# B Actual meaning of tension

#### donaldparida

I was having a lot of trouble understanding tension force in a string. So i decided to write a sort of essay on it. Here it is:
Tension/Tension Force

1.Tension/Tension force is the electromagnetic internal force transmitted through a rope, string, cable or a wire, when pulled taut by external forces.

2. It actually refers to an action and reaction pair of force, the action force being responsible for maintaining equilibrium of the string(actually the particles) and the reaction one being responsible for transmitting the force to the other end of the string.

3. Strictly speaking tension has no general direction but for a particular object a direction may be assigned. It is directed along the rope.

4.For different objects in a system, the direction of tension is different. To find the direction of tension for an object we draw the FBD of the body and then find the tension force for the body (the force among the two forces which acts on the body).

5.Strings, cables, ropes, etc. all consist of atoms. The distance between two atoms is called the interatomic distance. For a particular value of interatomic distance there exists no force between one atom and the adjacent atom. When the I.D. is greater than this value, there exist attractive forces between the two atoms (action force by the 2nd last atom on the last atom to bring it back to its initial position and reaction force exerted by the last atom on the 2nd last atom to transmit the force).

6.Thus the force applied at one end of the rope gets transmitted from one end of the rope to the other end of the rope without the rope breaking.

|<-.-> <-.-> <-.-> <-.-> <-.->F

(The dots represent the particles making up the string and the arrows represent the forces acting on the particles.

7.When stating the value of tension force for a particular point in a rope, the value of the force except the transmitting force is stated.

8.For simplification of problems, the net force acting on the string is required to be zero. And there should be no loss of energy through friction. Also the string should be rigid and inextensible. Therefore, it is considered massless, inextensible and frictionless.

For a massless rope,

Mass=0

Net Force=mass x acceleration

=>Net Force=0

Also acceleration is taken to be zero though it may have a non-zero value. (It is indeterminate)

The questioning of the acceleration of the string defeats the purpose of making the rope massless.

Tension in a massless rope is same throughout.

For a rope having mass,

Mass ≠ 0

Net Force = mass x acceleration

=>Net Force and acceleration = 0 or Net Force and acceleration ≠ 0

That is the acceleration is zero if net force is zero and the acceleration is non-zero if net force is non-zero.

Tension in a rope having mass is not same throughout. Since the mass of the rope is also pulled.

Rope->Massless->Net force on rope=0

Rope->Has mass->Net force on rope and acceleration may be 0 or may not be 0.

Note : The tension in a string may be due to the application of external opposite forces at the ends of the rope or due to the application of external force at one end of the rope, the other end being attached to an object.

On any segment of rope, the forces acting are the force applied and the tension force.

To find the value of tension we equate two expressions for net force acting on the required segment of the rope.

My question is that is this description of tension force correct?

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#### DrClaude

Mentor
5.Strings, cables, ropes, etc. all consist of atoms. The distance between two atoms is called the interatomic distance. For a particular value of interatomic distance there exists no force between one atom and the adjacent atom. When the I.D. is greater than this value, there exist attractive forces between the two atoms (action force by the 2nd last atom on the last atom to bring it back to its initial position and reaction force exerted by the last atom on the 2nd last atom to transmit the force).
I really don't understand why you bring in atoms. I don't see the point of clouding a completely classical concept with a very quantum object. In addition, the rope is usually considered as incompressible/unstretchable, which doesn't fit with a atomic/molecular picture.

Take the rope to be a classical, solid, flexible object.

#### donaldparida

I brought in atoms for sake of understanding what is actually happening at the atomic level.

• robphy

#### Dale

Mentor
I would drop all of the stuff about atoms and electromagnetism. If you are having trouble understanding tension in a rope then there is no way that electromagnetism or quantum mechanics will actually help.

The designation of a force as action or reaction is completely arbitrary. Your designation is fine as long as you understand that it isn't physically meaningful.

I usually think of tension as the forces on either end of a small segment of rope, so they would not be a third law pair

#### robphy

Homework Helper
Gold Member
In trying to understand forces, it is important to be able to identify the source of the force and the target of the force.
The "electric force on q1 due to q2" is better than the "electric force between the charges".
I think talking about "tension force in a string" is akin to "electric force between the charges".

Note that in a general-case atwood machine with a massless rope, the string is accelerating (as are the masses connected to its ends).

#### donaldparida

@Dale what is the problem in explaining tension using atoms and how does bringing them in(atoms and electromagnetic forces) be related to quantum mechanics? If we cannot use atoms for explaining tension then how are we supposed to explain what happens at the microscopic level,i.e., (what actually causes tension)?

#### Dale

Mentor
@Dale what is the problem in explaining tension using atoms
It is like trying to explain addition by using differential equations. Your explanation is more complicated than the original topic, so it is not a useful explanation. If someone does not understand a simple topic like addition then there is no way that an explanation in terms of a complicated topic like differential equations would help, similarly if someone does not understand a simple topic like tension then there is no way that an explanation in terms of a complicated topic like quantum mechanics will help.

I have a fundamental pedagogical disagreement with using quantum mechanical concepts to explain things that can be understood purely classically.

how does bringing them in(atoms and electromagnetic forces) be related to quantum mechanics?
Atoms are quantum mechanical, they don't exist in classical mechanics which treats an object as a continuum.

If we cannot use atoms for explaining tension then how are we supposed to explain what happens at the microscopic level,i.e., (what actually causes tension)?
Use Newton's laws and Hooke's law. That is all that is needed to explain tension.

• DrClaude

#### donaldparida

@Dale In the physics book by Kleppner and Kolenkow tension is described as an atomic force and described using atoms.

#### Dale

Mentor
Thank you for letting me know. I will avoid their book for any classes I teach.

Staff Emeritus
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