Question

A wooden block slides directly down an inclined plane with a constant speed of 6.0 m/s. What is the coefficient of kinetic friction if the incline is angled at 25º.

Answer 1

The free body diagram of the considered problem is (note: figure is a courtesy of https://sciencenotes.org/friction-example-problem-sliding-inclined-plane/):

As long as the velocity is constant, the net force should be equal to 0:

$\vec{N} + \vec{W} + \vec{F}_f = 0$

Projecting this equation on the x- and y-axis, we obtain:

$N = W \cos{\theta} \quad \Rightarrow N = mg \cos{25^\circ} \\ W \sin{\theta} = F_r \quad \Rightarrow mg \sin{25^\circ} = \mu N$

Combining the expressions together, we derive:

$\sin{25^\circ} = \mu \cos{25^\circ} \quad \Rightarrow \mu = \tan{25^\circ} \approx$ 0.47