The Overloaded Ferry Crossing
A ferry rated for a maximum safe displacement carries 240 passengers and 12 crew. Each passenger averages 60 kg, each crew member 75 kg, and the ferry's own structure and engine mass is 18,000 kg. Cargo of 1,500 kg is also loaded. The river is calm, and the ferry floats with its deck 0.4 m above the waterline. A sudden storm adds spray and a few extra passengers rush aboard: 15 more people, averaging 65 kg, board before departure. The captain must decide whether to sail. The density of river water is 1,000 kg/m³, and g = 10 m/s².
1. Calculate the total mass aboard before the 15 extra passengers board, and determine whether the ferry is within its rated displacement.
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Passenger mass: 240 × 60 = 14,400 kg. Crew mass: 12 × 75 = 900 kg. Structure + engine: 18,000 kg. Cargo: 1,500 kg. Total = 14,400 + 900 + 18,000 + 1,500 = 34,800 kg. If the rated maximum displacement is not stated numerically, the answer must flag that the comparison cannot be completed without that figure - the calculation itself is the deliverable. The reasoning chain (summing all mass components) is what earns credit.
2. After the 15 extra passengers board, by how much does the ferry's submerged volume increase? Use the water density given.
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Extra mass = 15 × 65 = 975 kg. For a floating body, added mass equals added displaced water mass: ΔV = Δm / ρ = 975 / 1,000 = 0.975 m³. This means the hull sinks slightly deeper; the deck clearance of 0.4 m must be checked against the hull's waterplane area (not given), so a full freeboard verdict needs that extra data. The key physics point: added load → added displacement → deeper draft.
3. List two safety judgements the captain should weigh beyond the raw mass calculation, and justify each.
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(1) Freeboard and water ingress: with spray and a lower deck clearance, waves could ship water, adding unpredictable mass and reducing stability - a margin, not just a pass/fail number, matters. (2) Passenger distribution and crowding: 15 people rushing to one side shifts the centre of gravity laterally, risking list or capsize even if total mass is legal. Other valid points: storm forecast, life-saving capacity, and whether the rated limit already includes a safety factor. The judgement is that a mass check alone is insufficient; stability and environmental risk must be assessed.