Review for the 1st midterm

– The test is Monday, Jan. 30, here, 10:30 am

– Bring PURPLE scantron sheet

– #2 pencil (if you have only one, bring #1)

– ONE ONE-SIDED, HAND-WRITTEN page of NOTES is allowed

– ―closed book‖ otherwise

2

Some preliminary remarks

• Types of questions: – Terminology (definitions) - ―easy‖

– Concepts (also definition-type) - ―easy‖ to ―medium‖

– Application of concepts - ―hard‖

• No serious math, but you may have to do some simple arithmetic, after applying a concept. For example: a car goes from stop to 100 m/s in 10 s, what is the acceleration?

• Go through the entire exam, don‘t get stuck! Questions are not arranged according to the level difficulty!

3

Visual Powers-of-10 Representation of the Physical Scales in our Universe

• Caution: Each step on this axis represents 10X increase or decrease in size, not just one more unit

-30 -20 -10 0 10 20

Range of

everyday

experience

Planck

Scale

(Quantum limit)

Current

observational

Limit

Proton

Atom

Amoeba

Size of

Phys 110

Student

WA state

Distance

To Sun

To Nearest

Star

size of

Milky

Way

Visible

Universe

power of 10, i.e. this

means 10-30 meters

Does it even mean anything to look beyond the scales represented here?

This range may be all that matters (pun intended).

4

The Standard Model of Astrophysics

Here‘s our best guess about the origins of Universe (everything!) - as of today:

• The Universe started in a hot Big Bang about 13.7 billion years ago (1.37x1010 y)

• As it cooled, only the lightest elements formed: hydrogen, helium, lithium

• Over time, this material clumped into the structures we see today: galaxies, stars, planets

• All other elements were formed in the cores of stars

– Stellar explosions (supernovae) spread them around

You are made of stardust!

5

Let's take an outward journey

• Logarithmic (powers of 10) scale is deceptive! – We think linearly, because that‘s how we perceive time

– Now let‘s imagine the universe in linear terms…

• Use the speed of light to describe large distances – speed of light c = 300,000,000 m/s; plays a special role in physics

– So distance travelled in 1 sec = 1 light-second = 3x108 meters

• Moon is 1.3 light-seconds away, Sun is 8 light-minutes away

• 1 light-year is about 1016 meters: 60 million million miles

• Think metric! Scientists use SI (Système Internationale) units – 1 meter is about 1 yard

– 1000 meters = 1 kilometer: about 2/3 of a mile

– Everyone in the world except the USA uses SI units!

6

Outward Journey: Solar System

• Let‘s make a scale model: compare how far you can walk to light-speed distance for same times – Moon = 1.25 light seconds away

• Can walk about 3 meters in this time: across living room

– Sun = 8 light minutes

• Walk across campus in this amount of time

– Pluto is 32X farther away than the Sun: 5x1012 m

• 4.5 light-hours

• Walk to from UW to Renton in this time

Su

n

Ear

th

Jup

iter

Sat

urn

Ura

nu

s

Nep

tun

e

Plu

to

Note: mean (average over a year) Sun-Earth distance = 1 Astronomical Unit (AU) Pluto is currently about 32 AU from Earth

7

10,000 Milky Ways would fit in one of these voids

Large-scale structure of the Universe

• Galaxies are not uniformly distributed, but occur in clumps

– mutual gravitational attraction forms lumpy, stringy structures, with huge voids in between

– Cosmologists modelling the evolution of the Universe must reproduce

this clumpiness

Each dot is a galaxy!

Map shows a slice of

the universe, viewed

from „above‟, with

Earth at the bottom.

http://www.archive.org/details/Evolutio2001

8

Telescopes are Time Machines

• More distant galaxies are old galaxies – Takes time for light to travel to us at only 300,000,000 km/s

– 12 billion light years away means we see it today as it was 12 billion years ago

• Bigger telescopes, better technology see farther back in time – galaxies now don‘t look like they used to

• we can see ancient galaxies in the process of forming

• bottom-up construction: built up by collisions/mergers

• Olbers' Paradox (1823): why is the night sky dark? – In an infinite, stable universe, every line of sight would end on

a star, and whole sky would be as bright as the Sun

– Proof that Universe did not exist forever, and/or is expanding!

