A potter's wheel—a thick stone disk with a radius of 0.420m and a mass of 120kg—is freely rotating at 53.0rev/min. The potter can stop the wheel in 5.50s by pressing a wet rag against the rim and exerting a radially inward force of 79.4N. Calculate the effective coefficient of kinetic friction between the wheel and the rag.
To calculate the effective coefficient of kinetic friction between the wheel and the rag, we need to first find the initial angular velocity of the wheel, and then use the work-energy principle to determine the frictional force acting on the wheel.
Let me break down the steps to get the answer:
Step 1: Convert the given angular velocity from revolutions per minute to radians per second.
To do this, we'll use the fact that 1 revolution is equal to 2π radians.
Angular velocity (ω) = (53.0 rev/min) × (2π rad/rev) × (1 min/60 s)
Step 2: Calculate the initial rotational kinetic energy of the wheel.
The formula for rotational kinetic energy is given as:
Rotational kinetic energy (KE) = (1/2) × moment of inertia × (angular velocity)^2
The moment of inertia (I) for a solid disk rotating about its central axis is given as:
Moment of inertia (I) = (1/2) × mass × radius^2
Step 3: Calculate the work done by the frictional force.
The work done by the frictional force (W) is equal to the initial rotational kinetic energy of the wheel.
Work done by friction (W) = Rotational kinetic energy (KE)
Step 4: Substitute the known values into the equations and solve for the effective coefficient of kinetic friction.
Frictional force (F) = Work done by friction (W) / Distance (d)
The distance (d) is equal to the circumference of the wheel, which is given as:
Circumference (C) = 2π × radius
Coefficient of kinetic friction (μ) = Frictional force (F) / (Normal force (N) × radius)
Normal force (N) = mass × acceleration (a)
Acceleration (a) = initial angular velocity (ω)^2 × radius
Now, let's calculate the effective coefficient of kinetic friction using these steps and the given values.