PHY101

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PHY101

• CHAPTER 1
• Measurement Unit
• Significant Figures
• Dimensional Analysis

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1.1. Measurement Units

• SI - International Metric System
• US - Customary System
• Basic Metric Units

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SI Prefixes
4
Metric Line
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Conversion Table
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Temperature Conversion
Converting Fahrenheit to Celsius
Converting Celsius to Fahrenheit
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Conversion in Metric system

• Example 1 Convert 50 mph to m/s.
• From 1 mile 1609 m

• Example 2 A hall bulletin board has an area of
  2.5 m2. What is this area in cm2?
  
• Because 1m100cm it is sometimes assumed that
  1 m2 100 cm2, which is WRONG. The correct
  conversion is

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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)

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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.

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Significant Figures - Practice

• Example 1 Find the area of a room 2.4 m by 3.65
  m
  
• 2.4m x 3.65m 8.76m28.8m2 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

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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

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Dimensional Analysis - Practice

• Example 1 Is an equation x v t a correct
  equation?
  
• x - is the distance in m
• v is the velocity in m/s
• t - is the time in s
• Dimensionally the equation is

• Example 1 Is an equation x a t2 a correct
  equation?
  
• a is acceleration in m/s2

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Practice

• Show that the equation x xo vt, where v is
  velocity, x and xo are lengths, ant t is time, is
  dimensionally correct
  
• A Boeing 777 jet has a length of 209 ft. 1 inch,
  and wingspan of 199 ft and 11 inches. What are
  these dimensions in meters?

• Determine the number of significant figures
• 1.007 m
• 8.03 m
• 16.272 kg
• 0.015 µs
• The two sides of right triangle are 8.7 cm (two
  significant figures) and 10.5 cm (three
  significant figures). What is the area of the
  triangle?