Question: The average person in the United States consumes $3.0$ pound-force [lbf] of sugar each week. If the specific gravity of sugar is $1.59$, determine the volume of sugar in liters [L] consumed by the average person in one year.
1. **State the problem:** We need to find the volume in liters of sugar consumed in one year by an average person who consumes $3.0$ lbf of sugar per week, given the specific gravity of sugar is $1.59$.
2. **Understand the given data:**
- Weekly sugar consumption: $3.0$ lbf
- Specific gravity of sugar: $1.59$
- Number of weeks in a year: $52$
3. **Recall the formula for volume using specific gravity:**
Specific gravity (SG) is the ratio of the density of a substance to the density of water. Since the density of water is $1.0$ g/cm$^3$, the density of sugar is:
$$\rho_{sugar} = SG \times \rho_{water} = 1.59 \times 1.0 = 1.59 \text{ g/cm}^3$$
4. **Convert pound-force to mass:**
Since pound-force is a force unit, we assume the problem means pounds mass (lbm) for sugar. $1$ lbm $= 453.592$ grams.
5. **Calculate the total mass of sugar consumed in one year:**
$$\text{Mass per year} = 3.0 \text{ lb/week} \times 52 \text{ weeks} = 156 \text{ lb}$$
$$\text{Mass in grams} = 156 \times 453.592 = 70760.352 \text{ g}$$
6. **Calculate the volume in cm$^3$ using density:**
$$V = \frac{\text{mass}}{\text{density}} = \frac{70760.352}{1.59} = 44472.65 \text{ cm}^3$$
7. **Convert cm$^3$ to liters:**
$$1 \text{ L} = 1000 \text{ cm}^3$$
$$V = \frac{44472.65}{1000} = 44.5 \text{ L}$$
**Final answer:** The average person consumes approximately $44.5$ liters of sugar in one year.