1.2 Measurement in Experiments

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1.2 Measurement in Experiments
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Learning Objectives

• List basic SI units and quantities they describe
• Convert measurements to scientific notation
• Distinguish between accuracy precision
• Use significant figures in measurements
  calculations

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Numbers as Measurements

• In science, numbers represent measurements
• Numbers involve three things
• Magnitude how much?
• Dimensions length, mass, time
• Units of what?

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The SI system

• The standard measurement system for science
• Formerly called the metric system
• Base units
• Basic units that are not a combination of some
  other units
• Derived units
• Are combinations of base units

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Base Units
Physical Quantity (Dimension) Unit Abbreviation
Mass Kilogram kg
Length Meter m
Time Second s
Electric current Ampere A
Temperature Kelvin K
Luminous intensity Candela cd
Amount of substance Mole mol
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Derived units

• Derived units are combinations of base units

Base Unit Derived Unit
m (length) m3 (volume)
kg (mass) m (length) s (time) N (newton) for force 1N 1 kgm s2
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Prefixes indicate orders of magnitude (powers of
10)
Power Prefix Abbrev Power Prefix Abbrev
10 -18 atto- a 10 -1 deci- d
10 -15 femto- f 10 1 deka- da
10 -12 pico- p 10 3 kilo- k
10 -9 nano- n 10 6 mega- M
10 -6 micro- µ 10 9 giga- G
10 -3 milli- m 10 12 tera- T
10 -2 centi- c 10 15 peta- P
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Converting Prefixes Units

• The main idea multiply the given unit by a
  conversion factor yielding the desired unit
• Conversion factor a ratio of two units that is
  an equivalent to 1.
• Example convert millimeters to meters
• 1 mm x 10-3 m 1 x 10-3 m
• 1 mm
• Practice 1A, 1-5

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Converting units of area and units of volume

• How many cm2 are in 1 m2?
• How many cm3 are in 1 m3?
• How many in3 are in 1 L?
• 1 in 2.54 cm
• 1 L 103 mL
• 1 mL 1 cm3

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Scientific Method
A way of thinking and problem solving A group of
related processes and activities
http//www.sciencebuddies.org/science-fair-project
s/overview_scientific_method2.gif
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Scientific Method Important Terms

• Law vs. Theory
• Fact / Observation
• Hypothesis
• Experiment

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Accuracy Precision

• Accuracy
• Nearness of a measurement to the true value
• Precision
• Degree of exactness or refinement of a
  measurement
• Repeatability of a measurement

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Precision

• describes the limit of exactness of a measuring
  instrument
• Significant figures reflect certainty of a
  measurement
• Are figures that are known because they are
  measured

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Uncertainty in Measurement

• No measurement is absolutely correct
• All measurements are approximations
• Estimated uncertainty
• ½ smallest increment of the instrument
• E.g. a ruler graduated in 0.1 cm units would be
  reported as 5.2 0.05 cm

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Estimated UncertaintyPercent Uncertainty

• Estimated uncertainty
• smallest increment of measurement
• E.g. a ruler graduated in 0.1 cm units would be
  reported as 5.2 0.1 cm
• Percent uncertainty
• ratio of estimated uncertainty to measurement
• E.g. 0.05/5.2 0.96
• Measurement is reported as 5.2 0.96

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Is this diamond yours?

• You have a diamond with a mass of 8.17 grams,
  measured on a scale with a precision of 0.05g
• You lend the diamond to a friend, who returns it.
  The returned diamond measures 8.09 g
• Is the diamond yours?

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Significant Figures

• Represent measured numbers and one final
  estimated digit
• Reflect the precision of an instrument
• Must be reported properly
• Require special handling in calculations

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Rules to determine significant digits

• 1. All non-zeros ARE
• 2. All zeros between non-zeros ARE
• 3. Zeros in front of non-zeros ARE NOT
• 4. Final zeros to right of decimal ARE
• 5. Final zeros without a decimal ARE NOT
• 6. Final zeros to left of decimal ARE

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How many significant figures?

• 50.3 20.001
• 3.0025 3426
• 0.892 210
• 0.0008 6.58 x 103
• 57.00 1.534 x 10-4
• 2.000000 2.00 x 107
• 1000 5000.
• 20. 30

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Rules of calculating with significant figures

1. When adding subtracting, final answer must have
   fewest decimal places present in the calculation.
2. When multiplying dividing, final answer must
   have fewest significant digits present in the
   calculation.
3. Number of figures in a constant are ignored wrt
   sig figs.

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1.3 Language of Physics

• Mathematics is the language of physics
• Data is collected in a table form
• Data is graphed to show relationship of
  independent dependent variables

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Data Table and Graph
Determining k through displacement Determining k through displacement Determining k through displacement
x (m) Force (N) mass (kg)
0.00 0.00 0.00
0.01 0.49 0.05
0.03 0.98 0.10
0.06 1.47 0.15
0.09 1.96 0.20
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Equations

• Equations indicate relationships of variables

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Evaluating Physics Equations

• Dimensional analysis can give you clues how to
  solve a problem
• Dimensional analysis can help check many types of
  problems because
• Dimensions can be treated as algebraic quantities
• Example derive a formula for speed
• Example How long would it take a car to travel
  725 km at a speed of 88 km/h?

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Order of Magnitude Estimates

• Physics often uses very large and very small
  numbers
• Using powers of ten as estimates of the numbers
  can help estimate and check your answers
• Example from the previous problem,