A block of mass $m = 5$ kg slides down an inclined plane that makes an angle $\alpha = 30°$ with the horizontal. The coefficient of friction between the block and the plane is $\mu = 0.2$. Find the acceleration of the block. The acceleration due to gravity is $g = 10$ m/s².
Resolve the weight into components: along the plane $mg\sin\alpha$, perpendicular to the plane $mg\cos\alpha$. The normal force is $N = mg\cos\alpha$, the friction force is $F_f = \mu N = \mu mg\cos\alpha$.
By Newton's second law along the plane:
$$ma = mg\sin\alpha - \mu mg\cos\alpha$$
$$a = g(\sin\alpha - \mu\cos\alpha) = 10(0.5 - 0.2 \cdot 0.866) \approx 3.27 \text{ m/s}^2$$
$a \approx 3.27$ m/s²