Final answer:
The coefficient of kinetic friction for the block on the incline is calculated by dividing the frictional force by the normal force. We need the block's mass, angle of incline, and either the acceleration or condition of constant velocity to find the frictional force and subsequently the coefficient of kinetic friction.
Step-by-step explanation:
The student is asking to find the coefficient of kinetic friction for a 4.60-kg block sliding down a rough 30.0° incline. To solve for the coefficient of kinetic friction (μ_k), we need to consider the forces acting on the block in parallel and perpendicular components relative to the incline.
The weight component of the block along the incline is given by mg sin(θ), where m is the mass of the block, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline. The normal force is mg cos(θ). The frictional force is equal to the coefficient of kinetic friction times the normal force (μ_kN), and it opposes the motion of the block down the ramp.
When an object is in motion down an incline and the coefficient of kinetic friction needs to be calculated, one can use the equation frictional force = μ_k × normal force. By rearranging the equation we get μ_k = frictional force / normal force. Knowing the mass of the block and the angle of the incline, along with the acceleration (if constant velocity, then acceleration is zero), one can find the frictional force (μ_k).
For example, if there was an instance where a block of mass m slid down a ramp at a constant velocity, we'd know that the net force is zero because acceleration is zero. Thus, the frictional force would equal the component of the block's weight along the ramp, and μ_k can be calculated accordingly.