Tension on string of submerged object.

  • #1
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Homework Statement


A hollow steel sphere of inner radius 0.9m and outer radius 1m is submeged 1000m below the surface of the sea. Take the density of water to be 1000 kg/m^3 and the density of steel to be 7.8 x 10^3. Calculate the tension in the wire to support the submerged sphere.


Homework Equations


B = ρ(f)V(f)g
W = mg



The Attempt at a Solution


T + B = mg.
Calculate T.
Is this correct? The 1000m below sea level is what's making me doubt myself. Should this be factored into the calculation?
 

Answers and Replies

  • #2
rock.freak667
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Your equation is correct however, I think the 1000 kg/m^3 for water they gave you would be at atmospheric pressure. You might need to get the density at 1000 m. However I don't think the value should vary by too much.
 
  • #3
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How would you go about calculating the density at a depth of 1000m?
 
  • #4
SteamKing
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Water is incompressible. The density of water at sea level is for all intents and purposes the same density at a depth of 1000 m.
 
  • #5
haruspex
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According to http://en.wikipedia.org/wiki/Properties_of_water#Compressibility, density increase at 1km due to compression would be only about 0.5%. In practice, higher salinity would be more important. As against that, g would be a tiny bit less. I don't think you're expected to take any of that into account for this question, since it does not specify a salinity or pressure for the given density.
 
  • #6
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Brilliant. Thanks for that. A little confused as to why the 1000 metres was actually specified so.
 
  • #7
haruspex
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Providing irrelevant data in a question is a practice to be endorsed. Out in the real world, most available data are irrelevant, and recognising which are relevant is an important skill.
 
  • #8
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That's true. Thanks for the explanations and help in general with that anyway.
 

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