Why Increasing Pully B's Diameter is Incorrect

[syang9]

http://dl.getdropbox.com/u/119319/pully-1.jpg

the book says the answer is C because 'increasing the diameter of the pully decreases the amount of force required to pull rope A'. I don't understand why increasing the diameter of pully B does not have the same effect (i.e., why D is incorrect.)

 

[mgb_phys]

If pulley A and B were the same size the force on the ropes would be the same - the machine wouldn't be doing anything.
So making pulley B larger (ie closer in size to A ) does what to the force?

What would you have to do to pulley B to make the force on A smaller (if you left pulley A the same size)

 

[syang9]

okay, i understand now.. the pulley system works because it reduces the torque that the mass exerts on the center rotation point, and increases the torque that the user (pulling on rope a) exerts on the center rotation point. increasing pulley B diameter would increase the clockwise torque from the mass, so decreasing the size of pulley B (and keeping the size of A constant) would have the same effect as increasing the size of pulley A.

 

[mgb_phys]

Exactly - you can also think of it as just a simple lever on a pivot in the centre.