Unit Conversion with Dimensional Analysis

Introduction

• Dimensional Analysis: Also known as the factor-label method or unit-factor method.
• Purpose: A versatile and powerful problem-solving technique for unit conversion.

Example 1: Converting Pounds to Kilograms

Problem

• A weightlifter can lift 495 lbs. Convert this to kilograms.

Solution Steps

1. Identify Conversion Factor:
   • 1 kg = 2.2 lbs.
2. Write Down the Initial Quantity:
   • Start with 495 lbs.
3. Set Up Conversion Fraction:
   • 2.2 lbs on the bottom (to cancel out pounds).
   • 1 kg on the top (to convert to kilograms).
4. Calculate:
   • In calculator: 495 lbs ÷ 2.2 = 225 kg.
5. Understanding the Fraction:
   • The fraction 1 kg / 2.2 lbs = 1 since they are equivalent.

Example 2: Converting Kilograms to Tons

Problem

• A car has a mass of 1920 kg. Convert this to tons.

Solution Steps

1. Identify Conversion Factors:
   • 1 kg = 2.2 lbs.
   • 1 ton = 2000 lbs.
2. Two-Step Conversion:
   • First convert kg to lbs, then lbs to tons.

Step 1: Convert kg to lbs

• Initial Quantity: 1920 kg.
• Conversion Fraction:
  • 1 kg on the bottom (to cancel out kg).
  • 2.2 lbs on the top.
• Calculate: 1920 kg × 2.2 = 4224 lbs.

Step 2: Convert lbs to tons

• Initial Quantity: 4224 lbs.
• Conversion Fraction:
  • 2000 lbs on the bottom (to cancel out lbs).
  • 1 ton on top.
• Calculate: 4224 lbs ÷ 2000 = 2.11 tons.

Combining Steps for Efficiency

• Combined Conversion:
  • Start with 1920 kg.
  • Multiply by (2.2 lbs / 1 kg).
  • Then multiply by (1 ton / 2000 lbs).
• Calculate Sequentially:
  • 1920 kg × 2.2 ÷ 2000 = 2.11 tons.
• Significance: Using conversion factors in fraction form simplifies knowing when to multiply or divide.

Conclusion

• Dimensional analysis is a robust method for solving complex unit conversions.
• Helpful to visualize each step and ensure correct unit cancellation.

Further Action

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