Final answer:
To find the coefficient of kinetic friction between the block and the ramp, we need to consider the forces acting on the block. The only horizontal force is the force of friction, which can be found using the equation Ff = μk * FN. We can find the normal force using the equation FN = mg * cosθ, and the force applied by the spring using Hooke's Law. Plugging in the given values and solving the equations, we find μk ≈ 0.47.
Step-by-step explanation:
To find the coefficient of kinetic friction between the block and the ramp, we need to consider the forces acting on the block. The only horizontal force is the force of friction. The vertical forces are the weight of the block and the normal force exerted by the ramp. The force of friction can be found using the equation Ff = μk * FN, where μk is the coefficient of kinetic friction and FN is the normal force. The normal force can be found using the equation FN = mg * cosθ, where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the ramp with the horizontal.
Since the block is moving at a constant speed, the force of friction must be equal in magnitude and opposite in direction to the force applied by the spring. The force applied by the spring can be found using Hooke's Law, which states that F = k * Δx, where k is the spring constant and Δx is the change in length of the spring. The coefficient of kinetic friction can be found by rearranging the equation for the force of friction: μk = Ff / FN.
Plugging in the given values, we have m = 4.4 kg, k = 12.4 N/cm * (9 cm) = 111.6 N, Δx = 11.0 cm, θ = arctan(39.2 cm / 78.5 cm), and g = 9.8 m/s². Substituting these values into the equations, we find that FN = mg * cosθ = 4.4 kg * 9.8 m/s² * cos(arctan(39.2 cm / 78.5 cm)), Ff = k * Δx = 111.6 N * (11.0 cm / 100 cm), and μk = Ff / FN. Solving these equations gives us μk ≈ 0.47.