PHY121 Summer Session I, 2006

1
PHY121 Summer Session I, 2006
Instructor Chiaki Yanagisawa

• Most of information is available at
• http//nngroup.physics.sunysb.edu/chiaki/PHY121
  -06.
• It will be frequently updated.

• Homework assignments for each chapter due a week
  later (normally)
• and are delivered through WebAssign. Once the
  deadline has passed
• you cannot input answers on WebAssign.
• To gain access to WebAssign, you need to obtain
  access code and
• go to http//www.webassign.net. Your login
  username, institution
• name and password are initial of your first
  name plus last name
• (such as cyanagisawa), sunysb, and the same as
  your username,
• respectively.

• In addition to homework assignments, there is a
  reading requirement
• of each chapter, which is very important.

• The lab session will start next Monday (June 5),
  for the first class
• go to A-117 at Physics Building. Your TAs will
  divide each group
• into two classes in alphabetic order.

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Chapter 1 Introduction

• Standards of Length, Mass and Time

• A physical quantity is measured in a unit which
  specifies
• the scale of the quantity.

• SI units (Systèm International), also known as
  MKS

A standard system of units for fundamental
quantities of science an international committee
agreed upon in 1960.

• Fundamental unit of length meter (m)

1 m 100 cm 1,000 mm, 1 km 1,000 m, 1 inch
2.54 cm 0.0254 m, 1 foot 30 cm 0.30 m
The meter was defined as the distance traveled by
light in vacuum during a time interval of
1/299,792,458 seconds in 1980.
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• Standards of Length, Mass and Time

• A physical quantity is measured in a unit which
  specifies
• the scale of the quantity (contd)

• Fundamental unit of mass kilogram (kg)

1 kg 1,000 g, 1 g 1,000 mg, 1 ton 1,000
kg 1 pound 0.454 kg 454 g, 1 ounce 28.3 g
The kilogram is defined as the mass of a specific
platinum iridium alloy cylinder kept at the
International Bureau of Weights and Measures in
France.

• Fundamental unit of time second (s or sec)

1 sec 1,000 msec 1,000,000 msec, 1 hour 60
min 3,600 sec, 24 hours 1 day
The second is defined as 9,192,631,700 times the
period of oscillation of radiation from cesium
atom.
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• Standards of Length, Mass and Time

• A physical quantity is measured in a unit which
  specifies
• the scale of the quantity (contd)

• Scale of some measured lengths in m

Distance from Earth to most remote normal
galaxies 4 x 1025
Distance from Earth to nearest large galaxy (M31)
2 x 1022
Distance from Earth to closest star (Proxima
Centauri) 4 x 1016
Distance for light to travel in one year (light
year) 9 x 1015
Distance from Earth to Sun (mean)
2 x 1011
Mean radius of Earth
6 x 106
Length of football field
9 x 101
Size of smallest dust particle
2 x 10-4
Size of cells in most living organism
2 x 10-5
Diameter of hydrogen atom
1 x 10-10
Diameter of atomic nucleus
1 x 10-14
Diameter of proton
1 x 10-15
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• Standards of Length, Mass and Time

• A physical quantity is measured in a unit which
  specifies
• the scale of the quantity (contd)

• Scale of some measured masses in kg

Observable Universe
1 x 1052
Milky Way Galaxy
7 x 1041
Sun
2 x 1030
Earth
6 x 1024
Human
7 x 101
Frog
1 x 10-1
Mosquito
1 x 10-5
Bacterium
1 x 10-15
Hydrogen atom
2 x 10-27
Electron
9 x 10-31
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• Standards of Length, Mass and Time

• Other systems of units

• cgs length in cm, mass in g, time in s
• area in cm2,
  volume in cm3, velocity in cm/s
• U.S. customary length in ft , mass in lb,
  time in s
• area in ft2 ,
  volume in ft3, velocity in ft/s

• Prefix

10-3
10-12
10-9
10-6
10-2
micro- (m)
pico- (p)
nano- (n)
milli- (m)
centi- (c)
103
109
106
101
1012
tera- (T)
giga- (G)
mega- (M)
kilo- (k)
deka- (da)
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• The Building Blocks of Matter

• History of model of atoms

nucleus (protons and neutrons)
Old view
proton
electrons e-
Semi-modern view
nucleus
quarks
Modern view
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• Dimensional Analysis

• In physics, the word dimension denotes the
  physical
• nature of a quantity

• The distance can be measured in feet, meters,
  (different
• unit), which are different ways of expressing
  the dimension
• of length.
• The symbols that specify the dimensions of
  length, mass and
• time are L, M, and T.
• dimension of velocity v L/T (m/s)
• dimension of area A L2 (m2)

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• Dimensional Analysis

• In physics, it is often necessary either to
  derive a
• mathematical expression or equation or to
  check
• its correctness. A useful procedure for this
  is called
• dimensional analysis.

• Dimensions can be treated as algebraic
  quantities
• dimension of distance x L (m)
• dimension of velocity v
  x/t L/T (m/s)
• dimension of acceleration a v/t
  (L/T)/T
• 
  L/T2
• 
  x/t2 (m/s2)

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• Uncertainty in Measurement

• In physics, often laws in form of mathematics
  are
• tested by experiments. No physical quantity
  can be
• determined with complete accuracy.