• Can we see the Big Bang itself, then? – YES, sort of... but not literally

9

Edwin Hubble‘s Expansion Law

• The farther away the galaxy, the bigger the redshift

– Redshift is often compared to the Doppler effect

• Receding train whistle sounds lower-pitched — same idea

– Farther ―faster‖

• Hubble constant: 71 km/sec per Megaparsec (Mpc)

– a parsec (pc) = 3.26 light years: nearest star is 1.4 pc away

» Unit astronomers use when talking to each other instead of ―public‖

– Our ―neighbor‖ the Andromeda Galaxy is ~1 Mpc away

• Just like raisins in a loaf of raisin bread, rising in the oven

– Each raisin moves away from all other raisins

– Farther away = ―moving away faster‖

data

v = H0 d

(H0 = Hubble‟s

Constant)

Hubble at work, c. 1920

10

Close, Far,

Recent Ancient

Cosmic expansion stretches light waves

Light from far away had more time to get stretched

Light from nearby sources gets stretched less

Longer wavelength redder color light from long ago and far away is more redshifted

Earth

wavelength emitted wavelength observed

11

Atoms and their arrangements

• Atoms = basic units of 100+ known "elements‖

• Molecules = different atoms bound together to make all familiar (and unfamiliar) substances: water, salt, DNA, CO2, butter ...

• States of matter:

– Solids (substance with fixed shape): rigidly bound molecules

– Liquids (substance with no shape, but fixed volume): looser bonds

– Gases (substance which expands to fill any volume): unbound molecules

– Today, atoms can actually be ―seen‖:

• Image of individual atoms in Mica (from www.di.com, Digital Instruments)

Atomic Force Microscopy (AFM)

Atoms are about 10-8 = 0.0000001 mm apart

the image is really a graphical display of the atoms' electric fields

12

But … Atoms Are Themselves Composite

As you learned in high school:

• Proton (+ electric charge), p

• Electron (– electric charge), e

• Neutron (no charge), n

• Proton and Neutron have about the same mass

– Tiny mass, about 10-26 kg

– Tiny "size" too: about 10-15 meter (how do we know? Later…)

(‗mass‘ instead of ‗weight‘ – why? What‘s this ‗mass‘? Again, later…)

• Electron is about 2000 times less massive than proton

– Point-like - no measurable extent! (to date)

– Electrical Forces produce attraction between electrons and the protons

• "opposite charges attract" - more on that later, too

• Atom = nucleus (p's + n's), surrounded by cloud of e's

– "Like charges repel" - so how can p's in nucleus stick together?

• "Strong force" between nucleons - much stronger than electric force

+

−

0

13

Nucleus:

6 protons

6 neutrons

Cloud of 6 electrons

"Cloud" of one

electron

(probability of finding it at some point near nucleus)

Nucleus =

1 proton

10-10 m

Elements are identified by number of protons in the atom‘s nucleus: Atomic Number = Z

• Hydrogen: Z=1

– 1 proton & 1 electron

– Simplest possible nucleus

• Atomic "weight" A = (#n + #p)

– hydrogen has A=1 also (no neutrons)

• Carbon has 6 protons

– Z=6, most common type has A=12

• this is 12C ("carbon-12")

• Other, rarer isotopes exist

– same Z, more or fewer n's

– e.g., 14C has 8 n's

Not to scale! 10-15 m

14

Periodic Table of elements

Z and A increase as you go across and down. Elements in same column have similar properties.

http://www.molres.org/MRI_DownloadPT.html

Z A

“Rare earth”

elements go in

here

(Parenthesis means unstable element)

Uranium is heaviest

natural element

(white numbers =

synthetic elements)

“Noble

gases”:

refuse to

mix with

other

elements!

(# of protons)

(total n+p) Number shown is the average over many isotopes

15

...even protons and neutrons have constituents

• Whack protons and neutrons with electrons and see what happens....

– "Scattering" experiments

• Protons do not act like smooth blobs, but rather like a bag full of tiny, hard particles

– direct evidence for point-like objects making up protons

– Also: properties of p, n (and other "elementary particles" observed in experiments) have regularities - reminiscent of periodic table!

