Archimedes Principal
A fisherman rowing his boat on a very small lake throws his anchor into the water. Does the water level of the lake rise, fall, or stay the same?
Labels: funphysics
posted by Rajesh Lal at
9:21 AM
Friday, August 7, 2009
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13 Comments:
Stay the same...
Read the title again Matt, I think it will fall.
It will fall... as long as the anchor is more dense than water, which it would have to be for it to be an anchor.
In the boat, it is displacing an amount of water equal to its weight. In the lake, it is displacing an amount of water equat to its volume.
The water level will fall, but not by much. The boat was displacing an amount of water equal to the weight of the boat and all it contents. If the anchor floated the water level would remain equal, but now the anchor hits the bottom and it only displaces the volume of the anchor. The volume of water displaced is much less than the weight of the anchor.
Thus the lakes water level falls.
offcourse it rises
how small is the lake?
Just big enough to hold the boat, but it gooes down to a deep depth.
It will stay the same. The combined density of the boat and anchor stay the same weather the anchor is in or out of the boat.
wtf people youre all idiots! exept the ones that say it will rise. the anchor displaces water and pushes the water level up!
Last anonymous, I'm probably wasting my breath, but, what you say would be true if the anchor had been thrown into the lake from the shore. It was actually thrown from the boat; you can't inore that.
Think of it using the following:
If the anchor was thrown from the shore into the boat, the boat would sink into the water and so push the water level up. Now throw it back to the shore, then throw it into the lake.
Both StueyRock and Ragknot gave a full and correct explanation.
theres not enough info to answer the question, the anchor could weigh nothing and actually float on top of the water, or it could be the size of the boat and weigh just ehough to sink it, but mass and density are needed to answer correctly
Last anonymous. There is enough information. All real anchors sink.
You should use common sense - the anchor sinking the boat isn't a sensible consideration. The fisherman is not likely to be rowing his boat under water.
You don't need actual densities or volumes as you are not being asked to calculate a value, only the direction (rise, fall or no change).
Ragknot had dealt with the floating anchor in his answer, though.
The given that the lake is very small is itself unecessary. The lake can be very large (but finite).
Pedant time. If the anchor weighed nothing, it would fly off into space.
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