Question

sprockets and chains
an industrial overhead door has a chain and sprocket system designed to reduce
the force needed by an operator to open and close the door. the system consists of
two individual systems that are connected through a live axle shaft. to operate the
door, the operator pulls a continuous loop of chain over a fixed 22 tooth sprocket
that is attached to a live axle shaft (system 1). a second 22 tooth sprocket is
attached to the live axle shaft and uses a chain connected to a 48 tooth sprocket
that is attached to a drum that drives the door.

1. sketch and annotate the drive train described above.
2. what is the overall system gear ratio?

formula substitute / solve final answer

Explanation:

Step1: Recall the gear - ratio formula

The gear ratio formula for two sprockets is \(r=\frac{N_2}{N_1}\), where \(N_2\) is the number of teeth on the driven sprocket and \(N_1\) is the number of teeth on the driving sprocket.

Step2: Identify the values of \(N_1\) and \(N_2\)

Here, \(N_1 = 22\) (driving sprocket) and \(N_2=48\) (driven sprocket).

Step3: Substitute the values into the formula

Substitute \(N_1 = 22\) and \(N_2 = 48\) into \(r=\frac{N_2}{N_1}\), we get \(r=\frac{48}{22}\).

Step4: Simplify the fraction

Simplify \(\frac{48}{22}=\frac{24}{11}\approx2.18\)

Answer:

The gear - ratio formula is \(r = \frac{N_2}{N_1}\). Substituting \(N_1 = 22\) and \(N_2 = 48\), we have \(r=\frac{48}{22}=\frac{24}{11}\approx2.18\). So the final answer is \(\frac{24}{11}\) (or approximately \(2.18\)).