Arubber boot is at rest on an inclined plane. when the angle of inclination of the plane is increased to 36.5°, the boot begins to slide down the incline. then, when the angle is decreased to 30.5°, the speed of the boot is constant. what are the coefficients of static and kinetic friction between the boot and the incline?

To solve this problem we will use the equations of kinetic and mechanical energy.

We start for the first angle where the given angle is 36.5 ° and the acceleration is zero.

The force equations would be given by:

Where is coefficient of friction (static)

If we make a sum of forces in the direction in which the block moves we will have the SinΘ Component and that of the friction force, so

solving for the coefficient,

We apply the same consideration for the angle of 30.5°, then we know that the coefficient (dinamic) is

this could be newton#'s law of cooling. the cooling curve is exponential