A particle of mass m is placed on an slope with an incline 30 degrees. Once released it accelerates down the line of greatest slope at 2 m s^-2. What is the coefficient of friction between the particle and the slope?

Resolve forces perpendicular to the slope. No acceleration in this direction hence resultant force in this direction must equal zero:R = mg * cos(30) Apply Newtons second law in the direction parallel to the slope:F = m * amg sin(30) - μR = maSubstitute in R = mg * cos(30) :mg sin(30) - μmg * cos(30) = macancel m:g sin(30) - μg * cos(30) = arearrange for μμ=(gsin(30) - a)/(gcos(30)) = (9.8sin(30)-2)/(9.8cos(30)) =0.342