Why Does a Rope Bend? Understanding the Tension and Forces at Play

[Frigus]

Suppose a rope is placed horizontally on a table and rope is perfectly ideal and I pulled the rope from one side in upward direction as rope is ideal so tension should be same, so the particle I pulled should have exerted equal force(due to tension)to the particle which is adjacent to it and this will going on in whole rope and if I am true (probably I am wrong somewhere as this doesn't happens) all particles should be pulled to same level as the particle I pulled.

 

[Mister T]

Saying that the particles are each exposed to the same force does not imply that the particles will all have the same displacement.

 

[Frigus]

Saying that the particles are each exposed to the same force does not imply that the particles will all have the same displacement.

Particles are not fastened to the table top.

Sir can you please give me the reason of the 1st line you have told and I also want to clarify one thing, I was talking about this to someone and he told me that tension in rope is produced only along the longitudinal Axis of rope is this case right.

 

[russ_watters]

Suppose a rope is placed horizontally on a table and rope is perfectly ideal and I pulled the rope from one side in upward direction as rope is ideal so tension should be same, so the particle I pulled should have exerted equal force(due to tension)to the particle which is adjacent to it and this will going on in whole rope and if I am true (probably I am wrong somewhere as this doesn't happens) all particles should be pulled to same level as the particle I pulled.

You are ignoring the other force: gravity.

 

[A.T.]

all particles should be pulled to same level as the particle I pulled.

Do you know this toy? It can do both, behave like rope or like you describe, depending on how you hold it.

 

[davenn]

You are ignoring the other force: gravity.

Exactly :)

 

[Frigus]

You are ignoring the other force: gravity.

Sir but isn't force of gravity same for all particles

 

[russ_watters]

Sir but isn't force of gravity same for all particles

All particles of the same mass, yes. But your applied pulling force isn't; it is applied to one end. If you're modeling the rope as a collection of connected particles, then one particle has a gravity force pulling down, an applied pulling force pulling up and a tension force pulling toward the rest of the rope. All the rest of the particles have only the gravity and tension forces. Clearly, when the rope is sitting on the table, if the applied force is greater than the weight of the last particle (and the tension is parallel to the table), the rope has to lift off the table.

 

[Frigus]

Do you know this toy? It can do both, behave like rope or like you describe, depending on how you hold it.

View attachment 253979

No sir I am not familiar with this.
Can you please give me some information fof this toy.

 

[russ_watters]

No sir I am not familiar with this.
Can you please give me some information fof this toy.

It was one I enjoyed as a kid. It's a snake, with single-axis joints between segments. So unlike a rope, it can sustain a force perpendicular to the rope -- but only on that axis. So when you hold it upright, it stands out horizontally, but when you rotate it 90 degrees, it falls down. Or to put it another way, if you hold it one way it is a rod and if you hold it another way it is a rope. But the reality is a rope and a rod differ only in degree of flexibility.

I think this may be your issue, from the OP:

...rope is perfectly ideal...

The example you are asking about is a specific non-ideal behavior of the rope, so it cannot be modeled using a "perfectly ideal" assumption. In a perfectly ideal rope, you cannot apply a force perpendicular to the rope, which is exactly what you are trying to do:

I pulled the rope from one side in upward direction...

Your constraint contradicts your description of what you are doing to the rope.

 

[A.T.]

No sir I am not familiar with this.
Can you please give me some information fof this toy.

It's very simple, and the picture pretty much says it all. Russ wrote more above.

The key is: To lift all segments at the same level by holding one end, the joints have to transmit not only a force, but also a torque. In the case of the toy snake they can only do it on one axis. In the case of the rope on neither axis.

 

[Frigus]

It's very simple, and the picture pretty much says it all. Russ wrote more above.

The key is: To lift all segments at the same level by holding one end, the joints have to transmit not only a force, but also a torque. In the case of the toy snake they can only do it on one axis. In the case of the rope on neither axis.

