PHY101 by HC11112406919

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									     PHY101

    CHAPTER 1
 Measurement Unit
 Significant Figures
Dimensional Analysis
        1.1. Measurement Units
• SI - International Metric System
• US - Customary System
• Basic Metric Units
 Quantity Length Mass      Time     El. Current   Temperature
 Unit     meter kilogram   second   Ampere        Kelvin
 Symbol m        kg        s        A             K
                 SI Prefixes
Power   Prefix   Symbol
10-18   atto     a
10-15   femto    f
10-12   pico     p
10-9    nano     n
10-6    micro    
10-3    milli    m
103     kilo     k
106     mega     M
109     giga     G
1012    tera     T
1015    peta     P
1018    exa      E
                           Metric Line
                           METRIC LINE


Tm      Gm       Mm   km     m          mm   um   nm   pm   fm   am   Length
Tg      Gg       Mg   kg     g          mg   ug   ng   pg   fg   ag   Mass
Tl      Gl       Ml   kl     l          ml   ul   nl   pl   fl   al   Capacity




     T - tera
     G - giga
     M - mega
     k - kilo               Center
     m - milli
     u - micro              m - meter
     n - nano               g - gram
     p - pico               l - liter
     f - femto
                 Conversion Table

    METRIC TO ENGLISH                       ENGLISH TO METRIC
From Metric   To English   Multiply by   From English   To Metric     Multiply by

meters        yards        1.09          yards          meters        0.91
meters        feet         3.28          feet           meters        0.30
centimeters   inches       0.39          inches         centimeters   2.54
kilometers    miles        0.62          miles          kilometers    1.61
grams         ounces       0.035         ounces         grams         28.35
kilograms     pounds       2.20          pounds         kilograms     0.45
liters        quarts       1.06          quarts         liters        0.95
liters        gallons      0.26          gallons        liters        3.78
    Temperature Conversion

Converting Fahrenheit to Celsius

            5( F  32)
         C
                 9

Converting Celsius to Fahrenheit

               9C
          F       32
                5
    Conversion in Metric system
• Example 1: Convert 50                • Example 2: A hall
  mph to m/s.                            bulletin board has an area
                                         of 2.5 m2. What is this
From 1 mile = 1609 m:                    area in cm2?
                                         Because 1m=100cm it is
50m 1609m 1h
                 22m / s              sometimes assumed that
 h    m    3600 s
                                         1 m2 = 100 cm2, which is
                                         WRONG. The correct
                                         conversion is:
                        2.5m2  2.5m  m  2.5 100cm 100cm  25000cm2  2.5 104
          1.2. Significant Figures
  The number of significant figures of a numerical
  quantity is the number of reliably known digits it
  contains.
• Zeros at the beginning of a number are not significant.
  They merely locate the decimal point.
   – 0.254 m - three significant figures (2, 5, 4)
• Zeros within a number are significant
   – 104.6 m - four significant figures (1, 0, 4, 6)
• Zeros at the end of a number after the decimal point are
  significant:
   – 2705.0 m - five significant figures (2, 7, 0, 5, 0)
Significant Figures - Conclusion
• The FINAL result of a multiplication or division
  should have the same number of significant
  figures as the quantity with the least number of
  significant figures that was used in the
  calculation.
• The FINAL result of the addition or subtraction
  of numbers should have the same number of
  decimal places as the quantity with the least
  number of decimal places that was used in the
  calculation.
    Significant Figures - Practice
• Example 1: Find the area of a room 2.4 m by 3.65 m:
2.4m x 3.65m = 8.76m2=8.8m2 Rounded to 2 sf - because 2 is least # of sf

• Example 2: Given the numbers 23.25, 0.546, and 1.058
    – add the first two
    – subtract the least number from the first
      1.3. Dimensional Analysis
• The two sides of an equation must be equal not only in
  numerical value, but also in dimensions (BOTH SIDES OF
  THE      EQUATION        ARE     NUMERICALLY      AND
  DIMENSIONALLY EQUAL). And dimensions can be
  treated as algebraic quantities.
• [L] - Length
• [M] - Mass
• [T] - Time
 Dimensional Analysis - Practice
• Example 1: Is an equation           • Example 1: Is an equation
  x = v t a correct equation?           x = a t2 a correct equation?
   – x - is the distance in m            – a is acceleration in m/s2
   – v = is the velocity in m/s                        [ L]
   – t - is the time in s                    [ L]            [T 2 ]  [ L]
                                                      [T 2 ]

   Dimensionally the equation is:
                 [ L]
        [ L]          [T ]  [ L]
                 [T ]
                        Practice
• Show that the equation x     • Determine the number of
  = xo + vt, where v is          significant figures:
  velocity, x and xo are          –   1.007 m
  lengths, ant t is time, is      –   8.03 m
  dimensionally correct           –   16.272 kg
• A Boeing 777 jet has a          –   0.015 µs
  length of 209 ft. 1 inch,    • The two sides of right
  and wingspan of 199 ft         triangle are 8.7 cm (two
  and 11 inches. What are        significant figures) and
  these dimensions in            10.5 cm (three significant
  meters?                        figures). What is the area
                                 of the triangle?

								
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