New insights on the falling ladder problem

A classical mechanics approach of the falling ladder problem with and without friction is presented. The ladder falls freely under the influence of gravity. As the ladder slides on the floor, it is free to lose its contact with the wall. The general nonlinear differential equation of motion is derived and solved numerically using the Runge–Kutta method implemented by MATLAB. The variation of the contact force with the wall is calculated and used for detecting the angle of separation from the wall. The motion after separation has two degrees of freedom and it is also solved by the Runge–Kutta method. It is shown that the separation time from the wall and the reaction forces are higher than the corresponding no-friction values.