Chapter 1Conservation of mass & energy

Symmetry

Physicists usually define symmetry as invariance under transformation

Triangle Rotation Triangle

Basically, an object or system is called symmetric when you observe it from a different perspective

And it remains unchanged

Most often we think of symmetry in terms of patterns or shapes

We encounter symmetry of translation, reflection, and rotation all around us…

Translationalsymmetry

Rotationalsymmetry

Reflectivesymmetry

The most obvious kind of isometry is called a translation, and amounts to just pushing an object in a straight line to a new location:

There is not a fixed point

another very familiar kind of isometry is rotation:

Translations have no fixed points at all, while rotations have exactly one (called a pivot point, around which everything rotates doesn't move at all.

Reflections are isometries that have infinitely many fixed points.

The least well-known kind of isometry is usually called a glide reflection. It is a kind of cross between a reflection and a translation:

if we consider both orientation and fixed point behavior, each type of isometry has a unique character:

What kind of symmetrydo you find with a

Checkerboard?

The laws of nature are also symmetrical

With respect to translation

Whether you perform an experiment in New York or Los Angeles, at the other edge of the Milky Way or in a galaxy a billion light-years from here, you will be able to describe the results using the same laws.

With respect to rotation

The laws look precisely the same whether we make measurements from the bottom, top, sides, etc. - physics has no preferred direction in space.

With respect to reflection

The laws of physics are the same in a right-handed system of coordinates as in a left-handed system

With respect to time

The laws work exactly the same in experiment today as they did on an experiment performed yesterday or last year.

One of Einstein’s main goals in his explanation of general relativity was to formulate a theory in which the laws of nature would look precisely the same to all observers. In other words, the laws had to be symmetrical under any change in our point of view in space and time

Conservation Laws

THE WORD CONSERVE DOES NOT HAVE ITS USUAL MEANING OF TRYING NOT TO WASTE SOMETHING.

The word “conserve” in physics means that aparticular measurable property of a closed

system does not change with time

THUS, A CONSERVED QUANTITY IS SOMETHING THAT YOU WOULDN'T BE ABLE TO GET RID OF EVEN IF YOU WANTED TO.

Since the total momentum in the system stayed the same, the momentum was “conserved”

Conservation ofAngular Momentum: The total angular momentum of the system is constant.

Conservation of Energy: the total energy of the system is constant.

Conservation of Momentum: the mass times the velocity of the center of mass is constant.

Symmetry & the Laws of Physics

The symmetry properties of a physical system are intimately related to the conservation laws

characterizing that system

Noether’s theorem states that each symmetry of a physical system implies that some physical property of that system is conserved.

Each conserved quantity has a corresponding symmetry

CONVERSELY…

Symmetry Space translation Time translation Rotation

Conserved quantity

Linear momentum Energy

Angular momentum

http://www.youtube.com/watch?v=trGhbuAkfuY

Everyone is familiar with energy but no one knows exactly what energy actually isFor our purposes we will define Energy asthe measure of the ability to generate motion.A system that has energy has the ability to do work (motion in action).Energy is measured in the same units (joules) as work because energy is transferred during the action of work.

The SI unit of energy is the joule, J, (rhymes with cool), named after the British physicist James Joule.

One Joule is the amount of energy required in order to heat 0.24 g of water by 1 °C. (The number 0.24 is not worth memorizing.)

Energy comparisons

Energy appears in different forms such as mass, heat, or motion

Energy can travel in different ways such as light, sound, or electricity

The workings of our universe—including all of ourTechnology—can be viewed from the perspectiveof energy flowing from one place to another and

changing back and forth from one form to the next

Physics Fundamental Principle:

CONSERVATION OF ENERGY

The total energy of a closed system always remains constant. Energy cannot be created or destroyed, but only transferred from one system to another

What is a system?

A ‘system’ just means a group of objects that can be treated as a single unit.

Example: our solar system

The law of Conservation of energy has many implications such as…

Your car will not run forever on one tank of gas

Don’t we create energy at a power plant?

No, we simply transform energy at our power plants

You can harness the same energy at home!!

Energy in the form of massEinstein showed that mass itself could be converted to and from energy, according to his celebrated equation E = mc2, in which c is the speed of light.

Thus we can view mass as simply another form of energy, and it is valid to measure it in units of joules.

The mass of a 15-gram pencil corresponds to about 1.3 × 1015 J.

We get almost all of our energy from the sunThe sun exchanges mass for energy

through a nuclear reaction

Cosmic rays, however, are continually striking you and your surroundings and converting part of their energy of motion into the mass of newly created particles. A single high-energy cosmic ray can create a shower of millions of previously nonexistent particles when it strikes the atmosphere.

