Question

Estimate the pressure on the mountains underneath the Antarctic ice sheet, which is typically 2 km thick.

Short answer

The pressure on the mountains is \(1.79 \times {10^7}\;{\rm{Pa}}\).

Step-by-step solution

Given Data

The thickness of the mountain is \(d = 2\;{\rm{km}}\).

Understanding the pressure

In this problem, the pressure on the mountain can be calculated by dividing the weight of the ice (mg) with the area (A).

Estimating the pressure on the mountain

The relation ofpressureis given by,

\(\begin{array}{l}P = \frac{F}{A}\\P = \frac{{mg}}{{\left( {\frac{V}{d}} \right)}}\end{array}\)…… (i)

Here, \(F\) is the weight of the ice, \(m\) is the mass of the ice, \(g\) is the gravitational acceleration and \(V\)is the volume.

The relation of volume is given by,

\(V = \frac{m}{\rho }\)

Here, \(\rho \) is the density of the ice.

On plugging the values in the equation (i),

\(\begin{array}{l}P = \frac{{mg}}{{\left( {\frac{m}{{\rho d}}} \right)}}\\P = \rho gd\\P = \left( {917\;{\rm{kg/}}{{\rm{m}}^3}} \right)\left( {9.80\;{\rm{m/}}{{\rm{s}}^2}} \right)\left( {2\;{\rm{km}} \times \frac{{1000\;{\rm{m}}}}{{1\;{\rm{km}}}}} \right)\\P = 1.79 \times {10^7}\;{\rm{Pa}}\end{array}\)

Thus, the pressure on the mountains is \(1.79 \times {10^7}\;{\rm{Pa}}\).