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'Moving Stonehenge' printed from https://nrich.maths.org/
If transporting the stones dry, the minimum volume of wood
required:
$(V_{stone}\rho_{stone} + V_{wood}\rho_{wood})g =
V_{wood}\rho_{water}g$
$\therefore V_{wood}(\rho_{water} - \rho_{wood}) =
V_{stone}\rho_{stone}$
$\therefore V_{wood} = \frac{V_{stone}\rho_{stone}}{\rho_{water} -
\rho_{wood}} = 13.05m^3$
$V_{wood}/(\pi r_{tree}^2) = length_{tree} = 415.4m$
That's nearly half a kilometer of sizeable trees!
If the stones could be transported wet, which would of course
require a river about 2 feet deeper, then less wood would have been
required:
$(V_{stone}\rho_{stone} + V_{wood}\rho_{wood})g = (V_{wood} +
V_{stone})\rho_{water}g$
$\therefore V_{wood}(\rho_{water} - \rho_{wood}) =
V_{stone}\rho_{stone}$
$\therefore V_{wood} = \frac{V_{stone}(\rho_{stone} -
\rho_{water})}{\rho_{water} - \rho_{wood}} = 8.55m^3$
$V_{wood}/(\pi r_{tree}^2) = length_{tree} = 272.2m$
That's still a lot of trees, but considerably fewer, maybe 25
large trees. That is the absolute minimum value though, at which
the object will have neutral buoyancy, i.e. will have the overall
density of water.