Final answer:
To calculate the coefficient of kinetic friction between the sled and snow, you can use Newton's second law of motion and the definition of kinetic friction. After finding the sled's acceleration with kinematic equations, you can determine the net force, subtract the frictional force to find the force of friction, and then use the normal force to calculate the coefficient of kinetic friction.
Step-by-step explanation:
To find the coefficient of kinetic friction between the runners of the sled and the snow, we can use the second law of motion and the definition of friction. The net force acting on the sled while it is accelerating can be calculated by subtracting the force of friction from the applied force. Using Newton's second law (F = ma), we know that the applied force minus the force of friction equals the mass of the sled multiplied by its acceleration (Fapplied - Ffriction = m × a). We also know that the force of friction is equal to the coefficient of kinetic friction times the normal force (Ffriction = μk × N), and since the sled is on a horizontal surface, the normal force is equal to the gravitational force on the sled (N = m × g).
First, we need to find the acceleration (a) of the sled. Since it starts from rest, we can use the kinematic equation v2 = u2 + 2as, where v is the final velocity, u is the initial velocity (which is zero in this case), and s is the distance covered. Solving for a we get a = (v2 - u2) / (2 × s). With the values v = 2.4 m/s and s = 9.9 m, we can calculate the acceleration.
Once we have the acceleration, we can find the net force (Fnet) acting on the sled using the equation Fnet = m × a. The only horizontal force besides the applied force is the force of friction, so we can then set up the equation 27 N - Ffriction = 18 kg × a to solve for Ffriction.
Finally, we can insert the values for Ffriction, the mass of the sled (18 kg), and the acceleration due to gravity (approximately 9.8 m/s2) into the equation Ffriction = μk × N to solve for μk, the coefficient of kinetic friction.