First of all, I have a confusion about the definition and idea of Tension.

For example, in my Physics Textbook, the idea of tension is written like this:

"Let's say there is a wire with a cross-section area of A and its length is $L_o$. If I hang the wire from a point and hang a weight of W on the other end of the wire, it will generate a repulsive force of T. This T is called the Tension Force."

For me, this only explains to me what force will we call tension force, but it doesn't quite explain to me what is exactly this Tension force or where it originates from. Also, I have been doing pulley problems (Figuring out the acceleration of weights hanging from pulleys) by first labeling all of the tension forces by $T_1$, $T_2$, and then doing some math with them to get my answer. But It bugs me that I am using these tension force values without even knowing where they came from or what they are.

My idea was, maybe Tension force comes from the intermolecular bonds between the molecules of the rope, rubber or wire, etc. But even then, I have some different situational questions. For example:

  1. Why you can't push a rope, copper wire against a wall?

  2. What happens when I pull on two ends of a wire with 2 different forces?

  3. Does the force increase proportionally to the applied force? Why does the wire break after a certain amount of force is exceeded.?

  4. Does the idea of tension apply to everyday objects,(for example, a coffee mug, glass pane, etc). If it does, can I use something like a heat map or 3D equation to describe the tension in every point of the object? [Edit: more concisely, is there a mathematical way to show the various amounts of tension forces on a 2D (like a metal sheet) and 3D objects (like a football ) instead of a 1D object(like a string)].

  5. If I take a metallic object like a paperclip or a thin wire. I can bend It multiple times and it eventually breaks into two pieces. I used to do this to pull of capacitors from old circuit boards. But does it happen with things like ropes or paper? If not, why it doesn't happen? ( Maybe it has something to do with intermolecular forces and the various internal stresses?)

  6. Let's say I have an iron bar and I have thrown it out into space. Does that iron bar have equal stress distribution or still uneven or will the stress on all points become zero? (Is there even such thing as zero stress?)

  • $\begingroup$ It is an electromagnetic force $\endgroup$ – Buraian Oct 2 '20 at 12:19
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    $\begingroup$ @Prithu biswas it is not fair to add question by editing a single question after someone answered your previous question. You could ask the same question next time. $\endgroup$ – A student Oct 2 '20 at 18:05
  • $\begingroup$ My apology.It is just that when I only start to understand something , I also want to get deep into the matter.I thought asking the same question on a another post will be weird,so I have been commenting and editing my extra question .Now you said that I can ask the same question on another post ,I will Definitely do just that next time.Hope you accept my apology.By the way,your answer was by far the best answer I have seen :) $\endgroup$ – Prithu biswas Oct 3 '20 at 6:24
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    $\begingroup$ @Prithu biswas I accepted that . No worries. I also had the same confusion a month ago when I was going through the chapters in my book. By the way,your answer was by far the best answer I have seen :) thanks for this . 🙂 $\endgroup$ – A student Oct 3 '20 at 9:20

Tension force like the normal force is just an aspect of the electromagnetic forces acting between molecules.

1 : You can't push something with a rope and if you try to do that the rope will buckle . Why ?

For this to understand , lets take an example of magnets.

When you bring like poles closer and closer , you experience greater and greater repulsive force (because the electron clouds surrounding the nucleus come very close and the coulomb forces increase) . Also you may have noticed that if you bring the like poles of the magnets more closer you get pushed sideways most of the times as shown below because of even a little disturbance in external force's direction.

enter image description here

This is what exactly happening inside a rope. When you try to push the molecules closer , the electron clouds just repel each other with lesser attractive forces from the nucleus and the molecules slip over each other due to a slight change in direction or point of application of the external force and most of the times this slipping buckles the rope from the sides.

2 : When pulled with two different forces the string will accelerate in the direction of net force depending on its mass.

3 : Yes the force increase proportionally with the external force for some extent and if you increase the external force to a greater magnitude , the intermolecular forces couldn't increase accordingly.

You can visualise the internal structure as this

enter image description here

When you try to elongate , the intermolecular forces respond accordingly but you know that even springs get deformed when you apply greater force and exactly in this way , the intermolecular attractions couldn't rise accordingly and things ( for your case , strings) break .

4 : Whatever you see around you either as a solid or as a liquid or gas , they all are under the influence of electromagnetic forces . In case of solids, molecules can be compressed but not by much amount (because they are already very close to each other ) which you can notice ( though you can notice the compression in some special kind of solids) and they can't be easily broken or elongated by stretching because of this electromagnetic force. Liquids can be compressed by a greater amount and gases by the greatest amount.

