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Announcements. Pick up “A,B,C,D” cards. Please bring them to class with you. Bring a calculator to lab. In many cases, you will need it. Course book “ A Tour of the Subatomic Zoo ” is available at Bookstore until April 15. So, please purchase it asap.

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Announcements l.jpg

Announcements

  • Pick up “A,B,C,D” cards. Please bring them to class with you.

  • Bring a calculator to lab. In many cases, you will need it.

  • Course book “A Tour of the Subatomic Zoo” is available at Bookstore until April 15. So, please purchase it asap.

  • In most cases, I will be making the lecture notes available on the morning of lecture. I encourage you to make a copy and bring them to class. Note that there are things I cover in class which are not on the slides. You are responsible for both, so please don’t miss class.

  • Yes, there is LAB this week.


Welcome to particle physics l.jpg

Welcome to Particle Physics

A blurb from the “Quarks Unbound” from the American Physical Society

  • “We’re barely aware that they are there, but the elementary particles of matter explain much of what we take for granted every day. Because of gluons binding the atomic nucleus, matter is stable and doesn’t crumble. Because of gravitons, our feet stay firmly planted on the ground. We see because our eyes react to photons of light. “

  • “Particle Physics explains the ordinary, and delights us with tales of the extraordinary. Antimatter annihilates matter. “Virtual” particles blink in and out of existence in the vacuum of space. Neutrinos zip through the Earth untouched.”

  • “Particle Physics doesn’t stop at the unusual either. It contemplates the cosmic too, exploring the origins of the universe and the symmetries that frame its design.”


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Aims of Particle Physics

  • To understand nature at it’s most fundamental level.

  • What are the smallest pieces of matter, and how do they make up the large scale structures that we see today ?

  • How and why do these ‘fundamental particles’ interact the way that they do?

  • Understand the fundamental forces in nature.


In this course my aim is to introduce you to nature at its most fundamental level l.jpg

In this course, my aim is to introduce you to nature at its most fundamental level

  • Some of the concepts you will encounter may not agree with your intuition, others will…

  • I strongly encourage you to ask questions in class. It will help you, your classmates, and me!

Before we can get to this, we will first spend some time on some basics, and then we’ll get to the meat later on….


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Sizes and Powers of 10

  • In describing nature, objects vary dramatically in size.

  • The solar system is about 10,000,000,000,000,000,000,000 timeslarger than an atom, for example  Scientific notation !

  • You should become comfortable with seeing scientific notation,in the context of relative sizes of objects.

  • Useful Web Sites which allow you to step through the powers of 10 are at:

  • http://cern.web.cern.ch/CERN/Microcosm/P10/english/P0.html

  • http://www.wordwizz.com/pwrsof10.htm

  • http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/


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Powers of 10

Positive

Powers

Negative

Powers

0 Power

100 = 1


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Scientific Notation

12500 = 1.25 x 10000 = 1.25 x (10 x 10 x 10 x 10) = 1.25 x 104

1.25x10?

1.2500

12500.0

Move decimal 4 places to right

0.00367 = 3.67 x 0.001 = 3.67 x (.1 x .1 x .1) = 3.67 x 10-3

3.67x10?

0.00367

3.67

Move decimal 3 places to left

The earth has a circumference of about 25,000 miles. How is thisexpressed in scientific notation?

A) 2.5x103 B) 25x104 C) 2.5x104 D) None of these

The sun has a radius of 695 million meters. How is this expressed in scientific notation?

A) 695x105 B) 6.95x108 C) 6.95x109 D) 6.95x106


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Multiplying powers of 10

The circumference of the earth is about 4x107 [m]. If I were totravel around the earth 3x102 times, how many [m] will I have gone?A) 7.0x109 B) 1.2x1010 C) 1.0x1015 D) 7.0x1015

(4x107) x (3x102) = (4x3) x (107x102) = 12x10(7+2) = 12x109

= (1.2x10) x109

= 1.2x1010

A bullet takes 10-3 seconds to go 1 [m]. How many seconds will it take for it to go 30 [m]?

A) 3.0x10-1 B) 3.0x10-2 C) 4.0x10-2 D) 4.0x10-1

(1x10-3) x (3x101) = (1x3) x (10-3x101) = 3x10(-3+1) = 3x10-2


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Dividing Powers of 10

A gas truck contains 4.6x103 gallons of fuel which is to be distributedequally among 2.0x104 cars. How many gallons of fuel does each car get?

A) 2.3x101 B) 2.3x10-1 C) 23 D) 2.3

The area of the U.S is about 3.6x106 [miles], and the population is about 300x106. On average, what is the population density in personsper square mile?A) 1.2x102 B) 1.2x10-1 C)1.2x10-3 D)1.2x10-2


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How many times larger is a kilometer than a micrometer ?

  • 1,000 B) 1,000,000 C) 1,000,000,000 D) 1x10-9

Common Prefixes

10-3 = “milli”

10-6 = “micro”

10-9 = “nano”

10-12 = “pico”

10-15 = “femto”

103 = “kilo”

106 = “mega”

109 = “giga”

1012 = “tera”

Commonly used prefixes indicating powers of 10

1 km = 103 m and there are 106 micrometers in a meter, so there are 109 (or 1 billion) micrometers in 1 km

How many 100 W bulbs can be kept lit with 100 Tera-Watts?A) 1.0x107 B) 1.0x109 C) 1.0x1012 D)1.0x1013


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Common Conversions

Length: 2.54 [cm] = 1 [inch]

Mass: 1 [kg] = 2.2 [lbs]Speed: 1 [m/sec] = 2.25 [mi/hr]

How many meters are there in a centimeter?

