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A skier starts from rest and slides at a constant velocity down a snow-covered bank that makes an 18° angle with the horizontal. What is the coefficient of friction between the skis and the snow?

a. 0.324
b. 0.500
c. 0.950
d. 1.000

User DanSogaard
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1 Answer

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Final answer:

The coefficient of friction for a skier sliding down a slope at constant velocity is determined by the tangent of the slope's angle, which for an 18-degree angle is approximately 0.324.

Step-by-step explanation:

The student's question pertains to the calculation of the coefficient of friction for a skier who slides down a slope at a constant velocity. When a skier is moving down a slope at constant velocity, the forces parallel to the slope (gravity and friction) are in balance, meaning the net force is zero. In this case, the force due to gravity along the slope is the skier's weight mg times the sine of the slope angle (sin(θ)), and the force of friction is the normal force (which is mg times the cosine of the slope angle, cos(θ)) multiplied by the coefficient of friction (μk). Thus, μk = tan(θ) when the skier's velocity is constant and acceleration is zero.

For an 18° angle, we calculate the coefficient of friction as follows:

μk = tan(18°) ≈ 0.324

Therefore, the correct answer is a. 0.324.

User Clexmond
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