Answer:
The average coefficient of friction is 0.104
Explanation:
Given;
velocity of the skier, v = 9.4 m/s
angle of inclination, θ = 16°
height of the slope, h = 12 m
Calculate the kinetic energy of the skier at the given velocity;
KE =¹/₂mv²
KE = ¹/₂m(9.4)²
KE = 44.18m
Calculate the potential energy of the skier up the slope;
PE = mghsinθ
PE = m x 9.8 x 12 x sin16
PE = 32.411 m
Calculate the friction force on the inclined plane;
Fk = μk x mgCosθ
Fk = μk x m x 9.8 x Cos16
Fk = μk x m x 9.421
Calculate the work done by friction;
Work done = Fk x d
Work done = μk x m x 9.421 x d
Work done = μk x m x 9.421 x 12
Work done = 113.052mμk
Apply the principle of conservation of energy;
KE = PE + work done by friction
44.18m = 32.411 m + 113.052mμk (factor out m and divide through by it)
44.18 = 32.411 + 113.052μk
44.18 - 32.411 = 113.052μk
11.769 = 113.052μk
μk = 11.769 / 113.052
μk = 0.104
Therefore, the average coefficient of friction is 0.104
