Final answer:
The coefficient of kinetic friction (μ) between block 1 and the inclined plane can be calculated using the tangent of the angle of the inclined plane, which is tan(22.0°) ≈ 0.404, because the system is moving at a constant velocity.
Step-by-step explanation:
To calculate the coefficient of friction (μ) between block 1 and the inclined plane, we can use the fact that the system is moving at a constant velocity. The force of gravity along the plane is m1g sin(θ), and the force of friction, which opposes it, must be equal to this force because the velocity is constant. The force of friction is μN, where N is the normal force. The normal force for block 1 on an incline is m1g cos(θ).
The formula for the force of friction is:
μ = frictional force / normal force
Given the angle θ = 22.0°, the mass m1 = 5.50 kg, and since the block is moving at constant velocity, the frictional force equals the component of gravity along the slope:
μ = (m1g sin(θ)) / (m1g cos(θ))
μ = tan(θ)
Therefore, the coefficient of kinetic friction for block 1 is equal to the tangent of the angle of the inclined plane.
μ = tan(22.0°) ≈ 0.404