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Difficulty: MediumBuoyancy and Archimedes' Principle

A heavy steel transport barge leaves the salty water of an ocean bay and enters a freshwater river. The total weight of the barge and its cargo remains exactly the same. Given that saltwater has a significantly higher density than freshwater, how will the depth that the barge sinks into the water (its draft) change, and why?

  1. It will sink deeper into the water, because it must displace a larger volume of the less-dense freshwater to equal its own weight.Answer
  2. B
    Its draft will remain exactly the same, because the required buoyant force depends entirely on the barge's total weight, which has not changed.
  3. C
    It will float higher in the water, because the lighter freshwater pushes upward against the hull with a greater pressure.
  4. D
    It will sink deeper into the water, because the lack of salt in the river water causes the barge's overall mass to increase.

Answer

The barge will sink deeper into the water because it must displace a larger volume of the less-dense freshwater to equal its own weight.
According to Archimedes' principle, a floating object displaces a weight of fluid equal to its own true weight. Because the barge's weight is constant, it must displace the exact same *weight* of water in both locations to stay afloat. Since freshwater is less dense (weighs less per unit of volume) than saltwater, a larger physical *volume* of freshwater must be displaced to equal the barge's massive weight. To displace more volume, the barge must sink deeper into the water, increasing its draft.

Step-by-Step Solution

1
Identify the conditions for a floating object.
A floating object is in equilibrium, meaning the upward buoyant force (FbF_b) must exactly equal the object's downward true weight (WW).
This is the fundamental principle of flotation derived from Archimedes' principle.
2
Relate the buoyant force to fluid density and displaced volume.
Buoyant force equals the weight of the displaced fluid, expressed as Fb=ρ×V×gF_b = \rho \times V \times g, where ρ\rho is fluid density, VV is displaced volume, and gg is gravity.
This formula shows how fluid properties generate the upward force.
3
Apply the relationship to the barge moving from saltwater to freshwater.
Since FbF_b must remain constant (because the barge's weight is constant), and the fluid density (ρ\rho) decreases in freshwater, the displaced volume (VV) must increase to compensate.
Displacing a larger volume of water means the hull of the barge must sink deeper (increasing its draft).

Key Concept

Buoyancy and floating equilibrium (Archimedes' Principle)
Estimated Time:1m 0s
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Topics

Buoyancy and Archimedes' Principle

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