

27
In Class Exercise 4

• How much volume must a raft with a total weight
  of 300lbs displace in order to float? See Example
  4.8 on p. 152

Known Unknown


Vraft ? ft3
wraft 300lb
Dw of water lb/ft3

• Dw w/V ? V w / Dw

28
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 ? 144psf
• 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!

29
Bernoulli's Principle applies to moving fluids

• When a fluid speeds up, pressure is lower where
  fluid is flowing faster
• Conservation of Energy approach good but think of
  it from atomic perspective
• F/A is Force from random collisions of molecules
  with Area of wall or pressure gauge
• More particles moving cooperatively forward means
  less sideways pressure

30
Misc. Bernoulli Links

• But forward pressure is greater (when the
  increased KE (since lowered pressure potential
  energy at site of tube constriction or narrowing)
  particles hit something, stop, and exert a F --
  since KE Work F d) -- see
  http//physics.bu.edu/py105/notes/Bernoulli.html
  and http//www.grc.nasa.gov/WWW/K-12/airplane/bern
  .html and http//frances.phy.cmich.edu/people/osbo
  rn/Physics110/book/Chapters/Chapter9.htmB and
  equation of continuity (http//oldsci.eiu.edu/phys
  ics/DDavis/1150/11FldMtn/cont.html)