It is possible the question is flawed.
The other end.
Would the normal reactions on either side not change suddenly?
I was assuming constant power. But why will it only slow down?
My doubt exactly.
What is this? Could you give me an example of such a problem? Maybe just link it.
Friction before force is applied, f=μmg.
After force is applied on element dx, at a distance x from hinge, the is a bending moment on that element dM which is given by normals on either side (say N1, N2) by dM=N1-N2 and N1+N2=mg+F.