Physics and Measurement

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Physics and Measurement

• This is an introductory Unit that is hopefully a
  review on Measurements, Dimensional Analysis,
  Conversion of Units, Significant Figures, and
  Order-of-magnitude Calculations

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1.1 Standards of Length, Mass, and Time

• The laws of physics are expressed in terms of
  basic quantities that require a clear definition.
  In 1960, an international committee established
  a set of standards for those basic quantities
  called fundamental quantities. The system is
  called the International System of units (SI).
  The Fundamental quantities are Length, Mass, and
  Time.

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1.1 Standards of Length, Mass, and Time

• Length
• Many units of length have been used. A few used
  in the English system
• Foot Length of King Louis XIVs foot
• Inch distance from the first knuckle to the
  second on a persons index finger
• Shoe size Measured in lengths of barley corns
• Fathom The distance between a persons
  outstretched hands.
• Furlong The distance a person wants to plow
  behind a horse before he wants to turn around and
  go the other way.

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1.1 Standards of Length, Mass, and Time

• Length
• In 1120 AD the king of England decreed that the
  standard of length would be the yard and that the
  yard would be precisely equal to the distance
  from the tip of his nose to the end of his
  outstretched arm.
• This is not a good standard since it changes
  through his life. (ones feet, hands, ears and
  nose grows until death)
• Also it would be hard to measure when he died.
• In 1799 the French standard became the meter.
• One ten-millionth of the distance from the North
  Pole to the equator. (Through Paris)
• Close to a yard in length. That is because that
  length is good for people to use as a measuring
  stick.

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1.1 Standards of Length, Mass, and Time

• Length
• The French made a platinum iridium bar the
  length they calculated for the meter.
• They made a mistake and so that bar became the
  standard length to which all other lengths were
  compared.
• It could be destroyed and then there would be no
  standard just as when the king died.
• In 1960 the meter was redefined as 1,650,763.73
  wavelengths of orange-red light emitted from a
  krypton-86 lamp.
• In 1983 the meter was redefined as the distance
  light travels in 1/299792458 second.

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1.1 Standards of Length, Mass, and Time

• Mass
• The SI unit of mass is the kilogram defined as
  the mass of a specific platinum-iridium alloy
  cylinder kept at the international Bureau of
  Weights and Measures at Sevres, France.
• There are 12 secondary standards through the
  world, 2 is the USA.

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1.1 Standards of Length, Mass, and Time

• Time
• Before 1967 the standard of time was defined in
  terms of the mean solar day for the year 1900.
  The second was 1/86400 of a mean solar day.
• In 1967 the second was redefined to take
  advantage of the high precision obtainable in a
  device known as an atomic clock.
• The second is now defined to be 9,192,631,770
  periods of the radiation from cesium-133 atoms.
• We will not go over sections 1.2, 1.3, or
  prefixes in class, however you are responsible
  for the material.

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1.2 Derived Units

• All other units are made up from the fundamental
  units

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1.3 Conversion of Units

• Read this section carefully. Try the following
  example.
• Find the density of water in slugs/fathom.
• You may find the inside of the back cover of your
  text to be very useful.
• I usually look up unknown conversions on the
  internet.

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1.4 Conversion of Units
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1.3 Precision

• You take a trip to Lake Erie in Pennsylvania.
  You zero the odometer your car, leave the
  driveway and get to the beach. You cant drive
  your car in the sand so you take the meter-stick
  and measure the distance from the bumper of your
  car to the water.

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1.3 Precision

• Distance in car 241.4 km
• Distance on beach 36.534 m
• What is the distance from your house to lake
  Erie?
• What precision can you get with a stick a meter
  long?
• One divided into decimeters?
• One divided into centimeters?
• One divided into millimeters?

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1.5 Rules for Significant Figures

• Significant Figures - The digits which indicate
  the number of units we are reasonably sure of
  having counted in making a measurement.

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1.5 Rules for Significant Figures

• Rules for Significant Figures
• All counted numbers have an infinite number of
  significant figures.
• Ex. 2 people are in the room.
• All constants have an infinite number of
  significant figures.
• Ex. The 2 and the ? in the circumference
  equation (2?r).
• All nonzero digits are significant.
• Ex. 3258 4 sig. figs.
• All zeros between nonzero digits are significant.
• Ex. 206 3 sig. figs.
• Zeros to the right of nonzero digits are not
  significant, unless indicated by a decimal.
• Ex. 200 1 sig. fig.
• Ex. 200. 3 sig. figs.

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1.5 Rules for Significant Figures

• Rules for Significant Figures
• Zeros to the right of a decimal are not
  significant.
• Ex. 0.0025 2 sig. figs.
• Zeros to the right of a decimal that follow a
  nonzero digit are significant.
• Ex. 0.0500 3 sig. figs.
• Ex. 0.2000 4 sig. figs.

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Mathematical Rules using Significant Figures

• Addition and subtraction Round all numbers to
  the least accurate measurement and then
  add/subtract .
• Ex. 12.02 1.2 103.456 12.0 1.2 103.5
  116.7
• Ex. 300 30 10. 300 0 0 300

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Mathematical Rules using Significant Figures

• Multiplication and division Perform operation
  and then round your answer according to the least
  precise factor.
• Ex. 3.54 x 4.8 x 0.5421 9.2113632
• Ans. in sig. figs. is 9.2

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Rounding

• Rounding Round down if the digits to be dropped
  are less than 5 or if the 5 is followed by zeros
  the preceding is even. Round up if the digit
  to be dropped is a 5 and is followed by other
  numbers of if the preceding is odd.
• Ex. Round to 3 significant figures
• 5.433 ? 5.43
• 3.635 ? 3.64
• 8.2451 ? 8.25
• 5.325 ? 5.32

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Rounding
Table 1 Significant Figures 2 sig. figs. 3
sig. figs. 4 sig. figs. 2300 5420 1521 40
. 600. 2502 5.2 73.0 4.050 0.16 0.915
0.3780 0.0078 0.0467 0.01520
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Scientific notation

• Scientific notation - Rules for putting a number
  into scientific notation.
• A positive power of ten indicates a number larger
  than one.
• A negative power of ten indicates a number
  smaller than one.
• The positive power of ten tells how many places
  the decimal point has been moved to the left.
• The negative power of ten tells how many places
  the decimal point has been moved to the right.
• The first number is greater than or equal to 1
  and less than 10 in any measurement expressed in
  scientific notation.

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Scientific notation

• Examples
• 360 3.6 x 102
• .000238 2.38 x 10-4
• 602000000000000000000000 6.02 x 1023