Thanks sir I got the point

 

[Mister T]

Sir can you please give me the reason of the 1st line you have told

In your original post you made the claim that all of the particles are exposed to the same force and should therefore have the same displacement. It is simply not true that when exposed to the same forces the particles will undergo the same displacement.

 

[Frigus]

In your original post you made the claim that all of the particles are exposed to the same force and should therefore have the same displacement. It is simply not true that when exposed to the same forces the particles will undergo the same displacement.

Sir I got answer"the bending is due to torque"

 

[sophiecentaur]

Suppose a rope is placed horizontally on a table and rope is perfectly ideal and I pulled the rope from one side in upward direction as rope is ideal so tension should be same, so the particle I pulled should have exerted equal force(due to tension)to the particle which is adjacent to it and this will going on in whole rope and if I am true (probably I am wrong somewhere as this doesn't happens) all particles should be pulled to same level as the particle I pulled.

There will always be some delay between the forces that you apply to one end of the rope and the displacement further along the rope. The result will always be a form of Wave Motion. For wave motion to occur, all you need is a changing force (alternating or single displacement), some distributed mass and a coupling force between the elements of the rope. The simplest model to deal with would be with the rope being moved sideways, from position A to position B and then stopped on a very slippery table, in which case, the wave would propagate along the rope and the whole rope would end up displaced .
In the case of your experiment, there is a restoring force pulling the rope downwards to the table and that will damp the motion. Any wave motion would be damped because gravity would tend to restore the rope's shape; once any part of the rope hits the table, the energy is lost. Final situation would be a length of rope hanging down to the table and the rope laying flat out to its end. This is much harder to analyse.

 

[sophiecentaur]

Sir I got answer"the bending is due to torque"

If the rope is ideally (i.e. very) flexible then there will be no torque; all forces will be longitudinal.

 

[jbriggs444]

If the rope is ideally (i.e. very) flexible then there will be no torque; all forces will be longitudinal.

Depends on where you choose the reference axis. It is, of course, perfectly possible to impart a rotation to a rope by pulling on one end. Kids do it on the playground all the time.

 

[sophiecentaur]

Depends on where you choose the reference axis. It is, of course, perfectly possible to impart a rotation to a rope by pulling on one end. Kids do it on the playground all the time.

I was thinking in terms of the Catenary curve of a chain, hung between two fixings. There is no torque there and neither would there be in a wave, set up. Of course, I refer to the local torque, rather than the torque between the ends etc..

 

[Frigus]

There will always be some delay between the forces that you apply to one end of the rope and the displacement further along the rope. The result will always be a form of Wave Motion. For wave motion to occur, all you need is a changing force (alternating or single displacement), some distributed mass and a coupling force between the elements of the rope. The simplest model to deal with would be with the rope being moved sideways, from position A to position B and then stopped on a very slippery table, in which case, the wave would propagate along the rope and the whole rope would end up displaced .
In the case of your experiment, there is a restoring force pulling the rope downwards to the table and that will damp the motion. Any wave motion would be damped because gravity would tend to restore the rope's shape; once any part of the rope hits the table, the energy is lost. Final situation would be a length of rope hanging down to the table and the rope laying flat out to its end. This is much harder to analyse.

Got it!
Thanks

 

[Frigus]

It was one I enjoyed as a kid. It's a snake, with single-axis joints between segments. So unlike a rope, it can sustain a force perpendicular to the rope -- but only on that axis. So when you hold it upright, it stands out horizontally, but when you rotate it 90 degrees, it falls down. Or to put it another way, if you hold it one way it is a rod and if you hold it another way it is a rope. But the reality is a rope and a rod differ only in degree of flexibility.

I think this may be your issue, from the OP:

The example you are asking about is a specific non-ideal behavior of the rope, so it cannot be modeled using a "perfectly ideal" assumption. In a perfectly ideal rope, you cannot apply a force perpendicular to the rope, which is exactly what you are trying to do:

Your constraint contradicts your description of what you are doing to the rope.

Thanks sir your post helped me a lot.