A commonly used unit of mass in the English system is the pound-mass, abbreviated lbm, where 1 lbm = 0.454 kg.What is the density of gasoline in pound-mass per cubic foot? (Assume the density of gasoline is 7.40 ✕ 10^2 kg/m3.)
(7.40 x 10^2 kg/m3)*(1lbm/0.454kg)= density in lbm/m^3
1m=3.28ft and (1m=3.28ft)^3= 1m^3=35.29ft^3
(Density in lbm/m^3)*(1m^3/35.29ft^3)= answer in lbm/ft^3
To find the density of gasoline in pound-mass per cubic foot, we need to convert the density of gasoline from kilograms per cubic meter (kg/m³) to pound-mass per cubic foot (lbm/ft³).
First, we need to convert the density of gasoline from kg/m³ to lbm/ft³ using the conversion factor:
1 lbm = 0.454 kg
1 ft = 0.3048 m
Converting the density of gasoline from kg/m³ to lbm/ft³:
density_lbft = density_kgm3 * (1 lbm / 0.454 kg) * ((0.3048 m / 1 ft)³)
Density of gasoline in lbm/ft³ is approximately:
density_lbft = (7.40 × 10^2 kg/m³) * (1 lbm / 0.454 kg) * ((0.3048 m / 1 ft)³)
Simplifying the equation:
density_lbft ≈ 740 * (1 / 0.454) * ((0.3048)³)
Evaluating the expression:
density_lbft ≈ 51.151 lbm/ft³
Therefore, the density of gasoline in pound-mass per cubic foot is approximately 51.151 lbm/ft³.
To find the density of gasoline in pound-mass per cubic foot, we need to convert the given density of gasoline from kg/m^3 to lbm/ft^3 using the conversion factors provided.
Step 1: Convert kg/m^3 to lbm/ft^3
1 lbm = 0.454 kg (conversion factor for mass)
1 m^3 = (3.281 ft)^3 = 35.3147 ft^3 (conversion factor for volume)
So, to convert the density from kg/m^3 to lbm/ft^3, we use the following conversion:
7.40 x 10^2 kg/m^3 * (0.454 lbm/1 kg) / (35.3147 ft^3/1 m^3)
Simplifying the expression:
= (7.40 x 10^2 kg/m^3 * 0.454 lbm/kg) / 35.3147 ft^3/m^3
= 3.084 lbm/ft^3
Therefore, the density of gasoline is approximately 3.084 lbm/ft^3.