When is the Mechanical Advantage of a Pulley Greater Than 1?

[Gear300]

For a pulley, when is it that the mechanical advantage is greater than 1 and when is it that it is equal to 1? If a rope was hung over a pulley with unequal weights applied to both ends, the larger weight (77kg) would pull the lesser weight (30kg) upward, and so what would the mechanical advantage there be?

The thing about this question is that if a rope were hung over a pulley and the tension at each point was the same (neglecting the mass of the rope and pulley), then how is it that if both ends of the rope point downward that the mechanical advantage becomes 2 (if there was just that one pulley)? Is the mechanical advantage any different if someone was applying a force to one end of the rope compared to gravity acting alone?

 

[Doc Al]

The mechanical advantage of a pulley has nothing to do with how much force you apply. What does affect mechanical advantage is the presence of friction (friction lowers the mechanical advantage) and whether the pulley is moveable or fixed.

 

[Gear300]

I see, I see. I understand, so it is the friction. Now, let's say that we had a single pulley (disregarding friction), what would be the mechanical advantage of using that one pulley?

 

[Doc Al]

Depends on how you use it. Is it moveable or fixed? For example, if the pulley is fixed to the ceiling, what's its mechanical advantage? (Figure it out by considering how much you have to pull down to lift up a given weight.)

On the other hand, what if you attach the pulley to the weight and tie one end of the rope to the ceiling. How much would you have to pull up to raise the weight in that case?

 

[Gear300]

So it varies based on the condition...I see. Thanks.