1.

1. Consider the following experiment: A bar is hanging with the top end fixed at x = 0, and the bar is stretched by a pressure (force per unit area) p applied uniformly to the free (bottom) end. What are the boundary conditions describing this situation?

2.

Suppose that a homogeneous bar (that is, a bar with constant stiffness k) of length ? has its top end fixed at x = 0, and the bar is stretched to a length ? + ?? by a pressure p applied to the bottom end. Take down to be the positive x-direction.

1. Explain why p and ?? have the same sign.

2. Explain why p and ?? cannot both be chosen arbitrarily (even subject to the requirement that they have the same sign). Give both physical and mathematical reasons.

3. Suppose p is specified. Find ?? (in terms of p, k, and ?).

4. Suppose ?? is specified. Find p (in terms of ??, k, and ?).

3.

A certain type of stainless steel has a stiffness of 195 GPa. (A Pascal (Pa) is the standard unit of pressure, or force per unit area. The Pascal is a derived unit: one Pascal equals one Newton per square meter. The Newton is the standard unit of force: one Newton equals one kilogram meter per second-squared. Finally, GPa is short...