a cylindrical buoy cross sectional area a and height l with a mass density pb. w

Question

a cylindrical buoy cross sectional area a and height l with a mass density pb. when its placed in water it floats upright. density of water is pw.

A) if water it is put into is a pond that's contained by a small dam, find the weight of the water that flows over the dam when the buoy enters the pond.

B) find the fraction of the buoy that's submerged.

C) a seagull sees the buoy floating in water lands on it, buoy sinks a fraction f of its lenght further in to water. what is the mass of seagulls?

Explanation / Answer

(A)For the buoy to be in equilibrium, the weight of the buoy equals the buoyant force, and equals the weight of the fluid the buoy displaces, i.e.,

Fbuoyancy = Wbuoy = Wwater

And we know that Wbuoy = bgal. Therefore,

Wwater = bgal.    This is the weight of water flows over the dam.

(B) The volume of water displaced is Vwater = Wwater /(wg)= bgal/(wg) = bal/w which also equals the volume of the bouy submerged. The fraction is then

f1 = Vsub/Vbouy = (bal/w)/al = b/w

(C) The total submerged fraction becomes

ft = f1+f = b/w+f

Total volume submerged is Vsub = (b/w+f)al which equals the the volume of water displaced.

Wwater = wgVsub = wg(b/w+f)al = bgal+fgwal which equals the weight of the buoy and the seagull, i.e.,

gbal+fgwal = gbal+Wseagull     Wseagull   = fgwal         mseagull   = fwal  

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