Dynamical friction force

Question

Let we have a ladder leaning on the wall. Initially we hold the ladder and as soon as we release it the ladder starts to slide.

My question: during the slide, are the friction forces at both ends constant or changing as the inclination angle changes (from $\theta_0$ to $0$)?

Addendum: Let assume $\theta$ in the angle between the ladder and the floor and the friction coefficient for both the wall and floor is $\mu$. Then we have fiction force between the ladder and the floor

$$F_f=-\mu mg \sin \theta,$$

and fiction force between the ladder and the wall

$$F_w=-\mu mg \cos \theta.$$

Since $\theta$ varies over time, both $F_f$ and $F_w$ will vary over time. And so the total force acting on the ladder, $F=mg-F_f-F_w$, also varies overtime. Am I correct?

Answer 1

The basics for sliding friction are here: http://hyperphysics.phy-astr.gsu.edu/hbase/frict3.html

The contact area and speed are not important, but the normal force -- the force normal to the contact surface -- is important.

Normal forces exist between the ladder and the wall, and between the ladder and the floor. Treating the ladder as a rigid body, and gravity as a constant, you use the angle of contact to resolve the total force of gravity into two parts, the wall and the floor.

Thus the force of friction, which resists the motion of the ladder, will vary with the angle. So the direct answer is no, it is not constant.

Answer 2

Due to its weight, the ladder presses on both sides which causes friction on both sides. As the ladder moves, the angle changes and with the changing angle, the pressure (force) it exerts on two sides decreases (or unbalances) because it is becoming more and more straight. So, the friction does decrease due to decreased press of the ladder.