Final answer:
Using the pulley ratio principle, the RPM of the motor is calculated to be 1360 RPM when the fan's 8" pulley is turning at 850 RPM, and the drive (motor's pulley) is 5".
Step-by-step explanation:
To find the RPM of the motor driving a fan via a pulley system, we can use the principle of pulley ratios. This principle tells us that the product of the diameter of the pulley attached to the motor (Dm) and the RPM of the motor (RPMm) will be equal to the product of the diameter of the pulley attached to the fan (Df) and the RPM of the fan (RPMf).
To solve for the RPM of the motor (RPMm), we can use the formula:
RPMm = (Df * RPMf) / Dm
Given our fan's pulley diameter is 8 inches and turns at 850 RPM, and the motor's pulley is 5 inches, the equation would be:
RPMm = (8" * 850 RPM) / 5"
Calculating this, we get:
RPMm = (6800) / 5
RPMm = 1360 RPM
Therefore, the motor is turning at 1360 RPM.