A block of wood with dimensions 0.12 by 0.34 by 0.43 cubic metres floats along a river with the broadest face facing down. The wood is submerged to height of 0.053 metres. what is the mass of the piece of wood.
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Given:
Dimensions of the block of wood = 0.12×0.34×0.43
Height at which the block is submerged = 0.053 m
To find:
Mass of the piece of wood.
Solution:
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 by the wooden block is.
= 0.34 * 0.43 * 0.053
= 0.00775 m³
We know that density = mass/ volume
So, mass = density * volume
Since the density of water is 1000 kg/m³, mass of displaced water:
= 1000 * 0.00775 = 7.75 kg
Therefore the mass of the block is 7.75 kg.
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