## Using linear programming for solving mechanical engineering problems: The ladder against a wall problem (part 2)

In my previous blog post I demonstrated how to use linear programming for solving the ladder against a wall problem. More specifically, the R code in that blog found the maximum position x a person could reach before the ladder starts sliding.

In this blog post I will go one step further. In particular, I will develop a solution strategy for finding the minimum angle θ such that a ladder doesn’t slip down. For simplicity, I will assume that no person is on the ladder, and that the ladder slips down due to its own weight (Q). Furthermore, I assume that both the wall and floor are rough surfaces. As a consequence, friction occurs between the top of the ladder and the vertical wall, and between the base of the ladder and the horizontal floor. This minimum angle problem is depicted in the following figure (with on the right-hand side a free body diagram). ## Using linear programming for solving mechanical engineering problems: The ladder against a wall problem

A person with weight Q stands on a ladder. This ladder is leaning against a vertical wall. What is the maximum position x this person can reach before the ladder starts sliding? This ladder against a wall problem is depicted in the following figure (with on the right-hand side a free body diagram). The following R code demonstrates how to use linear programming for solving the ladder against the wall problem.