Answered

Find the best solutions to your problems with the help of IDNLearn.com. Whether your question is simple or complex, our community is here to provide detailed and trustworthy answers quickly and effectively.

Activity 6: Calculate RPM

Copy this table into your book and calculate the RPM speeds for each gear system:

\begin{tabular}{|l|l|l|l|l|l|}
\hline
Input (effort) & Output (load) & Input RPM & Ratio & Output RPM \\
\hline
25 & 75 & 120 & & \\
\hline
20 & 120 & 120 & & \\
\hline
80 & 20 & 200 & & \\
\hline
40 & 200 & 150 & & \\
\hline
75 & 25 & 180 & & \\
\hline
\end{tabular}

Bevel gears are sometimes known as crown and pinion gears. The two gears intermesh at an angle and so change the direction of rotation.

Sagot :

GinnyAnsweridn
Let's go through the table and calculate the required ratios and output RPM for each gear system:

### Table Details:

1. Input (effort): The force or torque applied to the input gear.
2. Output (load): The force or torque exerted by the output gear.
3. Input RPM: The rotational speed of the input gear.
4. Ratio: The ratio of the output load to the input effort.
5. Output RPM: The resulting rotational speed of the output gear.

### Step-by-Step Calculations:

#### For Gear System 1:
- Input (effort): 25
- Output (load): 75
- Input RPM: 120

Ratio:
[tex]\[ \text{Ratio} = \frac{\text{Output (load)}}{\text{Input (effort)}} = \frac{75}{25} = 3.0 \][/tex]

Output RPM:
[tex]\[ \text{Output RPM} = \frac{\text{Input RPM}}{\text{Ratio}} = \frac{120}{3.0} = 40.0 \][/tex]

#### For Gear System 2:
- Input (effort): 20
- Output (load): 120
- Input RPM: 120

Ratio:
[tex]\[ \text{Ratio} = \frac{\text{Output (load)}}{\text{Input (effort)}} = \frac{120}{20} = 6.0 \][/tex]

Output RPM:
[tex]\[ \text{Output RPM} = \frac{\text{Input RPM}}{\text{Ratio}} = \frac{120}{6.0} = 20.0 \][/tex]

#### For Gear System 3:
- Input (effort): 80
- Output (load): 20
- Input RPM: 200

Ratio:
[tex]\[ \text{Ratio} = \frac{\text{Output (load)}}{\text{Input (effort)}} = \frac{20}{80} = 0.25 \][/tex]

Output RPM:
[tex]\[ \text{Output RPM} = \frac{\text{Input RPM}}{\text{Ratio}} = \frac{200}{0.25} = 800.0 \][/tex]

#### For Gear System 4:
- Input (effort): 40
- Output (load): 200
- Input RPM: 150

Ratio:
[tex]\[ \text{Ratio} = \frac{\text{Output (load)}}{\text{Input (effort)}} = \frac{200}{40} = 5.0 \][/tex]

Output RPM:
[tex]\[ \text{Output RPM} = \frac{\text{Input RPM}}{\text{Ratio}} = \frac{150}{5.0} = 30.0 \][/tex]

#### For Gear System 5:
- Input (effort): 75
- Output (load): 25
- Input RPM: 180

Ratio:
[tex]\[ \text{Ratio} = \frac{\text{Output (load)}}{\text{Input (effort)}} = \frac{25}{75} = 0.333 \][/tex]

Output RPM:
[tex]\[ \text{Output RPM} = \frac{\text{Input RPM}}{\text{Ratio}} = \frac{180}{0.333} \approx 540.0 \][/tex]

### Completed Table:
[tex]\[ \begin{array}{|c|c|c|c|c|} \hline \text{Input (effort)} & \text{Output (load)} & \text{Input RPM} & \text{Ratio} & \text{Output RPM} \\ \hline 25 & 75 & 120 & 3.0 & 40.0 \\ \hline 20 & 120 & 120 & 6.0 & 20.0 \\ \hline 80 & 20 & 200 & 0.25 & 800.0 \\ \hline 40 & 200 & 150 & 5.0 & 30.0 \\ \hline 75 & 25 & 180 & 0.333 & 540.0 \\ \hline \end{array} \][/tex]

This table includes the calculated ratios and output RPMs for each gear system.
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Thank you for choosing IDNLearn.com for your queries. We’re here to provide accurate answers, so visit us again soon.