5 : When you bend paperclips , the atoms are being separated from the point you are bending the clip . How do I know this ?

You might have noticed that by multiple bending , first of all the end becomes dull in colour than other parts of the clip and if you continue doing that , it eventually breaks. The dullness in colour is what suggesting that the atoms are being separated and there are lesser atoms to re - emit photons. When you unfold the clip , the atoms couldn't rearrange in the same earlier pattern and in this way the clip starts weakening. In case of ropes , it doesn't happen because the atoms in the ropes regain their original position and we barely notice any elongation or dullness and this property of regaining the original structure depends on the nature of atoms and the extent of intermolecular forces.

Consider the images below

enter image description here

enter image description here

Note : the image of the intermolecular structure is taken from here. The above two images are highly exaggerated and the atoms are in much close vicinity of each other.

Hope it helps 🙂.

  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$ – ACuriousMind Oct 3 '20 at 9:16
  • $\begingroup$ Re, "if you try to [push on a rope] that the rope will bend." A materials scientist might say that the rope would buckle. $\endgroup$ – Solomon Slow Dec 16 '20 at 18:20

A simplified explanation is as follows. When two molecules are some distance apart, there are some attractive forces between them, which dominate over the repulsive forces. As they keep coming closer, the repulsive forces keep getting stronger until at a critical distance, the forces are balanced.

The string when lying on the ground, is in equilibrium, because the attractive and repulsive forces between its molecules balance each other out. When we pull the string taut, we are actually slightly pulling its molecules apart, thus reducing the repulsive forces, which is why a net inward force is developed in the string. If we keep increasing the force, there will come a point where the repulsive forces are negligible. Now the attractive forces cannot increase any further, and after that point, the string breaks.

If a string is pulled with two different forces, say $10N$ from the left and $2N$ from the right, and its mass is $1kg$, then it will accelerate to the left with $8 m/s$. The tension linearly increases from $2N$ at the left end to $8N$ at the right end.

The molecular structure of strings is such that they can provide tension only in one direction. Everyday solid objects like glass also show tension as well as compression forces.

  • $\begingroup$ thank you for your answer.It seems like I learned about a new concept compression force.You said solid 3d or 2d objects like coffee mugs has this compression force.That is true.But does rope have compression forces? I mean if you push a rope (just assume for now it is attached to a wall),it doesn't even put any force on me and it just bends.Is the compression force too little for me to feel? $\endgroup$ – Prithu biswas Oct 2 '20 at 11:00
  • $\begingroup$ @Prithubiswas You certainly can push things with a rope. Of course depends on the actualy type of rope. But rope is not a kind of matter, it is a structure. Take a block of the rope material or even just a rope in a coil and you will see it certainly does have a compression force. $\endgroup$ – Vladimir F Oct 2 '20 at 17:47

Overall tension is a body reaction force to some stimulating force (weight,pulling,external, etc) and is a specific case of a more general body stress vector field, like :

enter image description here

And yes, tension increases proportionally to the force applied. Materials break when pressure applied to them exceeds/reaches ultimate tensile strength, measured in $\text{Pa}$ :

enter image description here

In above stress–strain graph it's an extreme point (1).

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    $\begingroup$ DId you make that animation? it's awesome $\endgroup$ – Buraian Oct 2 '20 at 13:34
  • $\begingroup$ @Buraian No, just found somewhere in internet. So picture credits should be given to somebody else. $\endgroup$ – Agnius Vasiliauskas Oct 2 '20 at 13:47
  • $\begingroup$ Can there be difference in stress distribution even if no external force is being applied? And can you use any arbitrary force-field F as your input to get a stress vector field? $\endgroup$ – Prithu biswas Oct 2 '20 at 13:47
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    $\begingroup$ @Prithubiswas Depends what you call "external". If own weight of body is internal force for you, then answer is yes. Because objects collapse under own gravity. Due to relative weight in each point, bottom of body will experience highest stress, compared to middle or top of it. Because when you go upwards - less mass is pressing that relative location. Thus body weight itself produces natural stress vector field. $\endgroup$ – Agnius Vasiliauskas Oct 2 '20 at 13:55
  • $\begingroup$ What equation was used to generate that stress vector field ? $\endgroup$ – Prithu biswas Oct 2 '20 at 14:22

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