A wooden block of volume 5.21 times 10^-4 m^3 floats in water and a small steel

Question

A wooden block of volume 5.21 times 10^-4 m^3 floats in water and a small steel object of mass m is placed on top of the block. When m = 0.330 kg, the system is in equilibrium, and the top of the wooden block is at the level of the water. (a) What is the density of the wood? kg/m^3 (b) What happens to the block when the steel object is replaced by a second steel object with a less than 0.330 kg? What happens to the block when the steel object is replaced by yet another steel object with a mass greater than 0.30 kg? The block will displace a smaller volume of water and will only be somewhat submerged by water. If greater than .330 kg, it will be fully submerged.

Explanation / Answer

while the system floats

B = w_total = w_block+w_stell

rho_water * g * V_submerged = rho_b * g * V_b + m_steel*g

m_steel = 0.330 kg

Vsubmerged = Vb = 5.21 x 10^-4 m^3

rho_block = (rho_water * Vb - m_steel)/Vb = rho_water - m_steeel/Vb

rho_block = 366.6 kg/m^3

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