1. The problem statement, all variables and given/known data A 30kg sled is sliding on a frictionless sheet of ice at a velocity of 4m/s. The sled encounters a rough patch of ice and begins to slow down. After traveling on the rough patch of ice for 3m, the sled's velocity is 2m/s. Determine the coefficient of friction between the rough ice and sled. 2. Relevant equations KE = (1/2)mv2 FF = uk * FN W = f * d v2 = vi2 + 2a(x - xi) 3. The attempt at a solution I begin by finding the Kinetic energy when the sled is on the frictionless sheet of ice: KE = (1/2)mv2 KE = (1/2) * (30) * 42 KE = 240J Then I find the Kinetic Energy when the sled is on the rough patch: KE = (1/2)mv2 KE = (1/2) * (30) * 22 KE = 60J I now note the amount of energy released due to friction: 240J - 60J = 180J I continue to evaluate the force acting on the sled when on the rough patch: W = fd 60J = f * 3m f = 20N Then I solve for acceleration in the rough patch: v2 = vi2 + 2a(x - xi) 4 = 0 + 2*a*3 a= (2/3) Now I sum the forces: 20N - (uk * (30kg * 9.8)) = 30kg * (2/3) uk = 0 This is obviously not correct as it states friction is present. I don't know where I'm making a mistake. Presumably my logic is incorrect, not the math itself. I think finding the kinetic energy for the frictionless surface was useless with the approach I'm taking. Could anyone please help me understand what's incorrect? Thanks.