Measurement Systems Significant Figures Dimensional Analysis

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Presentation transcript:

Measurement Systems Significant Figures Dimensional Analysis Physics 101: Chapter 1 Measurement Systems Significant Figures Dimensional Analysis

Measurement Systems SI – International System US – British System Basic Metric Units

Si Prefixes

Metric Line

Conversion Table

Temperature Conversion Conversion of Fahrenheit to Celsius Conversion of Celsius to Fahrenheit

Conversion into Metric 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 = 100 cm2, which is WRONG. The correct conversion is:

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 - three significant figures (2, 5, 4) Zeros within a number are significant 104.6 - four significant figures (1, 0, 4, 6) Zeros at the end of a number after the decimal point are significant: 2705.0 - 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 s.f. - because 2 is least # of s.f. Example 2: Given the numbers 23.25, 0.546, and 1.058 add the first two subtract the least number from the first

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 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 2: Is an equation x = a t2 a correct equation? a is acceleration in m/s2

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?