Given the ship light weight is 4000 tons, the ship can accommodate 50 people of 100 kg, fuel 500 cubic meters. A 4000 container cargo of 2800 kg. Ballast 40 per stability 100 cubic... Given the ship light weight is 4000 tons, the ship can accommodate 50 people of 100 kg, fuel 500 cubic meters. A 4000 container cargo of 2800 kg. Ballast 40 per stability 100 cubic meter. Total weight of cargo without container 700 tons. Read more

Steps to Solve

1. Calculate the weight of passengers

The total number of passengers is 50, each weighing 100 kg. The total weight of the passengers can be calculated as:

$$ \text{Weight of passengers} = 50 \text{ people} \times 100 \text{ kg/person} = 5000 \text{ kg} $$

2. Convert the weight of the ship and cargo to the same unit

The light weight of the ship is given as 4000 tons. Since 1 ton = 1000 kg, we convert the ship's weight to kilograms:

$$ \text{Weight of ship} = 4000 \text{ tons} \times 1000 \text{ kg/ton} = 4,000,000 \text{ kg} $$

3. Calculate the total weight of the crew and fuel

The weight of the fuel needs to be calculated based on 500 cubic meters. Assuming the density of fuel is approximately 850 kg/m³:

$$ \text{Weight of fuel} = 500 \text{ m}^3 \times 850 \text{ kg/m}^3 = 425,000 \text{ kg} $$

4. Calculate the total weight of cargo

The weight of the cargo excluding the container is given as 700 tons. Converting that to kilograms:

$$ \text{Weight of cargo} = 700 \text{ tons} \times 1000 \text{ kg/ton} = 700,000 \text{ kg} $$

5. Calculate the weight of the container cargo

The container cargo weighs 2800 kg, and the ballast's weight can be ignored in this context since it contributes to stability rather than total weight.

6. Determine the total weight of the ship when loaded

Now we can add all weight components together (the weight of the ship, passengers, fuel, cargo, and container cargo):

$$ \text{Total weight} = \text{Weight of ship} + \text{Weight of passengers} + \text{Weight of fuel} + \text{Weight of cargo} + \text{Weight of container} $$

So,

$$ \text{Total weight} = 4,000,000 \text{ kg} + 5000 \text{ kg} + 425,000 \text{ kg} + 700,000 \text{ kg} + 2800 \text{ kg} $$

Calculating:

$$ \text{Total weight} = 4,000,000 + 5,000 + 425,000 + 700,000 + 2,800 = 5,132,800 \text{ kg} $$

7. Convert the total weight back to tons if needed

If you want the total weight in tons:

$$ \text{Total weight in tons} = \frac{5,132,800 \text{ kg}}{1000} = 5,132.8 \text{ tons} $$