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# A piece of ice slides from rest down a rough 33.0° incline in twice the time it takes to slide down a frictionless 33.0° in- cline of the same length. Find the coefficient of kinetic friction between the ice and the rough incline.

Kevin Nash
6 years ago
When the ice block slides over a frictionless inclined plane with angle of inclination θ, the net force along the length of the inclined plane is responsible for accelerating the block. With no friction, the only force acting along the length of the inclined plane is the component of weight mg sin θ .
Therefore,
mg sin θ = ma1
a1 = g sin θ
When the ice block slides over a rough inclined surface with angle of inclination θ , the net force along the length of the inclined plane is the resultant of the weight acting along the length (mg sin θ) and the kinetic force of friction (fk) .
Therefore,

Here, μk is the coefficient of kinetic friction between the ice and the surface of inclined plane

Round off to two significant figures,
μk = 0.49
Therefore, the coefficient of kinetic friction is 0.49 .