You have a dumbwaiter in your dining room (cuz you\'re classy as hell). Unfortun

Question

You have a dumbwaiter in your dining room (cuz you're classy as hell). Unfortunately, it can only carry 5lbs of food, which is more than enough for one person, but you're entertaining guests (again, cuz you're classy as hell), so you decide to modify the set up. The original set up had a motor that produced 5ft.lbs of torque attached to wheel with a 1 foot radius, and and elevator's cable wrapped around that wheel. You decide to mesh a 2 foot wheel to the original 1foot wheel, and wrap the elevator cable around this new 2 foot wheel instead. Is this a good design? Why or why not? Explain.

Explanation / Answer

>> As, we know

T = F*r,

where, T = Torque

F = Force

and r = Distane of appliation of force

>> Now, T = 5 ft.lbs and it is fixed, according to motor

>> As, now, First 1 foot wheel is attached with motor, and then cable is wraped around 2 foot wheel

>> So, Due to meshing between both wheels, same torque will be transmitted to 2 foot wheel

>> Now, 5 = F*2

=> F = 2.5 lbs

>> So, our system can only take upto 2.5 lbs, which is less than the earlier

>> So, this is a bad design.

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