Question

In a pulley system, pulley A is moving at 1600 rpm and has a diameter of 15 inches. Three pulleys, B, C, and D, all of different sizes, are attached to a simple output axle. Speed and torque are changed within the system by moving the drive belt between pulleys B, C, and D.

A speed of 1800 rpm is required when the drive belt is connected to pulley B. Pulley B has a diameter of _________ inches (rounded to the nearest hundredth).
i) 12.33 inches
ii) 13.33 inches
iii) 14.33 inches
iv) 15.33 inches

A speed of 2000 rpm is required when the drive belt is connected to pulley C. Pulley C has a diameter of __________ inches.
i) 10 inches
ii) 12 inches
iii) 14 inches
iv) 16 inches

Pulley D has a diameter of 9.6 inches. A speed of __________ rpm is required when the drive belt is connected to pulley D.
i) 2400 rpm
ii) 2500 rpm
iii) 2600 rpm
iv) 2700 rpm

Answer 1

The diameter of pulley B is 13.33 inches, pulley C has a diameter of 14 inches, and pulley D has a speed of 2500 rpm.

Step-by-step explanation:

To find the diameter of pulley B, we can use the equation:

Speed(A) * Diameter(A) = Speed(B) * Diameter(B)

Given that Speed(A) = 1600 rpm and Diameter(A) = 15 inches, and Speed(B) = 1800 rpm, we can substitute these values into the equation to solve for Diameter(B). Rearranging the equation, we get:

Diameter(B) = (Speed(A) * Diameter(A)) / Speed(B)

Substituting the known values, we have:

Diameter(B) = (1600 rpm * 15 inches) / 1800 rpm = 13.33 inches

Following the same process, we can find that pulley C has a diameter of 14 inches and pulley D has a speed of 2500 rpm.