Micro-world Macro-world

Fall 2009Instr: Stephen L. Olsen

What does “Physics” mean?

Greek: φίσίσ

phisis

“things”“logic”

“The logic of things”

or “How things work”Chinese: 物理 WU LI

Nature

What kind of “things”?Ordinary-sized objects::

apples:

footballs:

ukuleles:etc.

Gigantic things

Earth

Sun

galaxies

etc.

Very tiny things

molecules

atoms

cells

quarks

Galileo Galilei1562 - 1642

1st “modern” scientist

Example of how Galileo thought:His experiments on motion on inclined planes

What if the 2nd track was horizontal?

Aristotle ~300 BC

Forces are needed to keep objects in

motion. A constant force will have a constant motion.

Physics book VII chapter 5

Galileo’s big idea

Forces are not needed to keep objects in

motion. They are only needed to change the

state of motion.

Actually, Galileo wasn’t first

Mozi ( 墨子 ) ~400BC

If there is no opposing force,

motion will never stop.

before Aristotle!

Object sliding on a surface

If there were no friction the book

would keep sliding.

Angels are not needed to keep planets moving in their orbits

Law of inertia

Discovered by Galileo, but as written by Newton:

Every object perseveres in its state of rest, or of uniform motion in a straight line, unless it is so compelled to change that state of motion by forces impressed thereon.

Comment on the Law of Inertia

•No mention of balls & tracks

•Applies to ordinary objects & also huge objects like galaxies and tiny objects like atoms & quarks

Galileo knew nothing of galaxies or quarks, but, thanks to his

imagination, his insight, based on observations of ordinary objects, proved to be a universal truth.

Units &

Reference Frames

Required for measurements/observations

English units

King’s foot

12 inches = 1ft5280 ft = 1 mile

One meter of length1 meter = 40 inches (1.1 yds)

10,000,000m

1m

About the distance from nose to the outstretched finger (of a pretty big guy).

Centimeters & millimeters

1 centimeter = 1/100 meters ( radius of a penny)

1 millimeter = 1/1000 meters ( thickness of a dime)

means “approximately equal to”

1cm

1mm

1km 5/8 mile

1000 m = 1 kilometer (km)

Motion depends on the circumstances of the observer (I)

•To us, both the red & blue cars move forward

•To someone in the red car, the blue car is going backwards

backward forward

Reference frames aka Coordinate systems

x

z

y

To describe the positionof an object: You needto define a coordinate system (reference frame)& determine 3 coordinates

e.g. x, y & z

Choices of location ofthe coordinate system& directions of the axesare up the observer.

z

x-axis(e.g. the 1st baseline)

y-axis(e.g. the 3rd baseline)

z-axis(vertical)

reference point(e.g. home plate)

Motion depends on the circumstances of the observer (II)

•In the fish’s reference frame, it is the ground that is moving

x

z

y

Some distancesNose to finger ~1m

Back of the room ~10mSNU library ~100mSNU main gate ~1000mIncheon ~50000mCenter of the Earth~6400000mEarth to Moon ~385000000mEarth to Sun ~150000000000mNext star ~40000000000000000m

We are only out to the next star & we are already running out of space

Some small sizes

• radius of a 10 won coin ~0.01 m• thickness of a 10 won coin ~0.001 m• thickness of a human hair ~0.000075 m• diameter of a red blood cell ~0.00000002 m• size of hydrogen atom ~0.00000000006 m• size of hydrogen nucleus ~0.0000000000000001 m

Again, the numbers become unwieldy& use up a lot of space

Exponential logic

Exponential logic powers of “2”

Area of a sheet of paper

28 cm

21.5 cm

Area =28 cm x 21.5 cm= 600 cm2

Cut it in half

Area of the remaining sheet after 1 cut

28 cm

21.5 cmArea =28 cm x 21.5 cm

Cut it in half again

2

2

2

= 600 cm2

=300 cm 2

= 600 (1/2)cm2

Area of the remaining sheet after 2 cuts

28 cm

21.5 cmArea =28 cm x 21.5 cm

Cut it in half again

2

22

2

= 600 cm2

2x2

=600 cm 2 x(1/2)2

=150cm2

Area of the remaining sheet after 3 cuts

28 cm

21.5 cmArea =28 cm x 21.5 cm

Cut it in half again

2

2x22

2

12

= 600 cm2

2x2x2

=600 cm 2 x(1/2)3

=75cm2

After 12 times

28 cm

21.5 cm Area =28 cm x 21.5 cm

26

2626 26

=0.15 cm2

Smallest piece ofpaper I can handle

= 600 cm2

26x26

=600 cm 2

x(1/2)12

= 600 cm2

4096

Imagine we did it 70 times

28 cm

21.5 cmArea =28 cm x 21.5 cm

235

235235

235

1,180,591,620,717,411,3??,???

