Question

A block of wood 0.12 m x 0.34 m x 0.43 m floats along a river with the broadest face down in the river. The wood is submerged to a depth of 0.053 m. What is the mass of the block? The density of water is 1000 kg/m3.

Answer 1

The mass of the block is 7.75 kg.

Explanation:

The mass of the block is equal to the mass of the water that is displaced. That is the rule of buoyancy. The buoyant force is equal to the weight of the mass of the fluid displaced.

So we need the volume of the water displaced. That volume is
`0.34 m "x" 0.43 m "x" 0.053 m = 0.00775 m^3`

Since `"density" = "mass"/"volume"`,

`"mass" = "density" * "volume"`

Therefore the mass of the displaced water is
`(1000 kg)/cancel(m^3) * 0.00775 cancel(m^3) = 7.75 kg`

And therefore the mass of the block is 7.75 kg.

I hope this helps,
Steve