## College Physics (4th Edition)

(a) The compressive stress at the bottom of the column is $\rho g h$ (b) The maximum height of a column is $7.6~km$ (c) This maximum height should not be a practical concern since we don't construct buildings with a height of $7.6~km$.
(a) We can find mass of the column: $m = \rho~V$ $m = \rho~\pi~r^2~h$ We can find the compressive stress at the bottom of the column: $Stress = \frac{F}{A}$ $Stress = \frac{mg}{\pi~r^2}$ $Stress = \frac{\rho~\pi~r^2~h~g}{\pi~r^2}$ $Stress = \rho g h$ The compressive stress at the bottom of the column is $\rho g h$ (b) We can find the maximum height of a column: $\rho~h~g = 2.0\times 10^8~Pa$ $h = \frac{2.0\times 10^8~Pa}{\rho~g}$ $h = \frac{2.0\times 10^8~Pa}{(2700~kg/m^3)(9.80~m/s^2)}$ $h = 7600~m$ $h = 7.6~km$ The maximum height of a column is $7.6~km$ (c) This maximum height should not be a practical concern since we don't construct buildings with a height of $7.6~km$.