Final answer:
The question involves calculating the power required by a motor to maintain the rotational speed of a grindstone while a knife is sharpened against it. Given the mass, radius, rotational speed, applied force, and friction coefficient, the power can be determined using the work and power formulas.
Step-by-step explanation:
The question is related to the adjustment mechanism of a grindstone and the power required to maintain its rotational motion during a sharpening process. We are given that a grindstone with a mass of 50 kg and radius of 0.8 m is rotating at a constant rate of 4.0 revolutions per second. When a knife is pressed with a force of 5.0 N against the grindstone and given the coefficient of kinetic friction is 0.8, we need to calculate the power provided by the motor to keep the grindstone rotating at the constant rate.
To solve this, we can use the formula for power (P), which is the work done per unit time. The work done by the frictional force is the product of the force, distance (circumference of the grindstone in this case) and the number of revolutions per second. The circumference of the grindstone (C) can be calculated as C = 2πr, where r is the radius of the grindstone. The force due to friction (Ff) is given by Ff = μ × N where μ is the coefficient of friction and N is the normal force (in this case equivalent to the applied force since it is pressed against the grindstone).
Therefore, Ff = 0.8 × 5.0 N = 4.0 N. The work done by the frictional force during one revolution is W = Ff × C, and the power is P = W × rotational speed. Substituting the given values and calculating will give us the power needed to maintain the grindstone's motion while sharpening the knife.