Answer:
The Ā average coefficient of friction is 0.104
Explanation:
Given;
velocity of the skier, v = 9.4 m/s
angle of inclination, Īø = 16Ā°
height of the slope, h = 12 m
Calculate the kinetic energy of the skier at the given velocity;
KE =Ā¹/āmvĀ²
KE = Ā¹/ām(9.4)Ā²
KE = 44.18m
Calculate the potential energy of the skier up the slope;
PE = mghsinĪø
PE = m x 9.8 x 12 x sin16
PE = 32.411 m
Calculate the friction force on the inclined plane;
Fk = Ī¼k x mgCosĪø
Fk = Ā Ī¼k x m x 9.8 x Cos16
Fk = Ā Ī¼k x m x 9.421
Calculate the work done by friction;
Work done = Fk x d
Work done = Ī¼k x m x 9.421 x d
Work done = Ī¼k x m x 9.421 x 12
Work done = 113.052mĪ¼k
Apply the principle of conservation of energy;
KE = PE + work done by friction
44.18m = 32.411 m + 113.052mĪ¼k (factor out m and divide through by it)
44.18 = 32.411 Ā + 113.052Ī¼k
44.18 - 32.411 Ā = 113.052Ī¼k
11.769 = 113.052Ī¼k
Ī¼k = 11.769 / 113.052
Ī¼k = 0.104
Therefore, the Ā average coefficient of friction is 0.104