= 5.1 x10-19 cm2

(about ½ the area of an atom)

=600 cm2 x

= 600 cm2

235x235

=600 cm 2 x(1/2)70

1

1

1,180,591,620,717,411,3??,???

is unwieldy ( 다루기 힘든 , 꼴 사나운 )

(1/2)70

Is more tractable

Difficult to manage

Tractableeasy to manage

Powers of 10

$ 100.0 = $ 10.00 x 10

Move the decimalpoint 1 place to the

left

multiplyby 10&

$0.01 = $00.1 x 1/10

Move the decimalpoint 1 place to the

right

divide by 10&

“penny”“dime”

Positive powers of 10

150000000000150000000000.15000000000.0 x 1011500000000.00 x 102150000000.000 x 10315000000.0000 x 1041500000.00000 x 105150000.000000 x 10615000.0000000 x 1071500.00000000 x 108150.0000000000 x 10915.0000000000 x 10101.50000000000 x 1011

= 1.5 x 1011

1500000000.00 x 10x10

11 jumps to the left +11 in the exponent

Some distances

• Nose to finger ~1 m• The back of the room ~10 m• SNU Library ~100 m• SNU Main gate ~1000 m• Incheon ~50000 m• Center of Earth ~6400000 m• Earth to Moon ~386,000,000 m• Earth to Sun ~150000000000 m• Next star ~40000000000000000 m

~5.0 x 104 m ~6.4 x 106 m ~3.86 x 108 m

~1.5 x 1011 m ~4.0 x 1016 m

nomenclature

• 103 = 1 thousand (kilo)

• 106 = 1 million (mega)

• 109 = 1 billion (giga)

• 1012 = 1 trillion (tera)

Small numbers

1 penny = $0.01

1 dime= $0.10

1 penny = 1/10th of a dime

$0.01 = $0.10x(1 /10)

Moving the decimal point 1 place to the right is the same as multiplying by 10

Negative powers of 10

0.00000000006 00.0000000006 x 1/10 00.0000000006 x 10 -1000.000000006 x 10 -1x10-1000.000000006 x 10 -20000.00000006 x 10 -300000.0000006 x 10 -4000000.000006 x 10 -50000000.00006 x 10 -600000000.0006 x 10 -7000000000.006 x 10 -80000000000.06 x 10 -900000000000.6 x 10 -10000000000006.x 10 -11

= 6.0 x 10-11

11 jumps to the right -11 in the exponent

Some small sizes

• radius of a 10 won coin ~0.01 m• thickness of a 10 won coin ~0.001 m• thickness of a human hair ~0.000075 m• diameter of a red blood cell ~0.00000002 m• size of hydrogen atom ~0.00000000006 m• size of hydrogen nucleus ~0.000000000000001 m

~7.5 x 10-5 m ~2.0 x 10-8 m

~6.0 x 10-11 m ~1.0 x 10-15 m

More nomenclature

• 10-2 = centi-

• 10-3 = milli-

• 10-6 = micro- ()

• 10-9 = nano-

• 10-12 = pico-

exponents are very important

Distance to the Sun: 1.5 x 1011m

Distance to next star: 4 x 1016 m

Exponents differ by 5

Light from the sun takes 8 minutes to

get here

Light from the next star takes 4 years to

get here

8 minutes from now

4 years from now?

Multiplying large numbersUse the rule:

(A x 10a ) x (B x 10b)

Number of people

In the USx average income/person

301,000,000 x $ 40,100

= 3.01x108 x $ 4.01x104

= (3.01 x $4.01) x (108 x 104)

= $12.1 x 108+4 =$12.1 x 1012 = $1.21 x 1013

on1/8/07

10a+b

=(AxB) x (10a x 10b)

Sum of everyone’s income

dividing large numbers

=US national debt# of persons in US

on818/07

Ax10a Bx10b

x= = x 10a x 10-b

$8,598,000,000,000301,000,000 persons

$8.60 x 1012

3.01 x 108 persons= =

$8.60 1012

3.01 108 personsx

= $2.86 x 1012- 8 /person

move b upstairs

= $2.86 x 104/person

(= $28,600/person)

AB

AB

10a 10b

& change sign

10a-b

$28,600 (ladies not included)