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******10 pts****** physics question?
We have just started to work with fluids in class and there are two questions in my book that I can't seem to work out.
1) A 7.07 kg piece of wood ({\rm{SG}} = 0.50) floats on water.What minimum mass of lead, hung from the wood by a string, will cause it to sink?
I thought it was 7.07 kg but that is wrong.
2)An undersea research chamber is spherical with an external diameter of 4.50 m. The mass of the chamber, when occupied, is 47100 kg. It is anchored to the sea bottom by a cable.
a)What is the buoyant force on the chamber?
b)What is the tension in the cable?
Any help would be greatly appreciated.
Thank you :)
1 Answer
- Anonymous9 years agoFavorite Answer
Your answer would be correct if the lead was infinitely dense, but of course, it's not. The wood+lead combo will sink when it's average density exceeds 1g/cc (that of water). Let L be the mass of lead, then we require
(7.07 + L) / ( 7.07/0.5 + L/P ) = 1
where P is the density of lead, 11.34 g/cc. Putting it together with proper (albeit mixed) units:
(7.07 + L)kg / ( 7.07kg/(0.5g/cc) + (L kg)/(11.34 g/cc) ) = 1 g/cc
solving: L = 7.75 kg
For the undersea chamber, volume = (4/3)PiR^3 = 47.713 m^3. Mass of water displaced is 47713kg, minus 47100kg dead weight = 713kg. Buoyant force = (713kg)(9.8 m/sec^2) = 6987 Newtons, which is the same as the tension in the cable.