Final answer:
To find the power provided by the motor, the frictional force due to the knife pressing against the grindstone is calculated and then multiplied by the velocity at the grindstone's edge. The result is approximately 80.4 W, so the correct choice is (a) 80 W.
Step-by-step explanation:
To determine the power provided by the motor to maintain the grindstone's constant rotation rate while a knife is pressed against it, one must consider the work done against frictional forces. Given that the knife applies a force of 5.0 N and there is a coefficient of kinetic friction of 0.8 between the grindstone and the knife, we can calculate the frictional force as the product of the normal force and the coefficient of friction.
The frictional force (F) acting at the edge of the grindstone is F = 5.0 N × 0.8 = 4.0 N.
Since power (P) is the product of the tangential force and the velocity (v) at the edge of the grindstone, and velocity can be found by the formula v = 2πr × frequency (f), where r is the radius and f is the frequency in Hz (rev/s), we can find the necessary power to maintain the rotation rate.
The frequency f is 4.0 rev/s, which is equivalent to 4.0 Hz, and the radius r is 0.8 m.
Therefore, v = 2π × 0.8 m × 4.0 s⁻¹ = 20.1 m/s.
Now, power P = F × v = 4.0 N × 20.1 m/s = 80.4 W.
The correct answer is option (a) 80 W, since the calculated power is very close to 80 W; any discrepancies could be attributed to rounding during calculations.