Mass and Buoyancy

[Mr. Twister]

Hello, I'm new to the forum.

 

Imagine this:

 

You are in a boat in the middle of a lake and decide to stop rowing for a while and have lunch. When you throw the heavy anchor overboard, does the water level in the lake rise, fall, or stay the same?

 

 

 

 

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[zule]

[hide]I think that the water level will fall: The anchor have a density much higher than the boat. Not only the material the boat is made is much lighter than the one which the one is made the anchor. Also, because of its shape, part of the boat volume is air, decreasing still more the whole density.

 

When the anchor is inside the boat, we can consider that it is part of the boat, increases the average density of the whole. The boat will sink deeper than without the anchor, displacing as much volume of water as volume of boat sinks.

 

When the anchor is taken out of the boat and into the water, the volume of the part of the boat sunk will decrease, and so will do the volume of water displaced, falling the water level. It is true that the water level also will increase the same volume as the anchor has. But as the relation mass/volume is higher in the anchor than in the boat, the volume increase due to put the anchor into water will be smaller than the one due to have the anchor in the boat.[/hide]

[Mr. Twister]

Yup, Zule is right!

Good Going!

 

 

 

 

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[Hobbes]

Yes, you're right. Since the anchor is heavy enough that it sinks (to the bottom), means that it's density is much higher than that of water. When it was in the boat, it displaced the amount of water that it would need to displace not to sink OR rise in the water, but rather "hovered" (like a sub-marine), which in volumetric terms is more than it displaced when thrown over-board.