Question

sprockets practice problems
pulleys and belts
in a pulley system, pulley a is moving at 1500 rpm and has a diameter of 15 in. three pulleys, b, c, and d, all of different sizes, are attached to a single output axle. speed and torque output are changed within the system by moving the drive belt between pulleys b, c, and d.

1. sketch and annotate the drive train described above.
2. a speed of 1750 rpm is required when the drive belt is connected to pulley b. what is the diameter of pulley b?
3. a speed of 2000 rpm is required when the drive belt is connected to pulley c. what is the diameter of pulley c?

Explanation:

Step1: Write the formula for pulley speed - diameter relationship

The relationship between pulley diameters (\(d\)) and rotational speeds (\(n\)) is given by \(d_1n_1=d_2n_2\). Here, \(d_1 = 15\) in, \(n_1=1500\) rpm, and \(n_2 = 2000\) rpm. We need to find \(d_2\) (diameter of pulley \(C\)).

Step2: Substitute the values into the formula

Substitute the values into \(d_1n_1=d_2n_2\). So, \(15\times1500=d_2\times2000\).

Step3: Solve for \(d_2\)

First, calculate \(15\times1500 = 22500\). Then, \(d_2=\frac{22500}{2000}\). Simplifying \(\frac{22500}{2000}=\frac{225}{20}= 11.25\) in.

Answer:

The diameter of pulley \(C\) is \(11.25\) in.