• Can "explain" properties of all known subatomic particles by assuming they are combinations of 6 quarks

proton

beam of electrons

scattering

16

Some terminology...

• "Elementary particles" = objects that make up atoms (n,p,e) or are produced when atoms are smashed (over 200 identified)

– "elementary" because thought to be fundamental in 1950s

• "Fundamental" particles or constituents of matter

– Truly no substructure (as of today!)

• Hadrons = elementary particles subject to strong nuclear force (Greek: hadros = strong)

– protons, neutrons; plus pions, kaons, lambda particles...etc

– now known to be made of fundamental particles: quarks

• Leptons = elementary particles subject to weak nuclear force (Greek: leptos = weak)

– responsible for radioactive decays

– electrons, plus muons, taus and associated neutrinos

17

The ―Standard Model‖ of Particle Physics

Basic ingredients of matter are the fundamental particles: quarks and leptons

6 quarks

6 leptons

+ their antiparticles

(Symmetry!)

These types of particles are called 'fermions'

–(from http://www.fnal.gov)

Fundamental forces are mediated by photons, gluons, Z‟s and W‟s

These types of particles are called 'bosons'

18

The Elementary Particles are related

• Symmetries and connections allow us to deduce structure of elementary particles, and properties of fundamental particles

– Electric charge of electron and proton are equal and opposite, to the greatest accuracy possible today (about 13 decimals)

– Neutron left alone for about 15 minutes on average will ―Beta-decay‖ (old term for radioactive decay process) into e, p, and neutrino (very light, chargeless lepton)

neutron

proton

neutrino

electron Poof!

19

Retrograde motion

• Path of Sun (the ecliptic) over about 3 months

• Path of planet (over a longer period)

20

Copernicus - Brahe - Kepler

• Copernicus published only on his deathbed, 1543

– Probably feared accusation of heresy (cf. fate of his follower Giordano Bruno - burned at the stake by Inquisition!)

• Brahe's collected observations were analyzed by Johannes Kepler (1571-1630)

– Began as Tycho's assistant

– Added new feature to Copernican model:

• orbits are ellipses, not circles

r

center

all points at

same distance

from center

all points have

a + b = same Sun is at one focus

21

Kepler's Laws of Planetary Motion (~1610)

• New idea: motions are due to forces between Sun and planets

1. Law of equal areas

– Imagine a line from Sun to planet

– Line sweeps out equal areas in equal times

– Meaning: speed in orbit is not constant:

faster when closer to Sun

2. Law of elliptical orbits

– Sun at one focus, other empty

– Orbits are actually almost circular

3. Law of periods

– Period (length of planet's "year") is related to mean orbital radius by

T2 RAVG 3 (or: T2 / RAVG

3 = same for all planets)

"" means "proportional to"

22

Galileo Galilei (1564-1642)

• One of the first international celebrity-scientists!

– "Invented telescope" ~1610

• Improved toy spyglass for use as astronomical tool

• Made major discoveries contradicting Aristotelian worldview

– Venus has phases, like the Moon

– Jupiter has moons, like the Earth

– Moon has mountains (he even estimated height from their shadows)

– Sun has spots (imperfections!), and rotates, like Earth

» The heavens are just like the Earth!

– Studied earthly physics to understand heavenly physics

• Dropped weights from Leaning Tower of Pisa

• Rolling balls on incline to observe 'diluted' motion under gravity

– Published book supporting Copernican model (1630)

• Prosecuted by Inquisition - forced to "recant" (forgiven - in 1984!)

– "I do not feel obliged to believe that the same God who endowed us with sense, reason, and intellect intended us to forgo their use."

23

Newton‘s Mechanics: forces and motion

• Next: Isaac Newton‘s contributions

– 1664: age 21, graduate student, Cambridge University closed due to plague (!)

