Sure, let's solve this step by step:

Step 1: Identify the forces acting on the skier
The forces acting on the skier are gravity, friction, and the normal force. The force of gravity can be split into two components: one that acts parallel to the slope (Fg_parallel = m*g*sin(θ)) and one that acts perpendicular to the slope (Fg_perpendicular = m*g*cos(θ)). The normal force is equal to the perpendicular component of gravity (Fn = Fg_perpendicular). The force of friction (Ff) is equal to the coefficient of friction (μ) times the normal force (Fn).

Step 2: Apply the principle of conservation of energy
The work done by the net force acting on the skier is equal to the change in the skier's kinetic energy. The work done by the net force is equal to the force times the distance over which the force is applied (W = F*d). The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy (ΔK = Kf - Ki).

Step 3: Set up the equation
The net force acting on the skier is the sum of the parallel component of gravity and the force of friction (F_net = Fg_parallel + Ff). Substituting the expressions for these forces gives F_net = m*g*sin(θ) + μ*m*g*cos(θ). The work done by the net force is W = (m*g*sin(θ) + μ*m*g*cos(θ))*d. The change in kinetic energy is ΔK = 0.5*m*vf^2 - 0.5*m*vi^2.

Step 4: Solve the equation for the coefficient of friction
Setting the work done by the net force equal to the change in kinetic energy gives (m*g*sin(θ) + μ*m*g*cos(θ))*d = 0.5*m*vf^2 - 0.5*m*vi^2. Solving this equation for μ gives μ = [(0.5*m*vf^2 - 0.5*m*vi^2) / (m*g*d) - sin(θ)] / cos(θ).

Step 5: Substitute the given values into the equation
Substituting the given values into the equation gives μ = [(0.5*vf^2 - 0.5*vi^2) / (g*d) - sin(30°)] / cos(30°) = [(0.5*5.3^2 - 0.5*8.2^2) / (9.8*2.4) - 0.5] / √3/2 = -0.036.

The negative value for the coefficient of friction indicates that the direction of the friction force was opposite to the direction assumed when setting up the equation. This means that the friction force was actually acting down the slope, helping the skier to slow down. The magnitude of the coefficient of friction is 0.036.

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Sure, let's solve this step by step:

Step 1: Identify the forces acting on the skier
The forces acting on the skier are gravity, friction, and the normal force. The force of gravity can be split into two components: one that acts parallel to the slope (Fg_parallel = m*g*sin(θ)) and one that acts perpendicular to the slope (Fg_perpendicular = m*g*cos(θ)). The normal force is equal to the perpendicular component of gravity (Fn = Fg_perpendicular). The force of friction (Ff) is equal to the coefficient of friction (μ) times the normal force (Fn).

Step 2: Apply the principle of conservation of energy
The work done by the net force acting on the skier is equal to the change in the skier's kinetic energy. The work done by the net force is equal to the force times the distance over which the force is applied (W = F*d). The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy (ΔK = Kf - Ki).

Step 3: Set up the equation
The net force acting on the skier is the sum of the parallel component of gravity and the force of friction (F_net = Fg_parallel + Ff). Substituting the expressions for these forces gives F_net = m*g*sin(θ) + μ*m*g*cos(θ). The work done by the net force is W = (m*g*sin(θ) + μ*m*g*cos(θ))*d. The change in kinetic energy is ΔK = 0.5*m*vf^2 - 0.5*m*vi^2.

Step 4: Solve the equation for the coefficient of friction
Setting the work done by the net force equal to the change in kinetic energy gives (m*g*sin(θ) + μ*m*g*cos(θ))*d = 0.5*m*vf^2 - 0.5*m*vi^2. Solving this equation for μ gives μ = [(0.5*m*vf^2 - 0.5*m*vi^2) / (m*g*d) - sin(θ)] / cos(θ).

Step 5: Substitute the given values into the equation
Substituting the given values into the equation gives μ = [(0.5*vf^2 - 0.5*vi^2) / (g*d) - sin(30°)] / cos(30°) = [(0.5*5.3^2 - 0.5*8.2^2) / (9.8*2.4) - 0.5] / √3/2 = -0.036.

The negative value for the coefficient of friction indicates that the direction of the friction force was opposite to the direction assumed when setting up the equation. This means that the friction force was actually acting down the slope, helping the skier to slow down. The magnitude of the coefficient of friction is 0.036.

Knowee AI · Accepted Answer

Sure, let's solve this step by step:

Step 1: Identify the forces acting on the skier
The forces acting on the skier are gravity, friction, and the normal force. The force of gravity can be split into two components: one that acts parallel to the slope (Fg_parallel = m*g*sin(θ)) and one that acts perpendicular to the slope (Fg_perpendicular = m*g*cos(θ)). The normal force is equal to the perpendicular component of gravity (Fn = Fg_perpendicular). The force of friction (Ff) is equal to the coefficient of friction (μ) times the normal force (Fn).

Step 2: Apply the principle of conservation of energy
The work done by the net force acting on the skier is equal to the change in the skier's kinetic energy. The work done by the net force is equal to the force times the distance over which the force is applied (W = F*d). The change in kinetic energy is equal to the final kinetic energy minus the initial kinetic energy (ΔK = Kf - Ki).

Step 3: Set up the equation
The net force acting on the skier is the sum of the parallel component of gravity and the force of friction (F_net = Fg_parallel + Ff). Substituting the expressions for these forces gives F_net = m*g*sin(θ) + μ*m*g*cos(θ). The work done by the net force is W = (m*g*sin(θ) + μ*m*g*cos(θ))*d. The change in kinetic energy is ΔK = 0.5*m*vf^2 - 0.5*m*vi^2.

Step 4: Solve the equation for the coefficient of friction
Setting the work done by the net force equal to the change in kinetic energy gives (m*g*sin(θ) + μ*m*g*cos(θ))*d = 0.5*m*vf^2 - 0.5*m*vi^2. Solving this equation for μ gives μ = [(0.5*m*vf^2 - 0.5*m*vi^2) / (m*g*d) - sin(θ)] / cos(θ).

Step 5: Substitute the given values into the equation
Substituting the given values into the equation gives μ = [(0.5*vf^2 - 0.5*vi^2) / (g*d) - sin(30°)] / cos(30°) = [(0.5*5.3^2 - 0.5*8.2^2) / (9.8*2.4) - 0.5] / √3/2 = -0.036.

The negative value for the coefficient of friction indicates that the direction of the friction force was opposite to the direction assumed when setting up the equation. This means that the friction force was actually acting down the slope, helping the skier to slow down. The magnitude of the coefficient of friction is 0.036.

A skier glides 2.4 m up a hill angled 30° above the ground. His speed slows from 8.2 m/s to 5.3 m/s. Determine the coefficient of friction of the hill with the skier? use grade 12 knowledge Answer question

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