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Zorluk: Çok zorBuoyancy and Archimedes' Principle

A maintenance barge is floating in a closed canal lock filled with water. The barge carries a heavy load of solid steel beams. If the crew unloads the steel beams directly into the water, causing them to sink to the bottom of the lock, what happens to the overall water level in the lock, and why?

  1. A
    The water level rises, because the submerged steel now displaces a volume of water equal to its heavy weight.
  2. B
    The water level remains the same, because the total mass of the barge, steel, and water in the lock system has not changed.
  3. The water level falls, because the sunken steel displaces less water than it did when its weight was supported by the floating barge.Cevap
  4. D
    The water level rises, because the steel beams displace more water when resting on the bottom than when sitting on the barge.

Cevap

The water level falls, because the sunken steel displaces less water than it did when its weight was supported by the floating barge.
When the steel beams are on the barge, they must displace a volume of water equal to their weight in order to float. Because steel is denser than water, this displaced volume of water is larger than the actual physical volume of the steel beams. When the beams are thrown overboard and sink, they only displace a volume of water equal to their own physical volume. Since they are now displacing a smaller volume of water than before, the overall water level in the lock falls.

Adım Adım Çözüm

1
Determine the volume of water displaced by the steel beams when they are floating on the barge.
The steel beams are part of a floating system, so they displace a weight of water equal to their own weight.
According to Archimedes' principle, a floating object displaces a volume of fluid whose weight equals the object's weight. The displaced volume is Vfloating=WsteeldwaterV_{floating} = \frac{W_{steel}}{d_{water}} where dd is density.
2
Determine the volume of water displaced by the steel beams when they sink to the bottom of the lock.
The steel beams are completely submerged, so they displace a volume of water equal to their own geometric volume.
A completely submerged object displaces a volume of fluid exactly equal to its own volume, so Vsubmerged=VsteelV_{submerged} = V_{steel}.
3
Compare the two displaced volumes.
Since steel is denser than water (dsteel>dwaterd_{steel} > d_{water}), the volume of the steel itself is much less than the volume of water that has the same weight. Therefore, Vsubmerged<VfloatingV_{submerged} < V_{floating}.
Density is mass divided by volume. For a given mass (or weight), a material with a higher density occupies a smaller geometric volume.
4
Determine the effect on the overall water level in the lock.
Because the total volume of water displaced by the system decreases when the steel is dropped to the bottom, the overall water level falls.
The water level in a closed system depends directly on the total volume of water being displaced by objects in the water.

Anahtar Kavram

Flotation equilibrium vs. Submerged volume
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Konular

Buoyancy and Archimedes' Principle

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