Although human beings have been able to fly hundreds of thousands of miles into outer space, getting inside the earth has proven much more difficult. The deepest mines ever drilled are only about 10 miles deep. To illustrate the difficulties associated with such drilling, consider the following:
The density of steel is about 7900 kilograms per cubic meter, and its breaking stress, defined as the maximum stress the material can bear without deteriorating, is about 2.0*10^9 pascals.
What is the maximum length (km) of a steel cable that can be lowered into a mine? Assume that the magnitude of the acceleration due to gravity remains constant at 9.8 meters per second per second.
Assume the cable is L meters deep into the Earth.
The cross-sectional area is A square meters for the cable.
then the volume of the cable V = ...
It finds the maximum length of a steel cable that can be lowered into a mine without deteriorating.