Question #1537

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.

Expert's answer

Denote V, ρ_{1} as a volume of the block and the dentiry respectively.

The mass of the block is**ρ**_{1}*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 **ρ**_{2} gV, ρ_{2} - is the density of the water of 1000 kg/m^{3}.

**Fa = 1000*9.8* V = 120 N**. Then **V = 120/(1000*9.8) = 0.012 m**^{3}.

Thus the density of the block is**ρ1 = 4.7[kg]/0.012[m**^{3}] = 383.83 kg/m^{3}.

The mass of the block is

Assume that the volume of sinker is infinitely small comparely with the block. In the water the weight of the system is

Thus the density of the block is

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