Answer :
Final answer:
The coefficient of friction between the ice skater's skates and the ice can be calculated using principles of physics. Our computation involves using the known initial velocity, distance, and applying equations related to kinetic friction, acceleration, and motion. We ultimately set up and solve an equation relating the friction force to the coefficient of friction and the skater's weight.
Explanation:
The coefficient of friction can be determined using the principles of physics, specifically the concept of kinetic friction. In this scenario, the ice skater is slowing down due to the friction between the ice and the skates, which eventually brings him to a stop. First, we need to employ the principle that the work done by the kinetic friction force (which is equivalent to the change in kinetic energy of the skater) is equal to the force of friction times the distance over which the force is applied.
Next, to calculate the friction force, we should use the following equation: F_friction = m*a , where m is the mass of the skater (which we don't know) and a is the acceleration. Given we know the initial velocity (v_i = 13.7 m/s) and that the final velocity (v_f) is 0 m/s, we can use the equation of motion v_f = v_i + a*t to calculate the acceleration. Replacing v_f, v_i, t in the previous equation, we can now solve for 'a'. After that, we replace 'a' in the friction equation to solve for F_friction.
Finally, knowing that the friction force is also equal to the coefficient of friction (u_k) times the normal force (N), we can solve for u_k. Here, we assume that the normal force is equal to the weight of the skater, hence mg where 'g' represents the acceleration due to gravity ( g ≈ 9.8 m/s² ) and 'm' is the mass of the skater. Solving, F_friction = u_k*m*g , we find the coefficient of friction between the skates and the ice.
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