Starting from rest, a block slides down an inclined surface that has an inclination of 30^ with the horizontal. It covers a distance of 8 m in the first two seconds. Determine the coefficient of kinetic friction between the block and the surface.

Step-by-step solution

Using the second equation of motion: s = ut + 1 2 at^2 Substituting the given values s = 8 m , u = 0 , and t = 2 s : 8 = 0 + 1 2 a(2)^2 8 = 2a a = 4 m/s ^2 The acceleration of a block sliding down a rough inclined plane is given by: a = g( - _k ) Substituting a = 4 m/s ^2 , = 30^ , and taking g = 10 m/s ^2 : 4 = 10 ( 1 2 - _k 3 2 ) 0.4 = 0.5 - _k 3 2 _k 3 2 = 0.1 _k = 0.2 3 0.11