• Accuracy of measurement depends on the
  sensitivity of the
• apparatus, the skill of the person conducting
  the measurement,
• and the number of times the measurement is
  repeated.
• For example, assume the accuracy of measuring
  length
• of a rectangular plate is -0.1 cm. If a side
  is measured to be
• 16.3 cm, it is said that the length of the side
  is measured to
• be 16.3 cm -0.1 cm. Therefore, the true value
  lies between
• 16.2 cm and 16.4 cm.

Significant figure a reliably known digit In
the example above the digits 16.3 are reliably
known i.e. three significant digits with known
uncertainty
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• Uncertainty in Measurement (contd)

• Area of a plate length of sides 16.3-0.1 cm,
  4.5-0.1 cm
• The values of the area range between
• (16.3-0.1 cm)(4.5-0.1 cm) (16.2
  cm)(4.4cm)71.28 cm2
• 71 cm2 and (16.30.1 cm)(4.50.1
  cm)75.44 cm2
• 75 cm2.
• The mid-point between these two extreme
  values
• is 73 cm2 with uncertainty of -2 cm2 .
• Two significant figures! (Note that 0.1
  has only one significant
• figure as 0 is simply a decimal point
  indicator.)

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• Uncertainty in Measurement (contd)

• Two rules of thumb to determine the significant
  figures

• In multiplying (dividing) two or more quantities,
  the number of
• significant figures in the final product
  (quotient) is the same as
• the number of significant figures in the least
  accurate of the
• factors being combined, where least accurate
  means having the
• lowest number of significant figures.

• Area of a plate length of sides 16.3-0.1 cm,
  4.5-0.1 cm
• 16.3 x 4.5 73.35 73 (rounded to two
  significant figures).

three (two) significant figures
To get the final number of significant digit, it
is necessary to do some rounding If the last
digit dropped is less than 5, simply drop the
digit. If it is greater than or equal to 5,
raise the last retained digit by one
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• Uncertainty in Measurement (contd)

• When numbers are added (subtracted), the number
  of decimal
• places in the result should equal the smallest
  number of decimal
• places of any term in the sum (difference).

• A sum of two numbers 123 and 5.35
• 123.xxx
• 5.35x
• ------------
• 128.xxx
• 123 5.35 128.35 128

zero decimal places
two decimal places
zero decimal places
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• Uncertainty in Measurement (contd)

• More complex example 2.35 x 5.86/1.57
• - 2.35 x 5.89 13.842 13.8
• 13.8 / 1.57 8.7898 8.79
• - 5.89 / 1.57 3.7516 3.75
• 2.35 x 3.75 8.8125 8.81
• - 2.35 / 1.57 1.4968 1.50
• 1.50 x 5.89 8.835 8.84

A lesson learned Since the last significant
digit is only one representative from a range
of possible values, this amount of discrepancies
is expected.
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• Conversion of Units

• Since we use more than one unit for the same
  quantity,
• it is often necessary to convert one unit to
  another

• Some typical unit conversions
• 1 mile 1,609 m 1.609 km, 1 ft 0.3048 m
  30.48 cm
• 1 m 39.37 in. 3.281 ft, 1 in.
  0.0254 m 2.54 cm
• Example 1.4
• 28.0 m/s ? mi/h

Step 1 Conversion from m/s to mi/s
Step 2 Conversion from mi/s to mi/h
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• Estimates and Order-of Magnitude

• For many problems, knowing the approximate value
  
• of a quantity within a factor of 10 or so is
  quite useful.
• This approximate value is called an
  order-of-magnitude
• estimate.

• Examples
• - 75 kg 102 kg ( means is on the order of
  or is
• approximately)
• - p 3.14151 (3 for less crude estimate)

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• Estimates and Order-of Magnitude

• Example 1.6 How much gasoline do we use?
• Estimate the number of gallons of gasoline used
  by all cars in the
• U.S. each year

Step 1 Number of cars
Step 2 Number of gallons used by a car per year
Step 3 Number of gallons consumed per year
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• Estimates and Order-of Magnitude (contd)

• Example 1.8 Number of galaxies in the Universe
• Information given Observable distance 10
  billion light year (1010 ly)
• 14 galaxies in
  our local galaxy group
• 2 million
  (2x106) ly between local groups
• 1 ly 9.5 x 1015 m

Volume of the local group of galaxies
Number of galaxies per cubic ly
Volume of observable universe
Number of galaxies in the Universe
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• Coordinate Systems

• Locations in space need to be specified by a
  coordinate
• system

• Cartesian coordinate system

A point in the two dimensional Cartesian system
is labeled with the coordinate (x,y)
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• Coordinate Systems (contd)

• Polar coordinate system

A point in the two dimensional polar system is
labeled with the coordinate (r, q)
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• Trigonometry

• sinq, cosq, tanq etc.

Pythagorean theorem
hypotenuse
side opposite q
side adjacent q
Inverse functions
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• Trigonometry (contd)

• Example 1.9 Cartesian and polar coordinates

Cartesian to polar (x, y)(-3.50,-2.50) m
Polar to Cartesian (r, q)(5.00 m, 37.0o)
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• Trigonometry (contd)

• Example 1.10 How high is the building

What is the height of the building?
r, hypotenuse
What is the distance to the roof top?