Dragging a string over a step

A simple problem in Newtonian mechanics is considered. The problem consists in finding the maximum value of the length xUP of the portion of string slowly dragged on a step of height h, when the string itself is initially placed to match the vertical profile of the step, the remaining part lying on the ground and the final portion being in static equilibrium during the dragging process. A straightforward analysis is required to find the solution. The problem can be proposed in a lecture or a demonstration in class on the role played by the coefficient of static friction in mechanics.