## Mechanical Advantage Question - Ropes

Strictly speaking, nothing can be said about the perfect number of rotations on stick.

It is advisable to have a large number of rotations around the package as not only will this create a friction to precent slipping it will also help decrease the pressure on rope which can cause stress and strain and break it.

However number of rotations on stick will depend upon the value of u, the strength of stick and man, the weight of books etc.
Because we want number of rotations such that the force of static friction is sufficient to prevent small movements but also isn't large enough that if movement takes place
the stick breaks (or the man fails to lift it)

However, in general number of rotations around stick should be as few as possible.

 Quote by Mdanner423 Static, the rope shouldn't be going up and down, but obviously would sway as you walk with it. Here's another way to phrase the question. Let's say you take a fishing pole with a lure on the end, does it take more or less force to lift the lure if you wrap the fishing line around the pole?

As M Quack rightly suggested
If its static wrt stick, it doesnt make a difference how many number of loops are present.

So force would be same.
 What you have calculated very nicely is the force needed to pull the rope off the stick. The question was how "easy" it is to carry the stick and package. Unless this is a rather nasty trick question, the force concerned is the force of gravity on the stick under static conditions. In this (admittedly simplified and restricted) case the force to pull the string off is irrelevant.

 Quote by M Quack You are forgetting your boundary conditions, which are F=0 at the free end of the rope, and F=mg at the end going towards the books, independent of the number of turns. Having more turns just means that you "distribute" the same friction force over more turns and more length of rope. The rope will be wound more loosly (many turns) or more tightly (few turns), which decreases or increases the friction.
 Quote by M Quack What you have calculated very nicely is the force needed to pull the rope off the stick. The question was how "easy" it is to carry the stick and package. Unless this is a rather nasty trick question, the force concerned is the force of gravity on the stick under static conditions. In this (admittedly simplified and restricted) case the force to pull the string off is irrelevant.
Hey,
I coudn't agree more. :-)
You are right but isn't this valid only during static condition.(I agree on whatever you have said uptil now, but only for static conditions.)

When the rope is not static, larger friction acts for more rotations which makes it tougher for man.
 If the package was nailed to the ground, more turns make it more difficult for the guy to get away :-) In a practical situation, I would want the situation to be static, i.e. more turns would be better because the threshold for sliding would be higher. But in a practical situation I would make a knot anyways.
 So in summary... It would be easier to carry with more turns as it would make it more stable, sway less back and forth, and make it harder for the rope to slide off the stick. It takes equal force (N) to lift the books against gravity regardless of the number of turns. Right?!
 Right.

 Quote by Mdanner423 So in summary... It would be easier to carry with more turns as it would make it more stable, sway less back and forth, and make it harder for the rope to slide off the stick. It takes equal force (N) to lift the books against gravity regardless of the number of turns. Right?!
Hey, i still would like to add an additional point as I tend to diagree (a bit)with the answer.(in good spirit,offcourse !:-) )

Suppose you had n turns on your stick at this moment.(in the situation you are talking about like no swaying....etc)

If you decide to Now
make n+1 turns , it would worsen the situation and not improve it .

Because in case any relative motion takes place(and i can guarantee you, practically it will not take place for both 2 or 5 turns but if does 5 turns is a burden rather than relief)

the force applied by us is higher in case of n+1 turns.(and the stick might break rendering the situation even more useless)

In essence having a larger number of turns increases the threshold of static friction thus decreasing probability of motion, but it also adds a factor of huge instability which equation T=T(0)e^u(theta) indicates.

If you take u = 1/2( a very practical value),then two rotations increases the force factor by 530 times, and four by (theta is 8pi)300,000 times.

You can think of how much effect 5 rotations would cause (in fact you can calculate).

Practically even few rotations (like 1 or two for a normal stick and string)will take care of all the factors you are worried about(threshold static friction.....etc) for a significant portion of the journey and adding more turns is hurting your chances rather than improving it
because if a slight amount of relative motion (though unlikely but still) takes place the stick will break or you wont be able to hold it