Overview
This lecture explains dimensional analysis (unit-factor method) for converting units, using step-by-step examples involving pounds, kilograms, and tons.
Dimensional Analysis Basics
- Dimensional analysis is a method for converting between units using conversion factors in fraction form.
- Always start by writing the quantity to be converted, including its units.
- Multiply the given quantity by a fraction representing the conversion factor.
- Place the unit you want to cancel on the bottom of the fraction and the desired unit on top.
- Units cancel out, leaving the desired unit for your answer.
Example 1: Pounds to Kilograms
- Given: 495 lbs; Convert to kg using the factor 1 kg = 2.2 lbs.
- Set up: (495 lbs) × (1 kg / 2.2 lbs).
- Pounds cancel, leaving kilograms.
- Calculation: 495 ÷ 2.2 = 225 kg.
Conversion Factor Principle
- Any conversion factor fraction (like 1 kg/2.2 lbs) equals one since the numerator and denominator represent the same quantity in different units.
Example 2: Kilograms to Tons (Multi-Step Conversion)
- Given: 1920 kg; Convert to tons (need kg→lb→ton).
- First conversion: (1920 kg) × (2.2 lbs / 1 kg) = 4224 lbs.
- Second conversion: (4224 lbs) × (1 ton / 2000 lbs) = 2.11 tons.
- Use significant figures based on the original value (3 significant digits here).
Shortcut: Combining Multiple Conversion Factors
- Combine steps: (1920 kg) × (2.2 lbs / 1 kg) × (1 ton / 2000 lbs).
- Multiply and divide from left to right: 1920 × 2.2 ÷ 2000 = 2.11 tons.
- This method works for any number of conversion steps.
Key Terms & Definitions
- Dimensional Analysis — A problem-solving method using conversion factors to change units.
- Conversion Factor — A ratio expressing how many of one unit equals another (e.g., 1 kg / 2.2 lbs).
- Significant Figures — The number of meaningful digits in a value, used to determine answer precision.
Action Items / Next Steps
- Practice unit conversions using the fraction method with various units and multiple steps.
- Ensure to use the appropriate number of significant figures based on starting quantities.