Question

A 65 kg skier slides down a 10 degree slope at constant speed. Determine the coefficient of kinetic friction between the skis and the snow.

Answer 1

The coefficient of kinetic friction between the skis and the snow is approximately μ_k ≈ 0.176.

Step-by-step explanation:

In order to determine the coefficient of kinetic friction
`(\(\mu_k\))` between the skis and the snow, we employed the equation for frictional force on an inclined plane. Given that the skier is sliding at a constant speed, the frictional force is equal to the component of the gravitational force parallel to the slope. This relationship can be expressed as
`\(\mu_k * m * g * \cos(\theta) = m * g * \sin(\theta)\),` where
`\(m\)` is the mass of the skier,
`\(g\)` is the acceleration due to gravity, and
`\(\theta\)` is the angle of the slope.

Recognizing that the mass
`\(m\)` and one factor of
`\(g\)`cancel out, the simplified equation becomes
`\(\mu_k * \cos(\theta) = \sin(\theta)\).` Solving for
`\(\mu_k\),` we find that
`\(\mu_k = (\sin(\theta))/(\cos(\theta))\)` . Substituting the given angle of the slope
`(\(\theta = 10^\circ\)),` we obtain
`\(\mu_k \approx \tan(10^\circ)\)` , yielding a final value of
`\(\mu_k \approx 0.176\).`

This signifies that the coefficient of kinetic friction between the skis and the snow is approximately 0.176, illustrating the mathematical derivation behind the determination of this crucial parameter governing the skier's motion on the inclined surface.