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Chapter 3: Measurement: Dimensional Analysis

Chapter 3: Measurement: Dimensional Analysis. Objectives. Construct conversion factors from equivalent measurements Apply the techniques of dimensional analysis to a variety of conversion problems Solve problems by breaking the solution into steps

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Chapter 3: Measurement: Dimensional Analysis

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  1. Chapter 3: Measurement: Dimensional Analysis

  2. Objectives • Construct conversion factors from equivalent measurements • Apply the techniques of dimensional analysis to a variety of conversion problems • Solve problems by breaking the solution into steps • Convert complex units, using dimensional analysis

  3. Conversion factors • Conversion factor • ratio of equivalent measurements. • example: 24 hrs = 1 day • They represent the same amount of time but are expressed with different numbers and units • used in dimensional analysis • usually written as a fraction • or

  4. Units arithmetic • Multiplication of units • add the exponents together • 3 m x 2 m = 6 m2 • 8 cm3 x 2 cm2 x 1 cm = 16 cm6 • Division of units • exponents and/or entire units cancel • Addition/subtraction of units • Units don’t change, but must be same before add/subtract • 8 mi - 5 mi = 3 mi 2

  5. Dimensional analysis • Dimensional analysis • way to analyze and solve problems using the units, or dimensions, of the measurements. • form of problem-solving • figure out units it takes to get from start to finish • line up all our conversion factors as fractions and cancel units that appear in both the numerators and denominators.

  6. Dimensional analysis practice Question 1 • How many seconds are in 3 weeks?

  7. Dimensional analysis practice Answer 1 • Given • 3 weeks • ? seconds • What We Know • 1 week = 7 days • 1 day = 24 hr • 1 hr = 60 min • 1 min = 60 sec • Work

  8. Dimensional analysis practice Question 2 • Convert gold’s density (19.3 g/cm3) to kg/m3.

  9. Dimensional analysis problems Answer 2 • Given • Gold = 19.3 g/cm3 • Gold = ? kg/m3 • What We Know • 1000 g = 1 kg • 100 cm = 1 m • Work

  10. Conversion memorization (for now) US to Metric • 1 in = 2.54 cm • 454 g = 1 lb Metric larger • 1 megameter (Mm) = 1,000,000 m • 1 kilometer (km) = 1000 m Metric smaller • 10 decimeters (dm) = 1 m • 100 centimeters (cm) = 1 m • 1,000 millimeters (mm) = 1 m • 1,000,000 micrometers (µm) = 1 m • 1,000,000,000 nanometers (nm) = 1 m

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