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PHY101 PowerPoint PPT Presentation


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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. SI Prefixes. Metric Line. Conversion Table. Temperature Conversion. Converting Fahrenheit to Celsius.

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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


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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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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 1m=100cm it is sometimes assumed that 1 m2 = 100cm2, which is WRONG. The correct conversion is:

Conversion in Metric system


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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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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

Significant Figures - Practice


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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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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

Dimensional Analysis - Practice


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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?

Practice


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