PHYSICAL SCIENCE PSC1121Physics in Films

LECTURE

Scale & Powers of Ten

Order of Magnitude

Units & Calculations

Fermi Problems (behind the envelope calculations)

Play Scale Video Clip

Scale is the method by which we estimate and measure distances and sizes.

Scale

This is a doll

This is a doll

•In everyday life we use our size as scale to decide if an object is large or small.

•We need a convenient method to represent algebraically (and also compare) sizes of a whole spectrum of objects that can be very small or very large. For example sizes of atoms and sizes of galaxies.

•A convenient way is the representation of numbers with the power of 10 method and the order of magnitude approximation.

POWERS OF TEN

1

10

100

1,000

10,000

100,000

1,000,000

= 100

= 101

= 102

= 103

= 104

= 105

= 106

1

0.1

0.01

0.001

0.0001

0.00001

0.000001

= 100

= 10-1

= 10-2

= 10-3

= 10-4

= 10-5

= 10-6

1. 0.5

2. 5

3. 50

4. 500

5. None of the above

Review QuestionWhat number is 510-5107

Play Powers of 10 Video Clip

The powers of ten way to represent numbers allows usto conveniently represent both very large and very small numbers.

Order of magnitude of a quantity is the power of 10 closest to the numerical value of our quantity. (It is the value of the quantity rounded to the nearest power of 10).

kgkgprotonaofmass 2727 10106726.1

mmm 65 10104.7655,735

6666

56166

1010110328.410327932723.4723.932,327,41010101010375.9000009375.0

mmmmm

Examples:

A lot of times when we study very large (e.g. the size of the galaxy) or very small quantities (e.g. the size of an atom) we don’t care for the exact value but only for a good approximation.

The Order of Magnitude of a quantity is the power of 10 closest to the numerical value of our quantity. (It is the value of the quantity rounded to the nearest power of 10).

Method to find the Order of Magnitude of a quantity:

Write the quantity as Ax10B where A is a number between 1 and 10 and B is a positive or negative integer.

If A is greater than 5 then replace it with 10=101, if A is less than 5 replace it with 1=100. The result is the order of magnitude of the quantity.

Order of magnitude of a quantity is the power of 10 closest to the numerical value of our quantity. (It is the value of the quantity rounded to the nearest power of 10).

kgkgprotonaofmass 2727 10106726.1

mmm 65 10104.7655,735

6666

56166

1010110328.410327932723.4723.932,327,41010101010375.9000009375.0

mmmmm

Examples:Orders of magnitudeActual quantities

There are questions like "how fast", "how far", or "how much" which, when answered, we must supply a unit of measurement:

How fast: 50

How far: 30

How much: 8

Because of this, numbers in science will always have "units". These units are just as important as the numbers when communicating observations.

Never write a number without its units.

miles per hour

miles

pounds

The British System of Measurement is commonly used as the day to day system in the United States. We are familiar with this system: we know about pounds, feet, and gallons. However, the British system is an impossible system to do conversions between units since the relations between units have no pattern (they are arbitrary). This system has become obsolete.

1 league = 3 miles

1 mile = 1760 yards

1 yard = 3 feet

1 foot = 12 inches

The International System of measurement(abbreviated SI) is commonly called the metric system in the United States. The relation between units are multiples of ten.

All science measurements are made using this system.

1 kilometer = 1000 meter

1 meter = 100 centimeters

1 centimeter = 10 millimeters

In the United States, the reluctance to adopt the metric system caused trouble as recently as 1999, when NASA's Mars Climate Orbiter

failed because engineers used English measurements instead of metric.

"The 'root cause' of the loss of the spacecraft was the failed translation of English units into metric units in a segment of ground-based, navigation-related mission software, as NASA has previously announced," said Arthur Stephenson, chairman of the Mars Climate Orbiter Mission Failure Investigation Board. "The failure review board has identified other significant factors that allowed this error to be born, and then let it linger and propagate to the point where it resulted in a major error in our understanding of the spacecraft's path as it approached Mars.

http://mars.jpl.nasa.gov/msp98/news/mco991110.html

International System of Units(abbreviated SI from Système Internationale)

Length meter mTime second sMass kilogram Kg

Quantity unit symbol

The meter, second, and kilogram are called base units in SI

Other units are expressed in terms of them

common prefixes in SI

μ micro 10-6

m milli 10-3

c centi 10-2

the prefix is read and multiplies the unit by

K kilo 103

M mega 106

G giga 109

Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10.

Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10.

common prefixes in SI

relation between SI and British systems

m yd 1 yd = 0.9 m m mile 1 mile = 1600 m mm in 1 in = 25 mm

metric British approximate relation

liter quart 1 quart = 1 liter liter gallon 1 gallon = 3.8 litersg lb 1 lb = 450 g

3cm

g

3mkg

gram per cubic centimeter

kilogram per cubic meter

Conversion of Units

Both of the above units measure the density of materials. Find their relation.