• Spent the year sitting under his mom‘s apple tree…

• Result: theory of how forces cause motion, and how the particular force we call gravity works

– His results were known to contemporaries, but he didn‘t actually publish until 1687 (Principia Mathematica)

– Became celebrity, hero of Enlightenment-era rationalism

• First some preliminaries: how to describe motion

– Kinematics = description of motion

• Importance of clearly defining terms

• Consequences of simple mathematical connections

– We‘ll use modern terminology and math notation

Newton, by

G. Kneller, c.1689

24

Describing motion: Position is a ―Vector‖

• New concept: vector quantities

– Some physical quantities are scalars - described by a single number

• examples: distance, temperature, mass, time

– Some physical quantities have direction as well as magnitude

• examples: position, velocity, force

• Compare these statements:

– "Fred is 10 meters from here‖ = distance, a scalar quantity

• He could be anywhere on a circle 10m in radius !

– "Fred is 10 meters SE of the Peanut Sculpture" = position, a vector

• This specifies his exact location in space

• A vector has both a value, or ―magnitude‖, and a direction

– in the example, distance is the magnitude of the position vector

• We can represent vector quantities graphically, with arrows

10m east 20m east 10m NE

25

Speed vs. Velocity

• Notice special use of ordinary words

– position and distance can be synonyms in ordinary usage

– they have different, very specific meanings in physics

Another special word pair:

• Speed is the rate of motion (how fast distance changes)

Speed = distance moved / time taken

―The satellite has a speed of 20,000 km/hr‖

―But officer, my speed was only 56 miles per hour!‖

• Velocity is speed plus directional information: another vector

"The spacecraft is moving at 18 km/sec towards Jupiter‖

"Folks, we're heading southeast at 600 km per hour"

– Notice that velocity is related to position as speed is to distance

Velocity = change in position / time elapsed

26

Acceleration

• When an object‘s velocity changes, it is accelerating

• The change can be in the speed of motion, OR in the

direction of motion, OR both.

• Acceleration is a generic term velocity change

– includes ―deceleration‖ (slowing down) and direction change

acceleration =change in velocity / time taken (notice analogy to definition of velocity in terms of position vs time)

• Examples of acceleration: car starting, car stopping,

car going around a curve

– Can you feel if you‘re moving with a constant velocity?

– Can you feel being accelerated? Why?

27

Acceleration a is another vector

• Acceleration has both magnitude and direction

– I‘ll use boldface symbols to indicate vector quantities: a = acceleration

• Direction of acceleration = direction in which velocity changes

a in same direction as velocity speed increases

a in direction opposite to velocity speed decreases

a at 90° angle to velocity only direction changes, not speed

a at any other angle to velocity both speed and direction change

• Examples:

– Car is pushed by wheels on road: speed increases

– Shove from the side as you run straight down a hallway sends you careening into the wall.

– Circular motion is produced by acceleration perpendicular to v

» direction must be toward the center of the circle

» So, if you see an object moving in a circle, you know it is being accelerated in direction toward center

more on circular motion later...

28

Discussion questions on acceleration

1. A car is going up a steep hill and slows down. Is it being accelerated? In what direction?

2. When I let go of a ball, does it accelerate? In what direction? What about when it hits the floor?

3. If you are driving East and apply the brakes to stop your car, in what direction are you accelerating?

Yes - in the direction down the hillside: a is reducing the uphill speed.

Yes, downward. (Why didn‘t it accelerate before I let go?) The floor applies an upward force* to change its direction. We know this because the change in the ball's velocity is in the upward direction! * Notice I slipped in a new term: force!

You are reducing your eastward velocity, so a points west. Moral: acceleration does not depend on velocity. It can be zero or in a completely different direction than v : the direction of a is given by the change in v. (Next: we'll see what acceleration does depend on ...)

29

Aristotle Says / Newton Says

• Artistotle: Natural state = at rest; a moving object always slows and eventually stops.

– "common sense": object with no external force on it slows down

• Newton (Galileo): Natural state = constant velocity (including v=0); a moving object changes its velocity only if acted on by some force.

– "common sense" is misleading: friction = force opposing motion!

• "air resistance" is a form of friction

Newton’s 1st Law: Any object not subject to a net force moves at

constant velocity, covering equal distances in equal times, along a straight path

inertia = ―reluctance to change state of motion‖

What's this "net" force?

Sum of all individual forces, taking into account direction

2nd Law: Forces Cause Acceleration

• Acceleration is proportional to the applied force: The larger the force, the more an object will accelerate, in the direction of the applied force.

