Which Pull Causes the Bird Feeder's Cord to Snap: Slow or Sudden?

[azure kitsune]

Homework Statement

A bird feeder of large mass is hung from a tree limb, as the drawing shows. A cord attached to the bottom of the feeder has been left dangling free. A child pulls on the dangling cord. The dangling cord is cut from the same source as the cord attached to the limb. Is the cord between the feeder and the limb more likely to snap with a slow continuous pull or a sudden downward pull?

Homework Equations

Newton's laws of motion?

The Attempt at a Solution

I think it does not matter and here is my reasoning:

The tension of the higher string must be greater than the tension of the lower string. When the child pulls on the lower string, the tensions of both strings should increase by the same amount. Therefore, the top string will always have higher tension and will snap first.

But I just feel that something is wrong about this, because (by problem construction theory ) one case should be the top string breaks and the other should be the bottom string breaks. And when I try to imagine it in my head, it seems like the bottom string will snap first if the pull is sudden.

What is the correct and why?

 

[PhanthomJay]

Problem construction theory(!) and your imagination both give you the correct answer. The upper string breaks first with the slow pull, which you have correctly reasoned and determined, per Newton 1. With the sudden pull, the lower string will break first, and the top string will see little increase in its initial at rest tension. It has to do with the string elongation(stretch) and the impulsive nature of the force applied over a very short time period (Newton 2). I'm hard pressed to give you a better explanation at this time. Think about it.

 

[azure kitsune]

Haha, hooray for problem construction theory!

Thanks for your explanation! I think I understand it a little. A sudden pull on the second string would give it a very large acceleration and therefore a really large force.

But wouldn't the first string experience this sudden pull too? I understand that it will take longer for it to experience it (Does the force have to travel upwards?). Is there a way to calculate the minimum acceleration required to snap the second string instead of the first?

And also, is the following situation similar to the problem? You have an object on a piece of paper. If you pull the paper slowly, then the object moves with the paper, but if you pull suddenly, the object does not move.

 

[PhanthomJay]

Haha, hooray for problem construction theory!

Thanks for your explanation! I think I understand it a little. A sudden pull on the second string would give it a very large acceleration and therefore a really large force.

Actually it's the large force that produces the acceleration of the mass, but if the strings were rigid ('ideal' inextensible strings), you could exert a large force with no acceleration.

But wouldn't the first string experience this sudden pull too? I understand that it will take longer for it to experience it (Does the force have to travel upwards?).

It does take a bit longer to transmit the force to the upper string (force traveling at the speed of sound or thereabouts), but this is not the crux of the matter. Since the force is impulsive, it is applied over a very short period of time (say .01 seconds , for example), and since the mass will accelerate due to the extension of the string (per extension = 1/2at^2), the t is so small that it doesn't have much time to extend, thus it's extension, and the force in the string, will be very small (just whatever extension the weight of the mass puts on it, not much more extension from the the additional force), and the lower string will break before the extension of the upper string is significant enough to break the upper string (force is proportional to extension, per Hooke's law)

Is there a way to calculate the minimum acceleration required to snap the second string instead of the first?

Hmm, I would think that if the force application period were long enough, that is, the force was not impulsive in nature, then there would be a minimum acceleration required, I'm thinking 'g', but Ill have to ponder it a bit. You ask darn good questions!

And also, is the following situation similar to the problem? You have an object on a piece of paper. If you pull the paper slowly, then the object moves with the paper, but if you pull suddenly, the object does not move.

That's a little different. You have a very low friction coefficient between the paper and the table, and between the object and the paper. When you pull slowly, with little force, you don't overcome the available static friction force between object and paper, so that the object moves along with it. When you pull quickly, with a large force, theers not enough friction force available to balance your pull (it excedds mu(N)), so the object stays more or less in place over the short time period.

I can tell from your posts that you will be (are) very good in Physics.

 

[azure kitsune]

Thanks for your help! =) I just started physics this year so I couldn't get some parts of your explanation but hopefully in a few months I will be able to. I think it's time for me to pile questions onto my teacher.

 

[mjHession]

I have recently encountered this same problem in a lecture I am watching from MIT on ITunes U, I am wondering if there is a relationship between the impulse of the pulled string and which string breaks. And if so how do we calculate which string breaks.

 

[titaniumpen]

mjHession, I encountered the same problem also from Lewin's lecture!

I did some googling and got this explanation:

The explanation involves the inertia of the ball. With a quick jerk, the ball has to accelerate, and a considerable force is required to do this if the mass of the ball is large (F = ma). On the other hand, with a slow pull, the acceleration is negligible, and the upper string is supporting the weight of the ball plus the tension in the lower string, causing the upper string to break. From Newton's second law, Tu - Tl = m(g-a) where Tu is the tension in the upper string, Tl is the tension in the lower string, m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s2) and a is the downward acceleration of the ball. Thus the upper string breaks when the downward acceleration of the ball is less than 9.8 m/s2; otherwise the lower string breaks.

http://sprott.physics.wisc.edu/demobook/chapter1.htm

But I still don't understand it. Why are you guys talking about impulse and extension, when supposedly this question only requires knowledge of the three laws of motion?