Example: The density of air is 1.3 kg/m^3. Change the units to slugs/ft^3. 1 slug = 14.59 kg, 1 m = 3.28 feet

Answer

To convert the density from kg/m^3 to slugs/ft^3, follow these steps: 1. Start with the given value: 1.3 kg/m^3. 2. Convert mass from kg to slugs using the conversion factor 1 slug = 14.59 kg. This gives (1.3 kg / 14.59 kg/slug) = 0.08910 slug. 3. Convert volume from m^3 to ft^3 using the conversion factor 1 m = 3.28 ft. Since the unit is cubed, the conversion factor is (1 m / 3.28 ft)^3 = 1/35.287552 m^3/ft^3. 4. Multiply the values together to perform the full dimensional analysis: (1.3 kg / 1 m^3) * (1 slug / 14.59 kg) * (1 m / 3.28 ft)^3. 5. Calculation: 1.3 / (14.59 * 3.28^3) = 1.3 / (14.59 * 35.287552) = 1.3 / 514.845 = 0.002525. Therefore, the density of air is approximately 0.0025 slugs/ft^3.