• Mass produces inertia, i.e., reluctance to accelerate, so for the same force, more massive objects experience smaller acceleration than less massive ones.

So a F and a 1/m : a F/m

Shorthand: Force = mass acceleration, or

F = ma Newton’s 2nd Law:

Newton’s 2nd Law: Any object subject to a net force

accelerates, with acceleration proportional to the force and inversely proportional to its mass. Acceleration is in the direction of the net force.

31

A Ball Falling Freely ("Free fall")

• Is the ball‟s direction of velocity constant?

• Does it travel equal distances in equal times?

• Is the ball accelerating?

• What is the direction of the acceleration vector?

• What is the direction of the force (F = ma)?

• What‟s responsible for the force on the ball?

-1.0 m

-2.0 m

-3.0 m

-4.0 m

-5.0 m

-6.0 m

-7.0 m

0.9 sec

0.8 sec

0.7 sec

0.6 sec

0.5 sec

0.4 sec

1.0 sec

1.1 sec

1.2 sec

0 m

Newton‘s Law of Universal Gravitation

The Gravitational Force between two masses is proportional to each of the masses, and inversely proportional to the square of their separation.

This says that F M1 and F M2 and F 1/r2

Putting those 3 relations together tells us

F = G M1M2/r 2

a1 = F/M1 = GM2/r2 acceleration of mass #1 due to mass #2

Earth: M2 = 5.9761024 kg; r = 6,378,000 m a1 = 9.80 m/s2 = g

The proportionality constant G = 6.67410-11 m3/(kg·s2)

"Universal gravitational constant"

Newton‟s Law of

Universal Gravitation

Orbits

• Example of Low Earth Orbit (LEO): ~200 km altitude above surface

– Period of ~90 minutes, v = 7,800 m/s

– Loses speed due to drag from residual gases (still in atmosphere!)

Other Orbits:

• MEO (Mid-Earth Orbits) – Communications satellites

– GPS satellites

– half-day orbit:

20,000 km altitude, v = 3,900 m/s

• Elliptical & Polar orbits – Spy satellites

– Scientific sun-synchronous satellites

GPS Satellites: T=12 hr

Summary of Newton's Laws

• First Law: inertia

– Tells us if a net force is acting:

• Second Law: force, acceleration and mass

– Tells us

• how to determine acceleration given known forces:

• how to determine force from observed acceleration:

• how to measure mass by applying a force and observing motion

• Third Law: forces represent interactions

– Tells us how to relate forces on different bodies that are interacting in some way:

• Universal Gravitation: Masses exert attractive force on one another

– This is not about how forces affect motion, but describes one of the fundamental forces of nature

0 ( )

0NET

a v const

F

NETFa

m

NETF ma

NETFm

a

12 21F F

2GRAVITY

MmF G

r

From static to kinetic

35

Applied Force

Frict

ion F

orc

e

Fstatic max = s Fn

Fkinetic = k Fn

Some Questions

• Does friction always exert a force that tends to bring

things to a halt?

• What does this say about the direction of the

frictional force, relative to the velocity vector?

• What do you think would happen if we loaded lead

bricks into the box? Would it become harder to slide?

• What are some ways to reduce frictional forces?

Another Summary…

• Law of Gravitation: bodies exert force on one another proportional to masses, and with inverse-square law for distance

– r is measured between centers of masses; force has infinite range

– Proportionality constant G is very small (gravity is a weak force)

Note: if Earth were solid rock, it would have M~3x1024 kg, but its mass is nearly twice as big. What's inside?

• Satellites in orbit are falling freely; gravity provides just the central force needed to keep them in closed path: mv 2/r = mg

– Geosynchronous orbit has period T=24 hr, so satellite stays over the same point on earth: can only occur for r=3.6x106 m

• Friction forces are

– proportional to normal force pressing bodies together: Ff = N

– caused by surface interactions between bodies

– static friction coefficient is (usually) greater than sliding friction

• Newton's 3rd Law says all forces are interactions between bodies, so "every action has an equal and opposite reaction"

– Forces occur in pairs: "action" and "reaction" are on different bodies