Pulley Small or Large for a Motor

[surajzakaas]

A motor can't lift a pale of water for given diameter of pulley. (consider the motor directly connected to the pulley). So, the diameter of the pulley should be Increased or decreased? Why?

 

[tiny-tim]

welcome to pf!

hi surajzakaas! welcome to pf!

tell us what you think, and then we'll comment!

 

[surajzakaas]

i thought the dia. should increase. but a friend said the dia should be reduced as the torque is constant. but i am unable to digest it.

 

[tiny-tim]

hi surajzakaas!

A motor can't lift a pale of water …

… a friend said the dia should be reduced as the torque is constant …

the torque from the motor is constant, but that isn't the same as the torque on the pulley …

it's easier if we say that the maximum tension in the rope is fixed …

what is your opinion then, and why??

 

[surajzakaas]

if max tension is fixed then reducing dia will reduce the torque on pulley and vice versa. and as motor can't lift up the mass the torque given by motor is less. so i guess reducing the pulley dia will work. but how will that work practically i don't know.
still the first solution that comes to my mind is to increase the dia. I don't know why!

 

[tiny-tim]

reading the question again, I'm not sure I've understood it correctly

is the other end of the rope holding the pail attached to the motor,

or is the rope just attached to the pulley, with the motor directly turning the axle of the pulley?

(if it's the latter, my previous comment about the tension in the rope was wrong )

 

[surajzakaas]

the rope is just attached to the pulley, with the motor directly turning the axle of the pulley.

 

[tiny-tim]

ah, so the driving torque τ on the pulley is constant

ok, the force mg needed to lift the pail is the the same as the force from the rope on the pulley

if the initial radius is r, then the inability of the motor to raise the pail can be written as the inequality τ < … ?

and so r needs to be …creased ? ​

 

[surajzakaas]

decreased.

 

[tiny-tim]

yup!