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The problem statement reads: A 3.15kg piece of wood (Spec. Grav. = 0.5) floats on water. What is the minimum mass of lead, hung from it by a string will cause it to sink?

Heres my reasoning. Since the log is floating, I know that it is in equilibrium, and therefore the Bouyant force Fb = force due to gravity. Thus Fb = 3.15kg *9.8m/s^2.

But I also know that an object will float on water if [tex]\rho_w[/tex] > [tex]\rho_o[/tex]

I know the specific gravity as 0.5 so I know that the density of the wood is one half that of the water!! So ive concluded that I must add enough lead to make the density of wood + density of added lead = density of water to get a minimum to sink. My only problem is, if density is m/V, how would i know what V to use?

Ok so let me think this--- I know mass of wood, and I know the denisty of it is 1/2 of water. So set 1/2 water density = m/V where m is the mass of the wood. Then solve for V and ill know the woods volume. But i Have no idea where to go from here! Sure i can look up density of lead in the book, but i dont know how much MASS to add! Would anyone happen to know how to approach this? THANKS!!!!!!