Question

**Can someone please help me solve these problems step by step, thank you!

1. If a 12-inch diameter driving Gear A has 100 tooth which turns CCW with a torque of 200 ft-lb and 100 rpm is meshed with Gear B, 25 tooth, turn along with Gear C, 50 tooth as they are a compound gear and Gear D, 150 tooth meshed with C.

-->sketch and annotate the gear train.

-->what direction does gear ratio B, C, and D turn?

-->what is the gear ratio for B, C, and D?

-->what is the angular velocity for gears B, C, and D?

-->what is the torque for gears B, C, and D?

-->what is the diameter of gears B, C, and D?


2. In a pulley system, pulley A is moving 1000 rpm and has a diameter of 18inches. There are two pulleys with different sizes, B moving ot 1575 rpm and C moving at 1850 rpm attached on a single axle.

-->sketch and annote the pulley system.

-->what is the diameter of pulley B and pulley C?

Answer 1

The answer is "
`\bold{11.428 \ in \ \ and \ \ 9.729 \ in}`".

Step-by-step explanation:

The second question solution can be defined as follows:

`N_A= 1000 \ rpm\\\\N_B=1575 \ rpm\\\\N_C=1850 \ rpm\\\\D_A= 18 \ in \\\\`

In point 1:

Calculating the value of the linear velocity is the same:

`\to V_A=V_B\\\\\to \pi D_A N_A=\pi D_BN_B\\\\\to D_B= (D_A * N_A)/(N_B)`

`=(18 * 1000)/(1575)\\\\=11.428 \ in \ \ \text{Diameter of pulley B}`

In point 2:

`\to V_A=V_C\\\\\to \pi D_A N_A=\pi D_C N_C\\\\\to D_C=(D_A * N_A)/(N_C)\\\\`

`=(1000 * 18)/(1850)\\\\=9.729 \ in \ \ \text{Diameter of pulley B}`