# Young's Modulus: maximum depth of mine

1. Nov 9, 2008

### mmylo

1. The problem statement, all variables and given/known data

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 2.0x10^9 pascals. What is the maximum length 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.

2. Relevant equations

Stress=F / A
Y=( F / A ) / ( delta L / L )

3. The attempt at a solution

I really don't know where to begin.

2. Nov 9, 2008

### PhanthomJay

mmylo, welcome to PF!
You don't need to know Young's modulus or deformations to solve this problem. It is asking you to find the maximum length of the cable such that the maximum stress, due to the cables weight, does not exceed the given value of the maximum stress allowed. The cable's weight is a function of its weight density, length, and area. It's stress is just F/A. Does this give you a clue to solve the problem?