Chapter 1 Class Notes



Chapter 1 Class Notes

Physics is concerned with the nature of physical reality, that is, things that can be measured with instruments.

Between 1600 and 1900, three broad areas were developed in what is now called Classical Physics and they are;

1. Classical Mechanics

2. Thermodynamics

3. Electromagnetism

We will be focussing on the Classical mechanics in this PS 150 class, chapters 1 - 12 in your textbook.

Overview of the Current State of Physics to be expanded upon in future 300 level Physics Classes

By 1905, it became apparent that classical physics failed to explain several phenomena, particularly those concerned with light and sub atomic particles. The famous scientist Albert Einstein led the development of three areas in Modern Physics;

1. Special Relativity

2. Quantum Mechanics

3. General Relativity

There are four basic forces in nature, the two most commonly experienced are Gravity and the Electromagnetic forces. Gravity is the force which holds us down on the Earth’s surface and governs the motion of planets in the solar system. The Electromagnetic force governs the motion of charged particles such as electrons and protons. Static electricity and lightning are common manifestations of this force. The two other forces prevail at the sub atomic level and therefore not commonly experienced by us, they are the Strong force which holds the constituent neutrons and protons together in atomic nuclei and the Weak force which governs radioactive decay.

The Unified Force Theory

Three of the four forces can be unified in a single wave-particle theory, with the exception being Gravity. There are serious problems with Gravity on both ends of the size spectrum. On the smallest scale, the sub-atomic particle that transmits gravity, called the Graviton, has not yet been detected, because it must have a large mass and therefore requires a very energetic particle accelerator to reveal it. On the larger scale, the classical theory of gravity causes the mass of galaxies to be greatly overestimated, a discrepancy that can only been reconciled by positing vast quantities of Dark matter whose composition and indeed, very existence, remains elusive. But more of that later on in your career, right now lets focus on Chapter 1.

Things You Need to Know about Chapter 1

1. Units

Units are very important. One of the things that distinguishes Physics from Mathematics is that all the numbers in Physics have units. This is because Physics numbers are all measures of some physical property, like size (length) or mass, for example.

Unless otherwise stated, all calculations in this class will be performed using SI (Systeme Internationale) Units, which include

physical property SI unit

length meters (m)

mass kilogram (kg)

time seconds (s)

2. Powers of Ten and Scientific Notation

Many of the calculations we will be doing in this class will result in very large or very small numbers. Rather than writing down alot of zero’s, we will use a mathematical short hand called scientific notation and it goes like this, starting with the big numbers,

Number scientific notation name common prefix

1,000,000,000 1 x 109 Billion

1,000,000 1 x 106 Million

1,000 1 x 103 thousand Kilo (eg. kilogram)

100 1 x 102 hundred

10 1 x 101 ten

1 1 x 100 one

On your calculator, you will see an exp or EE key. Please learn how to use it, as every calculator is different.

Now the small numbers,

Number scientific notation common prefix

0.01 10-2 centi (eg. centimeters or cm)

0.001 10-3 milli (eg. millimeters or mm )

0.000001 10-6 micro

0.000000001 10-9 nano

3. Unit Conversions

It is often necessary to convert units, for example, miles to kilometers. There is a conversion Table in Appendix G at the back of your textbook that you will find useful.

Example 1. How many km is 10 miles?

The easiest way to solve unit conversion problems is to write down the unknown quantity, in this case km, on the right hand side of the equal sign and the known or given quantity, in this case 10 miles, on the left hand side of the equal sign. Now draw a pair of brackets for the unit conversion factor, like this;

10 miles x ( ) = km

Now look up the appropriate conversion factor in Appendix G. You will see in the Table titled Length, that 1 km = 0.6214 mi(le). The conversion factor we want to place in the brackets must have kilometers on the top, in the numerator, and miles on the bottom, in the denominator, so that when we multiply by 10 miles, the units of miles cancel, leaving the answer in units of km, like this;

10 miles ( 1 km ) = 16.09 km

0.6214 miles

Notice that the multiplication symbol, x was dropped. This is customary in Physics and Math so as not to confuse the symbol with a variable x.

4. Precision of Answers

There are some rules that you can read about in section 1-6 in Chapter 1 concerning significant digits and decimal places, but the upshot for this class is that all the answers to calculations should be presented to an accuracy of one or two decimal places. Thus, the answer to Example 1 would be 16.1 miles, accurate to 1 decimal place. All the numeric answers to homework questions are provided on the class web-site .

5. Derived Units

Derived units are combinations of the base units, for example

speed = distance

time

has SI units of meters per second, usually written m/s. If you wish to convert a speed in miles per hour to meters per second you will now need two conversion factors, one converting miles to meters and the other converting hours to seconds.

Example 2. Express the speed 5 miles/hr in m/s.

As with the last example, leave a space for the answer on the right hand side of the equal sign, write down the question on the left hand side of the equal sign and two pairs of brackets for the two conversion factors;

5 miles ( ) ( ) = m

hr s

Now look in Appendix G for the appropriate conversion factors. In the Table titled length we see that 1 mile = 1609 m, and in the table titled Time we see that 1 hour = 3600 s, which comes from the fact that

60 minutes x 60 seconds = 3600 s

hour minutes hour

Inserting the appropriate conversion factors into the brackets above leads to the following result,

5 mile ( 1609 m ) ( 1 hr ) = 2.2 m

hr mile 3600 s s

Notice that we had to invert the time conversion factor to get the units of hours to cancel properly.

6. Math Tools

Mathematics is a tool that we use to solve physics problems. One of my previous students said “Physics gives Math a purpose” which I thought was very well put! So, I have devised the following problems that emphasize the particular math skills that you will need this semester. It is your responsibility to make sure that you know how to do these problems, or find out how to do them, either from me or your Math instructor. I will go through the answers at the beginning of our second class. You should attempt them well beforehand.

Linear Equations

Qu. 1 X + 3Y = 7 and 4X - 3Y = 12. Find X and Y.

Quadratic Equations

Qu. 2 20 = (392)1/2 t - 4.9 t2 Find t.

(Hint: the quadratic formula is t = [ -b +/- { b2 - 4ac }1/2 / 2a] )

Factors

Qu. 3 Factor X2 + 4X - 21

Qu. 4 The expression B2/ (R3 + B3)1/3

is equivalent to which of the following

B2/ (1 + B3 / R3 )1/3 , B2/ {R3 (1 + B3 / R3 )1/3} , or B2/ {R (1 + B3 / R3 )1/3}

Algebra

Qu. 5 Rearrange to make v the subject of the formula;

GMm = mv2

r2 r

Straight Line Formula

Qu. 6 What is the slope and intercept of the straight line connecting the following (x, y) pairs? (2, 16), (6, 32). Write down the equation of this line. (Hint: the equation of a straight line is y = mx + b).

Qu. 7 The speed of sound, v, is related to the frequency, f, and the wavelength L, according to the equation v = f L. If you were given a set of measurements of f and L and asked to find the velocity v, what graph should you plot? What would the intercept be?

Trigonometry

Qu 8. Find the angles given the lengths of the two shorter sides are 2 and 4cm. (Hint a2 = b2 + c2, and cosine = adjacent/ hypotenuse)

[pic]

Qu 9. Express the distance y in terms of the hypotenuse h and the angle θ

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Indices

Qu 10. Express the following in terms of 2 raised to some power

(22)6 =

(22)1/6 =

Logarithms

Qu 11. log10 (102) =

INV log10 (2) =

loge (ex) =

e1 =

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