Factors affecting how hard a man has to pull on a pulley

[voyager221]

A question has arisen (not homework) showing two pulley systems and a box being pulled up with a man pulling each. The question asks who has to pull hardest.

On one of them (A) the shafts (supporting the rope) are smaller whilst on the other (B) they are larger. The correct answer is that the man with the larger shafts has to pull harder. Is it due to shaft size?

I ask this because on B which is apparently a harder pull there appears to be a second pulley whereas on A there is only a single pulley. I thought the more pulleys the less effort... http://science.howstuffworks.com/transport/engines-equipment/pulley.htm

 

[haruspex]

Diagrams please.
Btw, the howstuffworks page is a little misleading. It shows some of the ropes inclined to the vertical. This will increase the tension required to lift the weight.

 

[Emilyjoint]

In these simple pulley arrangements the 'trick' is to look at the load...count how many ropes are supporting the load. There is really only one rope so the tension must be the same in every section. The load is divided between the ropes connected to the load.
If there is only 1 rope then the force = load
if there are 2 ropes from the load then the force is 1/2
if there are 3 ropes force = 1/3 and so on.
In the diagrams the angles are exaggerated to show the arrangement. I don't think they are meant to show real angles.
One more thing ! the puleys attached to the ceiling do not affect the size of the force, they only change the direction.

 

[haruspex]

In these simple pulley arrangements the 'trick' is to look at the load...count how many ropes are supporting the load. There is really only one rope so the tension must be the same in every section. The load is divided between the ropes connected to the load.
If there is only 1 rope then the force = load
if there are 2 ropes from the load then the force is 1/2
if there are 3 ropes force = 1/3 and so on.
In the diagrams the angles are exaggerated to show the arrangement. I don't think they are meant to show real angles.
One more thing ! the puleys attached to the ceiling do not affect the size of the force, they only change the direction.

True, but it sounds to me that it might be more complicated here, e.g. two pulleys fixed to a common shaft somewhere, perhaps multiple ropes. That's why I want to see a diagram.
And I still think the howstuffworks diagrams are misleading.

 

[voyager221]

Sorry for the late reply I hope you are still with me on this.

I don't know how to send a diagram it is in a book however I will attempt to describe it.

Pulley A shows a rope with no shaft at the top (however could this be a print error?) and a single rope descending to a shaft below which the rope extends to a parcel which is the object being lifted. The rope then extends sharply upwards to another shaft of identical size and then straight down to the person pulling on the rope.

Pulley B has a small shaft at the top again attached by rope to another shaft at the bottom below which is attached the parcel. This time, however, there are two ropes connecting the top shaft to the bottom one instead of one. A rope then extends upwards to another shaft and then down to the person holding the rope. The lower and upper shafts are bigger than A.

The correct answer is pulley B. Despite the pulley being more supported (I would have thought) by more ropes being attached A is easier to pull according to the answer book...

Hope this helps...

 

[haruspex]

Shame about the diagram because I'm struggling with your terminology.
Wherever you say "pulley" I think you mean a system of pulleys.
Wherever you say "shaft" I think you mean "pulley" (I.e. a wheel on an axle).
Where you say "the rope extends to a parcel", I'm guessing you mean that the rope goes under and around a pulley, and another rope/wire/whatever connects the axle of this pulley to the parcel.
If this is correct so far, in system A the man has to apply a pull of W/2; that puts tension of W/2 all along the rope, which means there are two lots of W/2 pulling up on the load.
In your description of B, you're not making clear the relationships between the rope and the pulleys. Sounds like it might be this:
- The rope starts at the bottom pulley and is attached there to the pulley's axle.
- It then pass over the first top pulley, back down under the bottom pulley, up over a second top pulley, and down to the man.
If that's right, the pull needed is now only W/3. So maybe it's just a mistake in the book. It bothers me that the pulleys are shown larger in B; it suggests I have not reconstructed the diagram correctly.

 

[voyager221]

Hi

Yes I mean a system of pulleys and by shaft I mean a grooved wheel along which cord passes so yes pulley.

I'm guessing you mean that the rope goes under and around a pulley, and another rope/wire/whatever connects the axle of this pulley to the parcel correct

The rope starts at the bottom pulley and is attached there to the pulley's axle.
- It then pass over the first top pulley, back down under the bottom pulley, up over a second top pulley, and down to the man.
correct

Indeed I am wondering if it is a mistake as like you I presumed the more ropes the less pulling force needed (though greater pulling distance) There was another error in the book where the answers made no sense and I discovered they were repeated.

When I say the shaft sizes vary: sorry I mean the grooved wheel size. I am not sure if this is of importance as the diagrams on this book can be pretty poor with the ink faded etc. What I don't understand is on A the rope at the top just ends with nothing to rotate around- am I to imagine some support? The wheels on A are near identical in size whereas on B they are notably larger except the top one which is smaller than either of the two wheels on A. (Two wheels on A and three wheels on B)

The poisition of the mans arms and legs is slightly different as well on A and B but I can't imagine this can have much effect.

The book is 'this is your passbook for mechanical aptitude' by national learning corporation