Reeving a Tackle to Advantage -- What am I Missing?

[Dockhead]

Originally Posted by Seaworthy Lass

Same diagrams as in Dockhead's first post have been drawn below, showing the purchase more clearly:

Makes no sense to me whatsoever. In both cases, if you pull the rope one meter, the two anchor points will approach each other exactly the same distance. Therefore, the force will be the same.

The fact that we designate one as "fixed" and one as "moving" is meaningless. The relative motion is the only thing which matters. There is something totally wrong with this picture.

[2Hulls]

Originally Posted by Dockhead

Makes no sense to me whatsoever. In both cases, if you pull the rope one meter, the two anchor points will approach each other exactly the same distance. Therefore, the force will be the same.

The fact that we designate one as "fixed" and one as "moving" is meaningless. The relative motion is the only thing which matters. There is something totally wrong with this picture.

Just count the number of lines to and from the movable block. That's the mechanical advantage. With each numerical increase of the MA, you have to pull that much more line to get the movable block to move a given distance. Very simple.

Dave

[Stu Jackson]

Did you not have a chance to read the wikipedia link I provided? It includes a discussion of
Rove to (dis)advantage



which I choose not to retype.

[Seaworthy Lass]

Originally Posted by Dockhead

Makes no sense to me whatsoever. In both cases, if you pull the rope one meter, the two anchor points will approach each other exactly the same distance. Therefore, the force will be the same.

That's just it - they won't!

In the first example moving the rope 1 m moves the two objects 0.5 m closer together.

In the second example moving the rope 1 m moves the two objects 0.33 m closer together.

[Dockhead]

Originally Posted by Seaworthy Lass

That's just it - they won't!

In the first example moving the rope 1 m moves the two objects 0.5 m closer together.

In the second example moving the rope 1 m moves the two objects 0.33 m closer together.

But it cannot be. Erase the words "fixed block" and "moving block". This is irrelevant to the geometry. This can only be a question of geometry; the motion is relative.

The geometry is exactly the same in both drawings.

[2Hulls]

Originally Posted by Dockhead

But it cannot be. Erase the words "fixed block" and "moving block". This is irrelevant to the geometry.

It can be and is and "movable" block is the key. You may have to see it in action in order for it to hit home. Every time you increase the number of lines to the movable block, you increase the length of line you need to pull in order to move the load a given distance. It's like lowering a gear in a transmission.

Dave

[Dockhead]

Originally Posted by 2Hulls

It can be and is and "movable" block is the key. You may have to see it in action in order for it to hit home. Every time you increase the number of lines to the movable block, you increase the length of line you need to pull in order to move the load a given distance. It's like lowering a gear in a transmission.

Dave

I don't know about that, but I just did empirical research. I rigged tackle in my salon according to SWL's drawings and measured the pull. Exactly 2:1 in both cases.

I would suggest trying it in real life, and measuring it.

[Dockhead]

Originally Posted by Seaworthy Lass

That's just it - they won't!

In the first example moving the rope 1 m moves the two objects 0.5 m closer together.

In the second example moving the rope 1 m moves the two objects 0.33 m closer together.

I would suggest rigging it up and trying it in real life. I cannot get this result empirically.

[s/v Jedi]

Gee.

Take a bucket filled with sand to exactly 10kg total.

Tie a rope to it's handle, lift up and note the tension is 10kg.

Now attach a block to the ceiling and reeve the rope through it and pull the bucket up by pulling down the rope. Here it comes: the force required is still 10kg. We have a sheave but it is rove to disadvantage!

Now attach a block to the bucket and reeve the rope that comes down from the ceiling through it and lift the bucket by pulling the rope up. Yay!! only 5kg required to lift it!

You will see that the number of sheaves at the side of the load that needs to move is what counts and the sheaves at the other side are just to get the rope back to the bucket without any advantage, i.e. they are 1:1 turning blocks.

