Ski boots are usually made with releasable bindings. This is done for safety – if you fall and your ski gets caught, the binding between the boot and the ski will release so the ski pops off rather than twisting your knee. Sometimes this leads to the embarrassing situation of you falling down while skiing, the ski popping off, and the ski continuing down the mountain without you. You're skiing down a slope angled at 15∘ with respect to the horizontal when this situation happens to you. Your ski continues down the slope at a constant speed of 4 m/s. What is the coefficient of friction between your ski and the slope?

Question

Ski boots are usually made with releasable bindings. This is done for safety – if you fall and your ski gets caught, the binding between the boot and the ski will release so the ski pops off rather than twisting your knee. Sometimes this leads to the embarrassing situation of you falling down while skiing, the ski popping off, and the ski continuing down the mountain without you. You're skiing down a slope angled at 15∘ with respect to the horizontal when this situation happens to you. Your ski continues down the slope at a constant speed of 4 m/s. What is the coefficient of friction between your ski and the slope?

Answer 1

v=const =>

mgsinα=F(fr) = μN= μmgcosα
sinα= μcosα
μ=tanα

Answer 2

To determine the coefficient of friction between your ski and the slope, we can use the relationship between the forces acting on the ski and the slope.

Let's break down the forces:

1. Gravitational force (Fg): This force acts vertically downwards and can be calculated using the formula: Fg = m * g, where m is the mass of the ski and g is the acceleration due to gravity (approximately 9.8 m/s^2).

2. Normal force (Fn): This force acts perpendicular to the slope and is equal to the component of the gravitational force acting in the perpendicular direction. On an inclined plane, Fn = Fg * cos(θ), where θ is the angle of inclination (15∘ in this case).

3. Frictional force (Ff): This force acts parallel to the slope and opposes the motion of the ski. The formula to calculate the frictional force is Ff = μ * Fn, where μ is the coefficient of friction.

Given that the ski continues down the slope at a constant speed of 4 m/s, we know that the net force in the horizontal direction is zero (since there is no acceleration).

The net force equation can be written as:

Fn * sin(θ) = Ff

Since Fn = Fg * cos(θ), we can substitute this value in the equation:

Fg * cos(θ) * sin(θ) = μ * Fn

Now, we can plug in the known values:

m * g * cos(θ) * sin(θ) = μ * m * g * cos(θ)

m and g appear on both sides and can be canceled out:

μ = sin(θ) / cos(θ)

Plugging in θ = 15∘:

μ = sin(15∘) / cos(15∘)

Using a scientific calculator, we can find:

μ ≈ tan(15∘)

μ ≈ 0.268

Therefore, the coefficient of friction between your ski and the slope is approximately 0.268.

v=const =>

0.268

haha man

To determine the coefficient of friction between your ski and the slope, we can use the relationship between the forces acting on the ski and the slope.