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A Trapped Boat


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5 replies to this topic

#1 BMAD

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Posted 18 February 2013 - 03:26 AM

Youre in a row boat, which is in a large tank filled with water. You have an anchor on board, which you throw overboard (the chain is long enough so the anchor rests completely on the bottom of the tank). Does the water level in the tank rise or fall?
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#2 vistaptb

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Posted 18 February 2013 - 03:50 AM

Spoiler for I think...


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#3 Debasis

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Posted 19 February 2013 - 10:48 AM

look down


Edited by Debasis, 19 February 2013 - 10:49 AM.

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#4 Debasis

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Posted 19 February 2013 - 10:49 AM

Spoiler for spoiler


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#5 Bozo

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Posted 23 February 2013 - 09:44 PM

Debasis does state Archimedes principle correctly,  But is that relevant here?  Is the density of the anchor the key to this one? 

 

If the weight and volume of the chain is negligible, then the anchor, resting "completely on the bottom of the tank" has effectively been thrown overboard - as the problem is stated its weight no longer is borne at all by the rowboat.  Here only the weight of the rowboat (including that of the anchor) and the volume of the anchor affect the level in the tank.  Let's assume that the iron anchor has a specific gravity of 8.  It is pushing the boat down into the water 8 units when it's in the boat, displacing 8 units of water and raising the tank level by a proportionate amount.  When thrown overboard it will displace 1 unit of water when it's immersed and no longer affect the boat's displacement.  As stated by vistaptb: "its relative weight should exceed its relative volume and thus push the water up further when it is in the boat."

An intriguing twist might have the anchor still weighting the boat because the chain is too short to reach the bottom.

 


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#6 ThunderCloud

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Posted 23 February 2013 - 10:08 PM

Spoiler for Actually, I agree with vistaptb...


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