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Physics Homework Question?
A skier traveling 11.0 m/s reaches the foot of a steady upward 20 ∘ incline and glides 14 m up along this slope before coming to rest.
What was the average coefficient of friction?
1 Answer
- electron1Lv 76 years ago
Since the skier is moving up the incline, there are two forces that are causing to decelerate. These forces the component of its weight that is parallel to the incline and the friction force.
Force parallel = m * 9.8 * sin 20
Ff = μ * m * 9.8 * cos 20
Total force = m * 9.8 * sin 20 + μ * m * 9.8 * cos 20
Total deceleration = 9.8 * sin 20 + μ * 9.8 * cos 20
As the skier moves 14 meters up the incline, the velocity will decrease from 11m/s to 0 m/s. Use the following equation to determine the deceleration.
vf^2 = vi^2 + 2 * a * d
0 = 11^2 + 2 * a * 14
28 * a = -121
a = -121 ÷ 28
This is approximately negative 4.32 m/s^2.
9.8 * sin 20 + μ * 9.8 * cos 20 = 121 ÷ 28
μ * 9.8 * cos 20 = (121 ÷ 28) – 9.8 * sin 20
μ = [(121 ÷ 28) – 9.8 * sin 20] ÷ 9.8 * cos 20
This is approximately 0.1053.
