September 8, 2009Physics I Lesson 1 Dr J. Tison 1 Scientific Discovery ( A mystery story) Curiosity and inquisitiveness of how natural phenomena occur

September 8, 2009 Physics I Lesson 1Dr J. Tison

1

Scientific Discovery( A mystery story)

• Curiosity and inquisitiveness of how natural phenomena occur

• Observe and interpret

• Imagination – Hypothesize meaning of observations– Create models and theories

• Test models and theories: experiments– Modify and retest


2

Refine models and theories

• Accepted theories– often proven incorrect by new evidence– create new or improved theories

• Example… – Ptolemy (ca 100AD) taught the earth is center

of solar system – Copernicus, then Galileo (ca 1500AD)

determined that the sun is the center of the solar system.


3

Symmetry in the universe?

• A scientist looks for…– Symmetry or commonality – Applies accepted theories, hypotheses, or models.

• Example…– Newton’s Law of Gravitational Force (2 masses):

• Fg = Gm1m2/r2

– Coulomb’s Law of Electrostatic Force (2 charges): • Fe = Kq1q2/r2


4

Expand the range of theories• Newton’s law of motion

– “classical” description of bodies in motion

• Einstein’s theories of relativity – “modern” physics extends to the wider range

of phenomena, in the universe

Newton’s Laws of Motion are used to describe most natural phenomena that are observed in normal everyday situations.


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Who’s on first? Models, Theories, Laws & Principles

• Model: Visual concept of what is observed

• Theory: Detailed description with measurable results to test model

• Law (e.g. Newton’s): Concise, general statements about how nature behaves

• Principle: (e.g. Archimedes) is a less general statement than a law


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Measurement and Uncertainty

Lord Kelvin (1824-1907):

• “… when you can measure what you are speaking about, and express it in numbers, you know something about it;

• … when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind;

• … it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced the stage of Science, whatever the matter may be”


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Measurements

• Some examples…– Distance, speed (and velocity) – Temperature – Time– Weight – And, many others.


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Measurement and Calculations

• Examples...– Speed = (distance)/(time) e.g. mph, ft/sec, etc

• 2 measurements: (1) distance; (2) time

– Momentum = (mass)∙(velocity) = (mass)∙(distance)/time

• 3 measurements: (1) mass; (2) distance; (3) time


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Undefinable Quantities

• Some physical quantities…– length, time, mass, temperature, are

fundamental and are not calculated from others

– International committees (e.g. SI) determine the “standard” for measuring undefinable quantities


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SI Base units: Length

Length: meter (m) – Length of the path traveled by light in a

vacuum, – During the time interval of 1/299 792 458 of a

second

Note: Speed of light is 299,792,458 m/s


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SI Base units: Mass

Mass: kilogram (kg) – Mass of a platinum-iridium cylinder

• (Bureau International des Poids et Mesures (BIPM), Sèvres, Paris (1st CGPM (1889), CR 34-38).

– Only base unit with a prefix (kg); • Gram is derived unit, equal to 1/1000 of a

kilogram;

– Only unit still defined by a physical prototype • (instead of a measurable natural phenomenon )


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SI Base units: Time

Time : second (s)

• Duration of exactly 9,192,631,770 periods of the radiation corresponding to

• Transition between two hyperfine levels of the ground state of the cesium-133 atom– at a temperature of 0º K


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SI Base Unit:Temperature, Kelvin (ºK)

• Thermodynamic temperature, ºK – Absolute temperature – Fraction 1/273.16 (exactly) of the

thermodynamic temperature at the triple point* of water

*Triple Point of Water: water, ice, and water vapour coexisting in a stable equilibrium :0.01 °C; 6.03 x 10-3 atm)

http://en.wikipedia.org/wiki/Water

http://en.wikipedia.org/wiki/Ice

http://en.wikipedia.org/wiki/Water_vapour

http://en.wikipedia.org/wiki/Water_vapour

http://en.wikipedia.org/wiki/%C2%B0C

http://en.wikipedia.org/wiki/Atmosphere_%28unit%29


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SI Base Unit: Ampere (A)

• Ampere: Constant current maintained in– Two straight parallel conductors of

• Infinite length and • Negligible cross-section, and• Placed 1 meter apart in a vacuum,

– Produces a force between these conductors

= 2×10 -7 n/m


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Systems of Units

• mks– SI – French Academy of Sciences – meter, kilogram, sec

• cgs– centimeter, gram, sec

• British

– foot, lb, sec


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Conversion between Units

Speed = distance/time– 1 m/s = (1m/s)(100cm/1m) = 100cm/s

– 1 m/s = (1m/s) (1in/2.54cm)(100cm/1m) = 3.94in/s

– 1 m/s = (1m/s) (1in/2.54cm)(100cm/1m (60s/min)

(60min/h)

= 14.2 x 103 in/h


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Uncertainty: Accuracy, Precision

Which has high accuracy? high precision? low accuracy? low precision?