3m

Kg3)100( cm

3000,000,1

1000cm

g1000

13cm

gg1000

This can also be written as

31000

mKg

3

1cmg

ENRICO FERMI (1901-1954) is an Italian physicist best known for his contributions to nuclear physics and the development of quantum theory. In addition to his contribution to theory, he is also noted as an experimentalist. Fermi was awarded the Nobel Prize for his physics work on the nuclear process. Shortly after receiving the Nobel Prize, Fermi was forced to flee Italy. He settled in the United States, first at Columbia University and then later at the University of Chicago. During World War II he was a member of the Manhattan project team that developed the atomic bomb in Los Alamos, Mexico.

Who is Enrico Fermi?

At 5:25, on a Monday morning in July of 1945, the world's first atom bomb exploded in the desert 60 miles northwest of Alamogordo, NM. 40 seconds later, the blast's shock wave reached the base camp, where scientists stood in stunned contemplation of the historic spectacle. The first person to stir was the Italian physicist Enrico Fermi, who was on hand to witness the culmination of a project he had helped begin.

Before the bomb detonated, Fermi had torn a sheet of notebook paper into small bits. Then, as he felt the first quiver of the shock wave spreading outward through the still air, he released the shreds above his head. They fluttered down and away from the mushroom cloud growing on the horizon, landing about two and a half yards behind him. After a brief mental calculation, Fermi announced that the bomb's energy had been equivalent to that produced by ten thousand tons of TNT. Sophisticated instruments also were at the site, and analyses of their readings of the shock wave's velocity and pressure, an exercise that took several weeks to complete, confirmed Fermi's instant estimate.

A Fermi question requires estimation of physical quantities to arrive at an answer. Throughout his work, Fermi was legendary for being able to figure out things in his head, using information that initially seems too meager for a quantitative result. The most famous Fermi problem was: “How many piano tuners are there in Chicago?”

He used a process of "zeroing in" on problems by saying that the value in question was certainly larger than one number and less than some other amount. He would proceed through a problem in that fashion and, in the end, have a quantified answer within identified limits.

In a Fermi question, the goal is to get an answer to an order of magnitude (a power of ten) by making reasonable estimations about the situation, not necessarily relying upon definite knowledge for an "exact" answer.

The point of Fermi problems is not only to show how much useful can commonly knowledge and how useful results could be obtained by doing simple calculations, but also to illustrate the difference between estimation and guessing.

Let us now try to answer the question “How many guitar shops are in Orlando?”. Faced with such a question without warning, one response would simply be to declare that you don't know and cannot know, and if forced to produce an answer to simply guess at one that is “plausible”.

In Science we do not guess, but we estimate.

The primary disadvantage of guessing is not that it yields imprecise answers. The problem is that we do not know how much confidence to place in the answer because the thought process from which it follows has not been clearly identified.

First, one must make some basic assumptions. They must be reasonable of course , but it is necessary that they are made explicitly, so that we can go back and check if our estimated answers are wildly in error.

This is how scientists find mistakes, and it amounts to being aware of the processes of one's thinking.

Estimation vs. guessing.

A guitar shop cannot stay in business unless there are customers and most of the customers are likely to be young people with age between 15 – 20 years old.

The population of Orlando is about 200,000 and let’s assume that approximately 10% are between 15 and 20 years old. That is at about 20,000 teenagers.

From these a large number say 60% (that is 12,000) are music lovers and they will buy some musical instrument.

Guitar is very popular and I estimate that half of the teens buying a musical instrument will buy guitar. That is 6,000 teens between the age of 15 and 20 will buy guitar.

Therefore within 5 years there will be approximately 6000 guitar sales, or about 1,200 a year.

How many guitar sales can sustain the business? Let’s say one or two a week, 5 or 6 a month or 60 -70 a year (the business does not sell only guitars). So I estimate about 15 – 20 businesses that sell guitars in Orlando.

•They will start with limited information.

•They will have to ask many more questions and they will utilize estimation (some algebra skills are important).

•It is the process rather that is important than "the" answer.

•They may have to go back, retrace their steps and improve their assumptions (estimations).

How could non science majors use the science knowledge they will get from

PSC1121 to solve the problems they will encounter in their profession?

Estimate the length of the Earth equator.Another Fermi Problem

Solution:

Time zones in mainland USA: 3

Time zones on Earth: 24

Therefore, a circle that goes around Earth has 8 times more zones. USA is about 3,000 miles long. This means that such a circle should be about 24,000 miles long.

However a circle that goes around Earth at the latitude of USA is not equal to the equator. It is a little less. So, let’s add about 1,000 miles:

length of equator = 25,000 miles

Hint: use the size of USA and the time zones (distance between meridians)

•What is the Mass of the Earth? •What is the mass in kilograms of the student body in your school? • How many golf balls will fill in a suitcase?• How many gallons of gasoline are used by cars each year in the United States? • How high would the stack reach if you piled on trillion dollar bills in a single stack? • What fraction of the United States area is covered by automobiles? • What is the weight of solid garbage thrown away by American families every year? • How many individual frames of film are needed for a feature-length film? How long is such a film?

Other Fermi Problems