What is the Input Torque for a Gearbox with Given Parameters?

[Jayohtwo]

Homework Statement

A gearbox and flywheel are as shown in FIGURE 4. The output shaft rotates in the opposite direction to the input shaft at 5 times its speed. The gearbox has an efficiency of 92%. If the flywheel is solid, has a mass of 50 kg, a diameter of 1.5 m and is to accelerate from rest to 300 revs min –1 in 1 minute:

(a) Calculate the torque required at input T1.

(b) Calculate the magnitude and direction of the torque required to hold the gearbox stationary (holding torque Th ). Show the direction of the holding torque applied to the shaft with the aid of a sketch

Homework Equations

efficiency = P_out/P_in = - ω_out×T_out/ω_in×T_in

T₁ + T₂ + T₃ = 0

The Attempt at a Solution

I've attached my working which includes values calculated for :

Power_out = 115.66 W
Power_in = 125.72 W
T_out = 3.68 Nm
Angular velocity α = 0.5236 rad/s²

The question is asking me for the input torque is it as simple as dividing output Torque by the efficiency ratio or have I missed out on another parameter? I know how to solve part B when I can calculate input Torque. Any assistance would be greatly appreciated thanks.

*I realize there's another thread posted about a year ago with the same question but it was asking for help on a different part which I've not got to yet.

 

[NascentOxygen]

Torque and gear ratio - http://mechanicalmania.blogspot.com.au/2011/07/how-does-gear-ratio-affect-torque.html

 

[Jayohtwo]

Torque and gear ratio - http://mechanicalmania.blogspot.com.au/2011/07/how-does-gear-ratio-affect-torque.html

I re-read the question and realized the answer was staring right back at me after reading your link. Feel a little bit silly but I've got the answer now thanks.