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Buoyant Force in Lake and Ocean

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"when a ship goes from the ocean into a lake, it will,"
Float lower in the water and require the same buoyant force to stay afloat.

I understand that the lake water is less dense than the ocean water, so the ship will sink further below the surface because its density is closer to that of the lake water. For that reason, it will displace more water. The buoyant force is defined as the mass of the volume of water displaced. My thinking was that since the lake water is displaced more, there is more mass, so the buoyant force would be increased.
However, I realize that I did not consider the fact that the density is different. Could someone explain to me how this works out? How are the masses of the two amounts of water the same?

I tried writing two equations to see it, but it doesn't really make sense

Densitysea = mass sea / volume sea

Density lake = mass lake / volume lake

In each, I guess density of sea and volume of lake would be increased, and somehow their masses would be the same.........
 

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"when a ship goes from the ocean into a lake, it will,"
Float lower in the water and require the same buoyant force to stay afloat.

I understand that the lake water is less dense than the ocean water, so the ship will sink further below the surface because its density is closer to that of the lake water. For that reason, it will displace more water. The buoyant force is defined as the mass of the volume of water displaced. My thinking was that since the lake water is displaced more, there is more mass, so the buoyant force would be increased.
However, I realize that I did not consider the fact that the density is different. Could someone explain to me how this works out? How are the masses of the two amounts of water the same?

I tried writing two equations to see it, but it doesn't really make sense

Densitysea = mass sea / volume sea

Density lake = mass lake / volume lake

In each, I guess density of sea and volume of lake would be increased, and somehow their masses would be the same.........

The thing to keep in mind is that when an object is floating, it is experiencing no net force up or down. This means that the weight down equals the buoyant force up. So whether the ship is in the ocean or a lake, it is the same ship weighing the same amount. Hence, the buoyant force offsetting the weight is the same in every fluid medium, including the lake and the ocean.

As you pointed out, the ship will sink lower in the lake water, because lake water is less dense than saltwater. As for the numbers, let's arbitrarily say the ocean water is 2% denser than the lake water. This would mean that the ship will displace 2% more lake water than saltwater, which means that the buoyant force didn't change. rholake < rhosaltwater by 2% and Vdisplaced in lake > Vdisplaced in ocean by 2%, so (rholake)(Vdisplaced in lake)g = (rhosaltwater)(Vdisplaced in ocean)g.

I hope this helps.
 
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