Chapter 1. Measurement

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Chapter 1. Measurement

• 1.What is Physics?      
• 2. Measuring Things      
• 3. The International System of Units      
• 4. Length      
• 5. Time       
• 6. Mass       
• 7. Changing Units
• 8.Calculations with Uncertain Quantities

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What is Physics? 

• Physics is the study of the basic components
  of the universe and their interactions. Theories
  of physics have to be verified by the
  experimental measurements.

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Measurement

• A scientific measurement requires
• (1) the definition of the physical quantity
• (2) the units.

• The value of a physical quantity is actually the
  product of a number and a unit .

• The precision of the measurement result is
  determined by procedures used to measure them.

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Basic Measurements in the Study of Motion

• Length  Our How far? question involves being
  able to measure the distance between two points.

• Time  To answer the question, How long did it
  take?

• Mass  Mass is a measure of amount of stuff.

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The Système International (SI) of units

• The SI, or metric system of units is the
  internationally accepted system of units for
  measurement in all of the sciences, including
  physics.
• The SI consists of base units and derived units
  (1) The set of base units comprises an
  irreducible set of units for measuring all
  physical variables (2) The derived units can be
  expressed in terms of the base units

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The SI Base Units
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• Time One second is the duration of 9.192631770
  109 periods of the radiation corresponding to
  the transition between the two hyperfine levels
  of the ground state of the cesium-133 atom.

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• Length One meter is the distance traveled by
  light in a vacuum in a time interval of 1/299 792
  458 of a second

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• Mass One kilogram is the mass of this thing
• (a platinum-iridium cylinder of
  heightdiameter39 mm)
• Atomic mass units (u)

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Scientific Notation

• All Physics quantities should be written as
  scientific notation, which employs powers of 10.

The Order of magnitude of a number is the power
of ten when the number is expressed in scientific
notation
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Example

• Determine the order of magnitude of the following
  numbers
• (a) A2.3104, (b) B7.8105.

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Changing Units

• In chain-link conversion, we multiply the
  original measurement by one or more conversion
  factors. A conversion factor is defined as a
  ratio of units that is equal to 1.

For example, because 1 mile and 1.61 kilometers
are identical distances, we have
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EXERCISE 1

• (a) Explain why it is correct to write
  1 min/60 s 1, but it is not correct to write
  1/60 1.
• (b) Use the relevant conversion factors and the
  method of chain-link conversions to calculate how
  many seconds there are in a day .

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EXERCISE 2

• The cran is a British volume unit for freshly
  caught herrings 1 cran170.474 liters (L) of
  fish, about 750 herrings. Suppose that, to be
  cleared through customs in Saudi Arabia, a
  shipment of 1255 crans must be declared in terms
  of cubic covidos, where the covido is an Arabic
  unit of length 1 covido48.26 cm . What is the
  required declaration?

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Density

• The density ? of a material is the mass per unit
  volume

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Calculations with Uncertain Quantities

• Significant Figures Read the number from left to
  right, and count the first nonzero digit and all
  the digits (zero or not) to the right of it as
  significant.

• Significant figures and decimal places are
  different
• The most right digit gives the absolute
  precision, which tells you explicitly the
  smallest scale division of the measurement.
• Relative Precision is the ratio of absolute
  precision over the physics quantity.

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EXERCISE  3

• Determine the number of significant figures,
  absolute precision, relative precision in each of
  the following numbers (a) 27 meters, (b) 27
  cows, (c) 0.003 429 87 second, (d) 1.970 500
  1011 coulombs, (e) 5280 ft/mi.

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EXERCISE 4

• Suppose you measure a time to the nearest
  1/100 of a second and get a value of 1.78 s.
• (a) What is the absolute precision of your
  measurement?
• (b) What is the relative precision of your
  measurement?

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A Simple Rule for Reporting Significant Figures
in a Calculated Result

• Multiplying and Dividing  When multiplying or
  dividing numbers, the relative precision of the
  result cannot exceed that of the least precise
  number used
• Addition and Subtraction  When adding or
  subtracting, you line up the decimal points
  before you add or subtract. This means that it's
  the absolute precision of the least precise
  number that limits the precision of the sum or
  the difference.
• Data that are known exactly should not be
  included when deciding which of the original data
  has the fewest significant figures.
• Only the final result at the end of your
  calculation should be rounded using the simple
  rule. Intermediate results should never be
  rounded.

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EXERCISE 5

• Perform the following calculations and express
  the answers to the correct number of significant
  figures.
• (a) Multiply 3.4 by 7.954.
• (b) Add 99.3 and 98.7.
• (c) Subtract 98.7 from 99.3.
• (d) Evaluate the cos(3).
• (e) If five railroad track segments have an
  average length of 2.134 meters, what is the total
  length of these five rails when they lie end to
  end?