Answer:
The maximum payload the zeppelin can carry at sea level is approximately 26,948.6 kilograms.
Step-by-step explanation:
To compute the maximum payload of the modern-day zeppelin at sea level, we need to consider the buoyant force acting on the zeppelin due to the displacement of air by the helium inside it. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the displaced fluid (in this case, air).
The formula for the buoyant force (B) is given by:
B = ρ_air * V_displaced * g
Where:
ρ_air is the density of air at sea level and standard atmospheric conditions (approximately 1.225 kg/m³).
V_displaced is the volume of air displaced by the helium inside the zeppelin (in m³).
g is the acceleration due to gravity (approximately 9.81 m/s²).
Now, to find the maximum payload (P) that the zeppelin can carry, we use the following equation:
P = W_total - W_zeppelin
Where:
W_total is the total weight that the zeppelin can support (includes the weight of the zeppelin structure, helium, and payload).
W_zeppelin is the weight of the empty zeppelin (structure and helium).
The weight of the helium can be calculated using the formula:
W_helium = ρ_helium * V_helium * g
Where:
ρ_helium is the density of helium at sea level and standard atmospheric conditions (approximately 0.1786 kg/m³).
V_helium is the volume of helium inside the zeppelin (8,890 m³).
g is the acceleration due to gravity (approximately 9.81 m/s²).
Now, let's plug in the values and calculate:
Calculate the weight of the helium inside the zeppelin:
W_helium = 0.1786 kg/m³ * 8,890 m³ * 9.81 m/s² ≈ 15,848.6 kg
Calculate the volume of air displaced by the helium inside the zeppelin:
V_displaced = V_helium = 8,890 m³
Calculate the buoyant force:
B = 1.225 kg/m³ * 8,890 m³ * 9.81 m/s² ≈ 108,738.05 N
Calculate the total weight the zeppelin can support:
W_total = B + W_helium ≈ 108,738.05 N + 15,848.6 kg * 9.81 m/s² ≈ 264,283.65 N
Finally, calculate the maximum payload:
P = W_total - W_zeppelin ≈ 264,283.65 N - 0 kg * 9.81 m/s² ≈ 264,283.65 N
So, the maximum payload the modern-day zeppelin can carry at sea level is approximately 264,283.65 Newtons (N). Keep in mind that this value is in terms of force (weight) and not mass. To convert it to kilograms, divide by the acceleration due to gravity (9.81 m/s²):
Payload (in kg) ≈ 264,283.65 N / 9.81 m/s² ≈ 26,948.6 kg
Therefore, the maximum payload the zeppelin can carry at sea level is approximately 26,948.6 kilograms.