Mass can be defined from two different perspectives:

1) Mass is the measure of the amount of matter that a body contains

2) Mass is a measure of the inertial property of that body, that is, of its resistance to change of motion (Inertia).

Physics Fundamental Principle:

CONSERVATION OF MASS the total mass of a closed system always

remains constant

All the physical stuff in our universe is called MATTER

Is Air Matter?

• What are the two criteria for matter?–Does it take up space?

–Does it have mass?

WATER STATES OF MATTER

Same for the cup of water as the iceberg

ARE THERE MORE THAN3 STATES OF MATTER?

Fermionic condensates

In order to understand what the numbers refer to we need to include “units”

Thus, many properties of matter are expressed quantitatively (associated with numbers)

In physics we study matter (and energy!) by measuring it

Physics uses a select groupof the SI units known

as MKS (meter, kilogram, second) system

lengthSI unit: meter (m)

mass SI unit: Kilogram (kg)

SI unit for time: seconds (s)

. NOTE: The short forms for SI units (such as mm for millimeter) are called symbols, not abbreviations

for most everyday experience prefixes we use are…

Scientific NotationScientists must often deal with extremely large or small numbers

Scientific notation is a way of expressing very large or very small numbers which are awkward to say and write.

WE NEEDSCIENTIFICNOTATIONFOR THESENUMBERS!

Writing a number in scientific notation:1) Put the decimal after the first digit and drop the zeroes2) Count the number of decimal places moved in step 13) Write as a product of the number (step 1) and 10raised to the power of the count (step 2)

The Andromeda Galaxy (the closest one to our Milky Way galaxy) contains at least 200,000,000,000 stars. So we would write 200,000,000,000 in scientific notation as:

2.0 x 1011 This number is read as follows: "two point zero times ten to the eleventh."

• Now we try a number that is very small.• Change 0.000000902 to scientific notation• The decimal must be moved behind the 9

• The coefficient will be 9.02• The decimal moves seven spaces to the right,

making the exponent -7• Answer equals 9.02 x 10-7

• Examples• Write each of the following numbers in

scientific notation:• (a) 93,000,000 • (b) .00005144 • (c) -33,452.8

• Changing numbers from scientific notation to standard notation.

• Change 6.03 x 107 to standard notation.• we can simply move the decimal seven places

to the right because the exponent is 7.• So, 6.03 x 107 = 60 300 000

• Now let us try one with a negative exponent.• Ex.2 Change 5.3 x 10-4 to standard notation.• The exponent tells us to move the decimal

four places to the left.• so, 5.3 x 10-4 = 0.00053

• Express in standard form:• 1. 1.09 x 103

• 2. 4.22715 x 108

• • 3. 3.078 x 10-4

• • 4. 9.004 x 10-2

• • 5. 5.1874 x 102 (This can be tricky!)

• Answers:• 1) 1090• 2) 422,715,000• 3) 0.0003078• 4) 0.09004• 5) 518.74

SCIENTIFIC CERTAINTY

Precision AccuracyAccuracy indicates how close a measurement is to the accepted value.

Precision indicates how close together or how repeatable the results are.

ACCURATE INACCURATE

Trial #1 #2 #3 #4 #5 Student A 14.8 14.1 14.5 14.6 14.2Student B 14.8 14.2 14.6 14.5 14.8Student C 14.6 14.5 14.5 14.4 14.6

PRECISION AND ACCURACY -- Quiz

Consider the data obtained for the length of an object as measured by three students. The length is known to be 14.54 cm. Which of the conclusions summarizes the data?

a) Student A has done the most precise work and student C the most accurate.b) Student C has done the most precise and accurate work.c) Student C has done the most precise work and student A the most accurate.d) Student C has done the most precise work and student B the most accurate.e) Student B has done the most precise work and student C the most accurate.

Significant figuresAll digits of a measured quantity are called

significant figures

Scientific uncertaintyall measurements contain some uncertainty. Such data is reported in significant figures to inform the reader of the uncertainty of the measurement. We record all significant figures unto the first uncertain number.

DIMENSIONAL ANALYSIS(also known as the factor-label method or unit-factor method)

Why is this important?Whatever you measure,

you have to use units

Example 2: If you are going 50 miles per hour, how many feet per second are you traveling?

Remember the “joule”, the unit for energy?

We will use dimensional analysis on every physics problem we attempt to solve this year

energy[ ] = mass×velocity2⎡⎣ ⎤⎦=grams×cmsec

⎛⎝⎜

⎞⎠⎟

2

=grams×cm2

sec2

or energy[ ] =kg×m2

sec2 ≡ joules

End of unit 1 part 1