Physics - Sink/Float Question

[shefv]

A barge carrying multiple containers is floating in an enclosed section of a canal. By mistake, a container falls off the barge into the water and sinks. With respect to an onlooker from the shore, what will happen to the water level in this section of the canal?

The answer says that the water level would decrease, I am confused.

I am thinking that when the containers are floating, the volume of water has not be displaced. When one container sinks, Vsubmerged = Vdisplaced, so wouldn't the water level rise in this case.

Can some explain this? Which equation are they using to get the answer? The solutions didn't mention any equation so I am confused.

Thanks

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[NextStepTutor_3]

This is a tricky one! The key is that a floating object displaces its own weight (think of a force diagram with "mg" pointing down and buoyant force, pointing up, perfectly counteracting that force). In other words, the fluid displaced initially corresponds to the weight of the barge and the containers it holds.

Now, what happens after the container falls off the barge? Once an object sinks, it no longer displaces its weight - it displaces its volume. For physics examples, it can always help to think about extremes. Imagine that instead of a regular container, the barge carried a brick that weighed 10000 kg (ridiculous, but bear with me). The barge will be sitting very low in the water, displacing a lot of fluid, while it carries that brick. However, as soon as the brick falls off the barge, it sinks straight to the bottom and cannot possibly displace more than the volume of itself (which, for a brick, is very small). Simultaneously, the barge starts to ride higher in the water - or float better - because it no longer has that weight dragging it down.

In short, the water level decreases because the boat, no longer weighed down, displaces much less water than before, while the container only displaces slightly more.

 

[NextStepTutor_3]

And in terms of equations? Just remember that for a floating object, buoyant force = weight of object. For a submerged object, buoyant force = (density fluid)(volume object)(g). Of course, buoyant force ALWAYS equals (density fluid)(volume fluid displaced)(g) - the only thing that varies is how that corresponds to the object.

Good luck!