Final answer:
To find the coefficient of kinetic friction for an object sliding down an incline at constant speed, set the force of kinetic friction equal to the component of gravitational force parallel to the incline and solve for the coefficient. In this case, the coefficient of kinetic friction is 0.5317.
Step-by-step explanation:
To find the coefficient of kinetic friction for a 5kg object sliding down a 28-degree incline at constant speed, we can use the principle that the net force on the object is zero when its velocity is constant. This means that the force of kinetic friction is equal to the component of gravitational force parallel to the incline's surface.
The gravitational force parallel to the incline is mg sin θ, which acts to pull the object down the incline. The force of kinetic friction, which opposes the motion, is μk mg cos θ. Since the object is moving at a constant speed, these forces must be equal. Therefore, μk mg cos θ = mg sin θ, and we can cancel the mg from both sides because they are common to both forces. This gives us μk = tan θ, where θ is the angle of incline.
Substituting the given values, we have:
μk = tan(28°) = 0.5317
Thus, the coefficient of kinetic friction is 0.5317.