Understanding Buoyancy: Calculating Mass of a Ship in Different Fluids

In summary, the conversation discusses a ship's movement from seawater to freshwater and the resulting change in its position. The ship sinks slightly when entering freshwater and returns to its original level when its 600,000-kg load is removed. The problem at hand is finding the mass of the ship before it was unloaded. The conversation also mentions difficulties with understanding volume and solving for the sum of forces. The solution manual suggests replacing Vg in the sea water equation, but there is confusion about whether the volume should also change when the load is removed. The conversation concludes with a reference to Archimedes and his principle about floating objects.
  • #1
knowNothing23
35
0
53 ••• [SSM] A ship sails from seawater (specific gravity 1.025) into
freshwater, and therefore sinks slightly. When its 600,000-kg load is removed, it
returns to its original level. Assuming that the sides of the ship are vertical at the
water line, find the mass of the ship before it was unloaded.

I'm afraid I have a horrible problem about my conception of volume.

I have solved for the sum of forces in the Y component in both cases. For water and sea water.
My solutions manual shows that one can solve for Vg in water and replace it in the sea water equation. I can't conceive, how this is possible, because a load is taken of the boat when it's in water. Shouldn't the volume change as well? There's more room in the boat.

Thank you.
 
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  • #2
The boat rises because it is lighter by 600,000 kg. Remember what Archimedes said about floating objects.
 
  • #3
True.

Thank you.
 

Related to Understanding Buoyancy: Calculating Mass of a Ship in Different Fluids

1. What is buoyancy and why is it important in calculating the mass of a ship?

Buoyancy is the upward force exerted by a fluid on an object immersed in it. In the context of a ship, it is the force that supports the weight of the ship and keeps it afloat. It is important in calculating the mass of a ship because it affects the ship's stability, draft, and overall performance.

2. How is buoyancy calculated?

Buoyancy is calculated using Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid displaced by the object. This can be represented by the equation Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

3. How does the density of the fluid affect the buoyancy of a ship?

The density of the fluid plays a crucial role in determining the buoyancy of a ship. If the density of the fluid is greater than the density of the ship, the ship will float. If the density of the fluid is less than the density of the ship, the ship will sink. This is why ships are designed to displace a volume of water that is greater than their own weight.

4. How does the mass of the ship affect its buoyancy?

The mass of a ship has a direct impact on its buoyancy. Heavier ships will displace more water and therefore have a greater buoyant force acting on them. This makes it easier for them to float compared to lighter ships. However, the mass of the ship also affects its stability and maneuverability, so it is important to strike a balance between buoyancy and other factors in ship design.

5. How do different fluids affect the buoyancy of a ship?

Different fluids have varying densities, which can affect the buoyancy of a ship. For example, a ship will float higher in saltwater than in freshwater, as saltwater has a higher density. Additionally, the temperature and salinity of the fluid can also impact its density and therefore the buoyancy of the ship. These factors must be taken into consideration when calculating the mass of a ship in different fluids.

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