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Fundamentals of Physics

Introduction & Chapter 1

Prof. Raymond Lee,revised 8-24-2010

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Physics

• Fundamental science• concerned with the basic principles of the Universe

• foundation of other physical sciences

• Divided into 6 major areas• Classical Mechanics

• Relativity

• Thermodynamics

• Electromagnetism

• Optics

• Quantum Mechanics

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Classical physics

• Mechanics & electromagnetism are basic to allother branches of classical physics

• Classical physics developed < 1900• Start with classical (AKA Newtonian) mechanics

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Classical physics, 2

• Includes Mechanics• Major developments by Newton, & continuing

through latter 19th century

• Thermodynamics

• Optics

• Electromagnetism• These last 3 not developed until latter 19th century

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Modern physics

• Began near end of 19th century

• Phenomena that could not be explained byclassical physics

• Includes theories of relativity & quantummechanics

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Classical mechanics today

• Still important in many disciplines

• Wide range of phenomena that can be explained withclassical mechanics

• Many basic principles carry over into otherphenomena

• Conservation laws also apply directly to other areas

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Objective of physics

• To find limited number of fundamental lawsthat govern natural phenomena

• To use these laws to develop theories thatcan predict results of future experiments

• Express laws in language of mathematics

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Theory & experiments

• Should complement each other

• When a discrepancy occurs, theory may bemodified

• Theory may apply to limited conditions• e.g., Newtonian mechanics confined to objects

traveling « speed of light

• Then try to develop a more general theory

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Quantities used

• In mechanics, use 3 basic quantities• Length

• Mass

• Time

• Will also use derived quantities• Those can be expressed in terms of basic

quantities

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Standards of measurement

• Standardized systems

• agreed upon by some authority, usually agovernmental body

• SI – Systéme International

• agreed to in 1960 by an internationalcommittee

• main system used in your text

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Length

• Units• SI – meter, m

• Defined in terms of meter – distance traveled by lightin a vacuum during a given time

• See Table 1-3 (p. 4) for representative lengths

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Mass

• Units• SI – kilogram, kg

• Defined in terms of a kilogram, based on a specificcylinder kept at International Bureau of Standards & inU. S. at NIST (copy at National Institute of Standards &Technology in Gaithersburg, MD)

• See Table 1-5 (p. 7) for masses of various objects

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Standard kilogram

(SJ 2008 Fig.1.1, p. 5)

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Time

• Units

• seconds, s

• Defined in terms of oscillation of radiationfrom cesium atom

• See Table 1.4 (p. 5) for some ~ time intervals

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Number notation

• When writing out numbers with many digits, space#s in groups of 3

• Examples:

• 25 100

• 5.123 456 789 12

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Reasonableness of results

• When solving a problem, check your answerto see if it’s reasonable (AKA giggle test)

• Reviewing tables of ~ values for length,mass, & time helps test for reasonableness

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Measurement systems

• US Customary (AKA English system)• everyday units

• Length is measured in feet

• Time is measured in seconds

• Mass is measured in slugs

• often uses weight, in pounds, instead of massas a fundamental quantity

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Prefixes

• Prefixes correspond to powers of 10

• Each prefix has specific name

• Each prefix has specific abbreviation

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Prefixes, cont.

• Prefixes can be usedwith any base unit

• Prefixes are multipliersof base unit

• e.g.:

• 1 mm = 10-3 m

• 1 mg = 10-3 g

(compare withTable 1-2, p. 2)

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Model building

• A model is a system of physical components

• Identify the components

• Make predictions about the behavior of thesystem• Predictions based on interactions among the

components and/or

• Based on interactions between the components& the environment

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Models of matter

• Some Greeks thoughtmatter is made of atoms

• J. J. Thomson (1897) foundelectrons & showed atomshad structure

• Rutherford (1911) proposedcentral nucleus surroundedby electrons

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Models of matter, 2

• Nucleus has structure, containing protons &neutrons• Number of protons ! atomic number

