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Hi James,

I have a question regarding weight of an object in water.  The exact scenario being debated is the weight of an object (hypothetically simply a 45 pound weight made of a common metal) and how much it would weigh in water.  If the weight was dropped into a pool and allowed to sink to the bottom, approximately how much would that object "weigh" when you dove to the bottom to retrieve it?  By how much of a percentage would the weight vary?  Thanks for your time!

Answer
First of all, the weight of the object is equal to,the force of gravity on the object and that will NOT change just because the object is submerged. What you are really looking for is the force needed to support the object when submerged and that is something entirely different.  The force needed to support a submerged object will be equal to the difference in the object's weight, the force of gravity on the object, and the weight of the displaced liquid. For typical metals the density is usually significantly greater than the weight of the liquid in which the object is submerged. For example, if the metal has a specific gravity of 10 - meaning that the object's density is 10 times that of water - and the object is submerged in water, the force needed to life the bject would be equal to the weight of the object minus th weight of the displaced water. In your specific case the weight of the object is 45 pounds. If the specific gravity of the object is 10 then the weight of the displaced wasr will be one tenth of the weight of the object or about 4.5 pounds. Therefore, the force needed to lift the submerged object would be:
F = 45.0 - 45/10 = 45.0 - 4.5 = 40.5 pounds
If the specific gravity of the object was 5 then the weight of the displaced water would be on fifth of the weigh of the object and the force needed to log the object would be:
F = 45.0 - 45/5 = 45.0 - 9.0 = 36 pounds
Finally, if the specific gravity of the object was less than that of water such as 0.5 then the buoyancy force of the displaced water would be greater than the weight of the object and the object would float!

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James J. Kovalcin

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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