[2Hulls]

Originally Posted by Dockhead

I don't know about that, but I just did empirical research. I rigged tackle in my salon according to SWL's drawings and measured the pull. Exactly 2:1 in both cases.

Well, you did something wrong. This is one of those "truths" that is not subject to opinion. I recommend you rig a real experiment and see for yourself.

Another way to visualize it: count the number of lines to/from the movable block. This is the multiplier over the amount of line you need to pull from the free end to make the load move one unit. With three lines to/from the movable block, you need to pull 3 times more line to move the load. You're applying a third of the force, but over three times the distance. You pull three feet to move the load 1 foot. Accordingly, to pull with a force of 30 pounds, you will need to pull with only 10, neglecting friction losses and the weight of the line if you're lifting vertically.

Dave

[Dockhead]

Originally Posted by 2Hulls

Well, you did something wrong. This is one of those "truths" that is not subject to opinion. I recommend you rig a real experiment and see for yourself.

Another way to visualize it: count the number of lines to/from the movable block. This is the multiplier over the amount of line you need to pull from the free end to make the load move one unit. With three lines to/from the movable block, you need to pull 3 times more line to move the load. You're applying a third of the force, but over three times the distance. You pull three feet to move the load 1 foot. Accordingly, to pull with a force of 30 pounds, you will need to pull with only 10, neglecting friction losses and the weight of the line if you're lifting vertically.

Dave

I'll be glad to be proven wrong -- why don't you try it?

[monte]

Originally Posted by Seaworthy Lass

That's just it - they won't!



In the first example moving the rope 1 m moves the two objects 0.5 m closer together.



In the second example moving the rope 1 m moves the two objects 0.33 m closer together.

Hehe that's backwardsaassways as well, where does the magic rope go? Pull 1m and the 2 lines in between the blocks in both your drawings shorten by .5 m each, bringing the objects .5m closer together. If the objects just move 33.3333 cm, where's the rest of the line? In the hat with the wabbit?

[Dockhead]

Originally Posted by s/v Jedi

Gee.

Take a bucket filled with sand to exactly 10kg total.

Tie a rope to it's handle, lift up and note the tension is 10kg.

Now attach a block to the ceiling and reeve the rope through it and pull the bucket up by pulling down the rope. Here it comes: the force required is still 10kg. We have a sheave but it is rove to disadvantage!

Now attach a block to the bucket and reeve the rope that comes down from the ceiling through it and lift the bucket by pulling the rope up. Yay!! only 5kg required to lift it!

You will see that the number of sheaves at the side of the load that needs to move is what counts and the sheaves at the other side are just to get the rope back to the bucket without any advantage, i.e. they are 1:1 turning blocks.

OK, that I believe!

But it's NOT the same as SWL's drawing. In your scenario, the rope is anchored at one end in one case, and not anchored in the other. That obviously changes the geometry.


Which block moves relative to the earth cannot possibly make any difference -- it is all relative motion. It is purely a question of geometry. This is probably confusion with the question of where the rope is anchored, which is a different question.

[Dockhead]

Originally Posted by monte

Hehe that's backwardsaassways as well, where does the magic rope go? Pull 1m and the 2 lines in between the blocks in both your drawings shorten by .5 m each, bringing the objects .5m closer together. If the objects just move 33.3333 cm, where's the east of the line? In the hat with the wabbit?

Monte is right!

And it can be demonstrated empirically in a couple of minutes if you have a couple of blocks lying around.

[2Hulls]

Originally Posted by Dockhead

I'll be glad to be proven wrong -- why don't you try it?

Well, I'm sorry, you are wrong and I don't need to try it again. This is basic physics. It is not a matter of opinion. I don't know what else to say about this point. It may not be intuitive to you until you see it applied. Then you'll say, "Duh!".

Try thinking of it this way: If you pull a line three times the distance to move a load only one times the distance, what is the mechanical advantage? 3, right? So set up a rig and measure the distances. There will not even be any fractions. It'll be all integers - whole numbers.

Dave