• Number of protons & neutrons ! mass number

• Protons & neutrons are made up of quarks

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Modeling technique

• Important technique is to build a model for aproblem• Identify a system of physical components for the

problem

• Make predictions of the system’s behavior basedon interactions among its components and/orcomponents & environment

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• Density is an example of a derived quantity

• It is defined as mass/unit volume: " = m/V (Eq. 1-8, p. 7)

• Units are kg/m3

• See Table 14-1 (p. 360) for " values ofrepresentative materials

Density

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Atomic mass

• The atomic mass is total # of protons &neutrons in element

• Can be measured in atomic mass units, u

• 1 u = 1.6605387 x 10-27 kg

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Basic quantities & their dimension

• Dimension has a specific meaning — denotesphysical nature of a quantity

• Dimensions are denoted with square brackets• Length [L]

• Mass [M]

• Time [T]

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Dimensional analysis

• Technique to check correctness ofequation or to assist in deriving it

• Treat dimensions (length, mass, time,combinations) as algebraic quantities

• add, subtract, multiply, divide

• Both sides of equation must have samedimensions

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Dimensional analysis, 2

• Limitation: can’t give numerical factors

• Dimensions of some common quantities given below

(SJ 2008 Table 1.5, p. 8)

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Symbols

• Symbol used in an equation not necessarily thesymbol used for its dimension

• Some quantities have 1 symbol used consistently

• e.g., time nearly always denoted t

• Some quantities use many symbols, depending uponspecific situation

• e.g., lengths may be x, y, z, r, d, h, etc.

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Dimensional Analysis, example

• Given equation: x = 1/2 at 2

• Check dimensions on each side:

• The T2s cancel, leaving L for dimensions of each side

• equation is dimensionally correct

• constant 1/2 has no dimensions

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Units conversion

• If units are inconsistent, convert to consistent ones

• Units can be treated like algebraic quantities (i.e., canceleach other)

• See inside of text’s back cover for a list of conversionfactors

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Units conversion, 2

• Always include units for every quantity; youcan carry units through entire calculation

• Multiply original value by a ratio = 1

• Example:

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Order of magnitude

• Approximation based on several assumptions• may need to modify assumptions if we need more

precise results

• Order of magnitude is power of 10 that applies

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Uncertainty in measurements

• Uncertainty in every measurement -- this uncertaintycarries over through the calculations

• need to account for this uncertainty

• Use rules for significant figures to ~ uncertainty inresults of calculations

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Significant figures

• A significant figure is one that’s reliably known

• Zeros may or may not be significant• Those that position decimal point aren’t significant

• To remove ambiguity, use scientific notation

• In a measurement, significant figures includethe first estimated digit

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Significant figures, 2

• 0.0075 m has 2 significant figures• leading zeros are placeholders only

• can write in scientific notation to show more clearly: 7.5 x10-3 m for 2 significant figures

• 10.0 m has 3 significant figures• decimal point gives information about measurement’s

reliability

• 1500 m is ambiguous• Use 1.5 x 103 m for 2 significant figures

• Use 1.50 x 103 m for 3 significant figures

• Use 1.500 x 103 m for 4 significant figures

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Significant figures, 3

• When multiplying or dividing, number of significantfigures in final answer = number of significant figuresin quantity with smallest # of significant figures.

• e.g.: 25.57 m x 2.45 m = 62.6 m2

• 2.45 m limits your result to 3 significant figures

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Significant figures, 4

• If adding or subtracting, # of decimal places in result= smallest # of decimal places in any term in sum.

• e.g.: 135 cm + 3.25 cm = 138 cm

• 135 cm limits answer to units decimal value

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Significant figures, 5

• Rule for addition & subtraction differs from rulefor multiplication & division

• For adding & subtracting, # of decimal places isprime consideration

• For multiplying & dividing, # of significant figuresis prime consideration

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Rounding

• Last retained digit increases by 1 if lastdigit dropped > 5

• Last retained digit remains as it is if lastdigit dropped < 5

• If last digit dropped = 5, round retaineddigit to nearest even number

• Saving rounding until final result helpseliminate error accumulation