MatterChapter 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

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)

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

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

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

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)

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 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

Different forms & phases of matter Four phases of matter:

1. solid rigid and retains shape (when no external forces) -- atoms are

tightly bound (imagine they're connected with stiff springs)

2. 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

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)

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)

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

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

SCALAR

VECTOR = 60mph North

Same pressure in every direction

In Class Exercise #1: Convert 1 lb/in2 = ??? lb/ft2

Known Unknown

p = 1lb/in2

12in = 1ft

p = ? lb/ft2

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!

1 in2

1 lb

144 lb

1 ft2

Pressure on BOTH is 1 psi!(stilletos are lethal!)

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

P = F/A = 80lb/20in2 = 4psi

Known Unknown

Fone foot = 80lb pone foot = ? lb/in2

Aone shoe = 20in2

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 pressure;

Volume goes down Pressure goes up

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 = D*g

Can be used to calculate weight w = Dw x V

Density

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.

D = m/V m = D*V w = m*g

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 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)

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

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

Contd.

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

Weight of displaced water =

FB

Weight of object = w = m*g

FB

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 #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

Dw = w/V V = w / Dw

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 → 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!

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

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/osborn/Physics110/book/Chapters/Chapter9.htm#B and equation of continuity (http://oldsci.eiu.edu/physics/DDavis/1150/11FldMtn/cont.html)