Topic 1: Physics and physical measurement

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Topic 1 Physics and physical measurement

• 1.2 Measurement and uncertainties

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The SI system of fundamental and derived units

• 1.2.1 State the fundamental units in the SI
  system.
• 1.2.2 Distinguish between fundamental and derived
  units and give examples of derived units.
• 1.2.3 Convert between different units of
  quantities.
• 1.2.4 State units in the accepted SI format.
• 1.2.5 State values in scientific notation and in
  multiples of units with appropriate prefixes.

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SI System

• In old days, units were random
• Communication difficulties
• SI Systéme International (metric system)
• Developed on orders of King Louis XVI of France

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Seven Base (Fundamental) Units
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Evolution of base units

• Meter
• 1/10,000,000 the distance from the north pole to
  the equator, measured along a line passing
  through Lyons, France (1790)
• Distance between two lines engraved on a
  platinum-iridium bar in Paris. (1875)
• the distance traveled by light in a vacuum
  during a time interval of 1/299,792,458 s (1984)

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Evolution of base units

• Second
• 1/86,400 of the mean solar day
• the duration of 9,192,631,770 periods of the
  radiation corresponding to the transition between
  the two hyperfine levels of the ground state of
  the cesium 133 atom
• Vibrations of a cesium-133 atom in an atomic
  clock

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Evolution of base units

• Kilogram
• Mass of exactly one cubic decimeter of water
  (1790)
• The mass of the international prototype of the
  kilogram (1899)

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SI System vs. British SystemMultiples of 10

• SI Units (Metric)
• 1000 m 1 km
• 1 m 100 cm
• 1 cm 10 mm
• 1000 g 1 kg

• British System
• 1 mi 5280 ft
• 1 ft 12 in
• 1 yd 36 in
• 16 oz 1 lb

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Seven Base (Fundamental) Units

• All other units can be derived from first three
  base units (meter, kilogram and second)

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Derived SI Units
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Important Non-SI Units
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Example

• Which one of the following are base units
• ampere
• coulomb
• meter
• second
• newton
• kilogram

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Common SI Prefixes
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Conversions Factor Label Method

• Convert 1 year to seconds
• Convert 1 mi to inches

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Uncertainty and error in measurement

• 1.2.6 Describe and give examples of random and
  systematic errors.
• 1.2.7 Distinguish between precision and accuracy.
• 1.2.8 Explain how the effects of random errors
  may be reduced.
• 1.2.9 Calculate quantities and results of
  calculations to the appropriate number of
  significant figures.

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Systematic vs. Random Errors

• No measurement is ever perfect
• Random Error
• If the readings of a measurement are above and
  below the true value with equal probability
• Usually caused by unknown and unpredictable
  changes in the experiment. These changes may
  occur in the measuring instruments or in the
  environmental conditions.
• i.e. reaction time on a stopwatch
• i.e. irregular changes in the heat loss rate from
  a solar collector due to changes in the wind.

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Systematic vs. Random Errors

• Systematic Error
• Can be detected by using a different method or
  apparatus and comparing results
• Usually come from the measuring instruments. They
  may occur because
• there is something wrong with the instrument or
  its data handling system, or
• because the instrument is wrongly used by the
  experimenter.
• i.e. an offset zero on a scale

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Systemic vs. Random Error
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Random or systematic?

• random
• random
• systematic
• random
• systematic
• systematic

• Changes in conditions such as temperature,
  pressure, etc
• Malfunction of a piece of apparatus
• An observer consistently making the same mistake
• A different person reading the instrument
• Apparatus calibrated incorrectly
• Energy converted to heat due to friction on a
  pulley

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Reducing Random Error

• Can be reduced by repeating measurement many
  times and taking the average
• Systemic error will not be affected by this
  process
• Error Analysis
• What difference did friction and air resistance
  make?
• How accurate were the measurements of length,
  mass and time?
• Were the errors random or systemic?

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Precision vs. Accuracy
Precise but not accurate
Neither precise nor accurate
Precise and accurate
Accurate but not precise
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Precision vs. Accuracy
Precise and accurate
Precise but not accurate
Neither precise nor accurate
Accurate but not precise
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Precision vs. Accuracy

• Systematic errors may yield precise results but
  will limit accuracy
• Random errors may average out to an accurate
  result but will limit precision

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Significant Figuresreading smallest division
on measuring instrument
About 5 cm
5 cm 1
About 4.6 cm
4.6 cm 0.1
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Significant Figures

• 5 cm 1 cm ? 1 significant figure
• 4.6 cm 0.1 cm ? 2 significant figures

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Significant Figure Rules

• All nonzero digits are significant
• 1.234 g has 4 significant figures
• 1.2 g has 2 significant figures
• Zeroes between nonzero digits are significant
• 1002 kg has 4 significant figures
• 3.07 mL has 3 significant figures

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Significant Figure Rules

• Leading zeros to the left of the first nonzero
  digits are not significant such zeroes merely
  indicate the position of the decimal point
• 0.001o C has only 1 significant figure
• 0.012 g has 2 significant figures
• Trailing zeroes that are also to the right of a
  decimal point in a number are significant
• 0.0230 mL has 3 significant figures
• 0.20 g has 2 significant figures

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Significant Figure Rules

• When a number ends in zeroes that are not to the
  right of a decimal point, the zeroes are not
  necessarily significant
• 190 miles has 2 significant figures
• 50,600. has 5 significant figures

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• Determine the number of significant figures
• 50.3
• 3.0025
• 0.892
• 0.0008
• 57.00
• 2.000000
• 1.09
• 0.000004
• 3.000
• 9.0

3 5 3 1 4 7 3 1 4 2
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Significant Figure Rules

• Rule for Adding Subtracting
• Final answer has same number of digits after
  decimal as number with fewest digits after
  decimal
• Rule for Multiplying Dividing
• Final answer has same number of significant
  figures as number with smallest number of
  significant figures

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• Solve with significant figures
• 97.3 5.85
• 123 x 5.35
• 3.461728 5.2631
• 125.39 - 3.581
• 439.50 / 16.3

103.2 658
8.7248 121.81
27.0
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Uncertainties in calculated results

• 1.2.10 State uncertainties as absolute,
  fractional and percentage uncertainties.
• 1.2.11 Determine the uncertainties in results.

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Uncertainties in calculated results

• Reaction time error for a 1.0 s measurement on a
  stopwatch could be reasonably stated as 0.1 s
• Absolute uncertainty Has a magnitude and a unit
• 1.0 s 0.1s

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Uncertainties in calculated results

• Can also be stated as a fractional uncertainty
• 1.0 s 1/10
• Can also be stated as a percentage uncertainty
• 1.0 s 10

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Uncertainties in Results

• Addition or Subtraction
• Add absolute uncertainties
• Multiplication or Division
• Add percentage uncertainties

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Uncertainties in graphs

• 1.2.12 Identify uncertainties as error bars in
  graphs.
• 1.2.13 State random uncertainty as an uncertainty
  range () and represent it graphically as an
  error bar.
• 1.2.14 Determine the uncertainties in the
  gradient and intercepts of a straight-line graph.

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Uncertainties in graphs

• Data will always have a value. This must also
  be shown on a graph
• Error bar lengths represent the uncertainty.
• Can be on both sides of axis
• Best fit line must be drawn through error bars
• Outliers must be discussed in error analysis

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