Answer to Question #1537 in Mechanics | Relativity for Alexis

Question

A block of wood weighs 46.2 N in air. A sinker is hanging from the block, and the weight of the wood-sinker combination is 235.8 N when the sinker alone is immersed in water. When the wood-sinker combination is completely immersed, the weight is 115.8 N. Find the density of the block.

Answer 1

Denote V, ρ₁ as a volume of the block and the dentiry respectively.
The mass of the block is ρ₁*V = 46.2/9.8 = 4.7 kg. The weight of the sinker is 235.8-46.2 = 189.6 N.
Assume that the volume of sinker is infinitely small comparely with the block. In the water the weight of the system is
235.8 - Fa = 115.8, where Fa - is the Archimede's force of ρ₂ gV, ρ₂ - is the density of the water of 1000 kg/m³.
Fa = 1000*9.8* V = 120 N. Then V = 120/(1000*9.8) = 0.012 m³.
Thus the density of the block is ρ1 = 4.7[kg]/0.012[m³] = 383.83 kg/m³.