Let θ = Maximum angle of inclined plane for which the block does not slide
Coefficient of static friction, μs = 0.81
Coefficient of kinetic friction, μk = 0.69
Angle of inclined plane = 37 degrees
Static friction = fs
Component of the weight along the plane = M g sin θ
Component of the weight perpendicular to the plane = M g Cosθ
Condition for the book not to slide,
Static friction = M g Sin θ
fs = M g sin θ ...............(1)
N = M g Cos θ .............(2) ( where N = Normal force )
By dividing ( 1) with (2)
fs / N = tan θ
But, fs / N = μs
Hence, tan θ = μs
Maximum angle of inclined plane for which the block does not slide, θ = arc tan ( μs )
= arc tan ( 0.81 )
= 39o