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X Y

• X = average value – sometimes written as= <x>

• Y = calculated difference from <x> – Y is measure of “precision”– % = y/x ∙ 100

• Multiple measurements as in a “Gage R&R” – 5 or 10 measurements.– Static or dynamic– 3 days


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All Measurements have Uncertainty

• Random Errors: statistical – Repeatability and reproducibility– Unpredicable fluctuations in temperature or line

voltage– Mechanical vibrations of an experimental setup– Unbiased estimates of measurements by observer

• Systematic Errors: determinate

– Measurement device: – Instrument calibration– Personal error, e.g. parallax reading of a gage


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How to…

• Obtain greater accuracy – Minimize systematic errors

• Obtain greater precision – Minimize random errors


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Metrology System Specification


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Hip Replacement Metrology


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Hip Joint Metrology Result


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Camshaft Metrology


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Gears


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Significant Figures

• Number of directly read + one estimated number– All non-zero digits– Leading zeros not significant– Zeros (a) between non-zero, and (b) at end, if

measured, are significant – Least count:

• Smallest subdivision on the measurement scale

• “Meter stick is calibrated in cm with a millimeter least count


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Significant Figures: Example

• 12.3 cm– # significant figures = 3

• 0.0123cm – # significant figures = 3

• 12.03 cm– # significant figures = 4

• 12.30 cm– # significant figures = 3 or 4?


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Significant Figures in Calculations

• Calculating with Significant Figures– Use the least # significant figures– 12.3 x 1.2 = 14.76 = 15

• there are 2 s.f. in 1.2

– 12.3 x 1.20 = 14.76 = 14.8• There are 3 s.f. in 1.20 and 12


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Significant Figures in Calculations

• Calculating with Significant Figures– Use the least # significant figures– 12.3 x 1.2 = 14.76 = 15

• there are 2 s.f. in 1.2

– 12.3 x 1.20 = 14.76 = 14.8• There are 3 s.f. in 1.20 and 12


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Scientific Notation

• Powers of 10 – Usually expressed as 1 digit to left of decimal

point– 1,234.0 = 1.234 ∙ 103 – Alternative notation

• Doesn’t require superscripts (simplifies typing)• 1,234.0 = 1.234E3

• Scientific calculator display


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Scientific Notation

Speed of light: – 186,282 mi/s → 1.86282 ∙ 105 mi/s– 299,792,458 m/s → 2.99792458 ∙ 108 m/s

Gravitational constant– Standard format: 0.0000000000667300 m3 kg-

1 s-2

– Scientific notation: 6.67300 ∙ 10-11 m3 kg-1 s-2

–


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Computations in Powers of 10

• Adding/subtracting– All values must be have same “power of ten”

• Multiplying/dividing– Write each number in scientific notation, i.e. x.yz ∙ 10a– Multiply the numbers as standard numbers– Add/subtract the exponents for the “power of ten

term”• 12.3 x 123.0 = • (1.23 ∙ 101) x (1.23 ∙ 102) = • 5.129 ∙ 103 = 5.129E3


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Powers of Ten Prefixes

10-24 to 1024

• See names Table 1-4

• Most common – 10-12 pico – 109 giga– 10-9 nano-– 103 kilo– 106 mega


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Order of Magnitude

Estimate value to approx. “Power of Ten”– Order of Magnitude (OM) of 100 is 102– ≈ is mathematical operator meaning “roughly”


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Dimensions, Dimensional Analysis

Convenient way to • Verify proper mathematical relationships• Check correctness of calculations• Make sure all terms to be added or subtracted

have same ‘units of measure’


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Lesson 1: Summary

• Scientific Discovery– Models, Theories, Laws, Principles

• Physical Quantities– Undefinables, standards, SI

• Mass, Length, Time, Temperature, etc– Definables

• Velocity, Acceleration, Force, Momentum, etc– Systems of Units

• MKS• CGS• British


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Lesson 1: Summary

• Measurements– Accuracy and Precision– Uncertainty

• Random and Statistical Errors• Determinant and indeterminate• % Uncertainty

– Significant Figures• Calculators and reported values

• Calculations– Scientific Notation

• Powers of 10

– Order of Magnitude (OM)– Dimensional Analysis

Documents

September 8, 2009Physics I Lesson 1 Dr J. Tison 1 Scientific Discovery ( A mystery story) Curiosity and inquisitiveness of how natural phenomena occur