Skiing Physics: Finding the Angle of the Slope

What is the angle of the slope down which a skier with a mass of 65.0 kg can coast at a constant velocity and a coefficient of friction of 0.1?

a) 5.7 degrees b) 10.2 degrees c) 15.4 degrees d) 20.1 degrees

Answer:

The angle of the slope down which a skier with a mass of 65.0 kg can coast at a constant velocity and a coefficient of friction of 0.1 is approximately 5.7 degrees.

Explanation: To find the angle of the slope down which a skier with a mass of 65.0 kg can coast at a constant velocity with a coefficient of friction (μk) of 0.1, we can use principles of mechanics and friction.

Since the skier is coasting at a constant velocity, the net force along the slope must be zero. This means that the gravitational force component along the slope must equal the frictional force opposing the motion.

The force of gravity along the slope is given by Fg = m × g × sin(θ) and the frictional force is Ff = μk × N, where N is the normal force. On an inclined plane, N equals m × g × cos(θ).

By equating the two forces and solving for θ, we get:

m × g × sin(θ) = μk × m × g × cos(θ)

tan(θ) = μk

Substituting μk = 0.1 and using a calculator to find the arctangent, we find that θ ≈ 5.7 degrees, which corresponds to option (a) 5.7 degrees.