A) 100 B) 0.01 C) 1000 D) 0.001

How many inches in 1 kg ?

A) 2.54 B) 25.4 C) less than 25 D) None of these


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Units

  • Joe asks Rob… “About how much does your car weigh” ?

    Joe answers … “About 1.5”

  • Is Joe’s answer correct or incorrect?

Physical quantities have units !!!!!!!!

  • All physical quantities have units, and they must be used.

  • One exception is if you are talking only about a pure number.

    For example: How many seats are in this classroom?

  • I will often use brackets to indicate units:1 kilogram == 1 [kg]


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Variables/Symbols

  • It is often more convenient to represent a number using a letter. For example, the speed of light is 3x108 [m/sec]. To avoid having to write this every time, we simply use the letter c which represents this value. That is c = 3x108 [m/sec].

  • We might use the expression, “the particle is moving at 0.1c”. This should be interpreted as “The particle is moving at 1/10th of the speed of light.”

  • We will often use letters to represent constants or variables, so you must become comfortable with this.


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Proportionality

What do we mean when we say:“Quantity A is proportional to quantity B”

This means the following:

1) If we double B, then A also doubles.

2) If we triple B, then A also triples.

3) If we halve B, then A also halves.

This is often written as: AaB

The circumference of a circle, C, is proportional to the radius, R.If the radius is increased by a factor of 10, what happens to the circumference?

It increases by a factor of 10


Proportionality exercises l.jpg

l

  • What’s the area of this square?

2l

l

Area = base * height = 2l*2l = 4l2 = 4(1 cm )2 = 4 cm2

Proportionality Exercises

  • Consider this 1 cm square

l

  • What is its area?

Area = base * height = l*l = l2 = (1 cm )2 = 1 cm2

If we double the length of the side, we quadruple the area?


Proportionality exercises cont l.jpg

A=p(22) = 4p

A=p(42) = 16p

Since A a r2, (A=pr2) doubling the radius quadruples the area !

Proportionality Exercises (cont)

The area of a circle is proportional to the radius squared.What happens to the area of a circle if the radius is doubled?

Radius = 2 cm

Radius = 4 cm

A=pr2


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Inverse Proportionality

What do we mean when we say a quantity V is inversely proportional to another quantity, say d.V a (1/d)

It means:

If we double d, then V is reduced by a factor of 2If we quadrupled, then V is reduced by a factor of 4.

Why?

We know that Vda (1/d)If we double d, then d  (2*d), soV2da [1/(2d)] = (1/2) (1/d) = (1/2) Vd.In the same way, show that V4d = (1/4) Vd


Exercises l.jpg

  • The force of gravity is known to be inversely proportional to

  • the square of the separation between two objects. What happens to the

  • force between two objects when the distance is tripled?

  • Increases by a factor of 6

  • Decreases by a a factor of 8

  • Decreases by a factor of 9

  • Decreases by a factor of 6

Exercises

  • The electric force between two charges is also known to be inversely

  • proportional to the square of the separation. What happens to the force

  • if the distance is reduced by a factor of 10.

  • Increases by a factor of 10

  • Increases by a a factor of 100

  • Decreases by a factor of 10

  • Decreases by a factor of 100


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Algebra

If a car is going 20 [mi/hr] for 4 [hrs], how far does the car go?

A) 80 [mi] B) 5 [mi] C) 20 [mi] D) none of these

What did you do to arrive at this result?

  • You multiplied the speed (20 [mi/hr]) by the time (4 [hrs]).

  • So, to get the distance, you did this: distance = velocity * timed = v*t


Algebra cont l.jpg

Algebra (cont)

If a biker goes 20 [mi] in 2 [hrs], what is the bikers average speed ?

A) 20 [mi/hr] B) 5 [mi/hr] C) 10 [mi/hr] D) 40 [mi/hr]

What did you do to arrive at this result?

  • You divided the distance (20 [mi]) by the time (2 [hrs]).

  • That is, you reasoned: average velocity = distance / time

    v = d / t

Is this equation and the previous one expressing different relationships among the variables v, d and t?


Algebra cont21 l.jpg

d = v * t

(1/t)*

*(1/t)

d = v

(1/t)*

d / t = v

v = d / t

Algebra (cont)

NO!

d = v * t

v = d / t

Are expressing thesame relationship. Thevariables are just shuffled around a bit!

and

  • To cast the first form into the second:

d = v * t

Multiply both sides by (1/t):

The factor of t * (1/t) = 1, so

And, (1/t)*d = d/t,

Or, just switching sides…


An important example l.jpg

An important example

Einstein’s famous Energy-mass relation:

E = m c2

Can be rearranged to read:

m = E / c2

Note that the units of mass can also be expressed in units ofEnergy / (speed)2(We’ll come back to this point later…)


Summary l.jpg

Summary

  • For this module, you should be comfortable with:

  • Using and manipulating powers of 10 (division, multiplication).

  • Understanding what “proportional to” and “inversely proportional to” mean.

  • Simple conversion of units, if you are given the conversion factors. (e.g. [in.] to [cm], [cm] to [m]., etc)

  • Basic algebra and manipulating equations such as, E=mc2,c=fl , E=hf , etc.

  • Understanding prefixes, such as Giga, Tera, Mega, etc.


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