Final answer:
To determine the effective coefficient of kinetic friction between the wheel and the rag, one must calculate the angular deceleration of the wheel and use it, along with the wheel's moment of inertia, to find the torque caused by the force of the wet rag and thereby the frictional force.
Step-by-step explanation:
The student is asking about the effective coefficient of kinetic friction between a potter's wheel and the wet rag used to stop it. To find this coefficient, we first need to understand the concept of torque caused by friction and its relation to angular deceleration. The potter's wheel has an initial angular velocity which can be calculated from the given 50.0 revolutions per minute (rev/min). The wheel comes to rest in 6.00 seconds due to the force applied by the rag, which allows us to calculate the angular deceleration. The torque (τ) created by the force (F) through the radius (r) can be expressed as τ = Fr. As the torque is due to friction, it also relates to the coefficient of friction (μ) through the equation τ = μ • F • r. By arranging this formula, we can solve for the coefficient of kinetic friction. Knowing the mass (m) and radius (r) of the wheel, the moment of inertia (I) for a disk is I = 1/2 • m • r². Using Newton's second law for rotation, we can relate torque to the moment of inertia and angular acceleration (α), as τ = I • α. Finally, by comparing both expressions for torque, we can calculate the coefficient of friction. It is important to convert the angular velocity to radians per second (rad/s) and to account for the radial distance when applying the force.