# Tension on the string.

Discussion in 'Physics & Math' started by ash64449, May 22, 2013.

1. ### ash64449Registered Senior Member

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790
Hello friends,

I have heard that when we suspend a body of mass m with the help of a string, there happens to be another force called tension applied by the string upwards.

Why is there tension in the first place? Does it depend on gravitational force?(weight of the body?).

Does Tension arise due to the weight of the body and if there was no weight for the object,will there be any tension?

It is possible for you people to help me understand the concept of tension by giving some similar example but too different? i mean Tension in the form of another way?

2. ### hansdaValued Senior Member

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1,641
This wiki article on tension, explains well.

3. ### ash64449Registered Senior Member

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790
No.it doesn't explain satisfactorily.

It describes what tension is but doesn't say how that Tension happens..

4. ### TachBannedBanned

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The atoms (or molecules) in a material are held together by the electromagnetic force. This force keeps the atoms (molecules) tightly packed for certain materials (like metal, carbon fiber) or not at all (like gas) or in - between (like liquids). When you apply external force, the em force resists it (as in the case of metals) , up to a certain point, where the external force overcomes the em force and the material breaks.

5. ### RJBeeryNatural PhilosopherValued Senior Member

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Jeez Tach, a straight-forward answer with no flippant remarks about the ignorance of the OP and no demands for gratitude? I'm sincerely impressed.

6. ### TachBannedBanned

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5,265
The answer depends on the character and the attitude of the person asking the question. I even gave you a few answers without commenting.

7. ### RJBeeryNatural PhilosopherValued Senior Member

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I noticed that as well, thought it was an oversight. But this is starting to look like an actual pattern of behavior. :thumbsup:

8. ### AlphaNumericFully ionizedModerator

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Tach has explained the physical origin of the tension force, its electromagnetic in origin. The compression or extension of a spring is due to the same thing, except springs can be compressed to give a force, unlike a string. An inelastic string will not stretch at all, while an elastic one will stretch when you put it under tension until the tension cancels out the force on the ends, ie like the gravitational force from an object suspended from the end of the string.

There can be tension in a string without a mass on it, though very little. The string has to hold up its own weight, ie if you suspend a string from the corner of a table then the string's weight has to be held up by the table corner, so the top bit of the string has some tension in it due to the string below it. At the midpoint of the string it'll only have enough tension to hold up half the string, ie the string below that point. If the string is elastic this means it'll be slightly longer than its length when you lie it all on a table. Similarly if you hold the two ends in separate hands and pull your hands apart to a distance equal to the length of the string then it'll stretch slightly, bowing downwards, because gravity it still working on it, though it'll only be a little. Often things are simplified in school examples by saying the string is massless. The result is that the tension is the same throughout, as there's no gravitational pull due to the string mass to counter.

The value of the tension is determined by the forces necessary to keep the system steady. A mass hanging from a string, like a pendulum, will induce a tension in the string such that the string's upwards pulling tension on the mass cancels out gravity. So in the case of a massless inelastic string the tension due to a mass M hung from one end will be T=-mg. The minus sign is because it pulls the opposite way to gravity.

If the string can stretch then it will do so until the forces cancel. Strings and springs are often simplified in their behaviour by assuming Hooke's law. Suppose you've got a string of natural length L. If you stretch it by some amount x you'll feel a tension. Hooke's law says if you stretch it another length x you'll feel twice the tension. In other words the tension T is proportional to the amount stretched, x, giving $T = -kx$. Minus because it pulls in the opposite direction to the stretch and k is just the proportionality constant. Therefore if you hang a mass M from the end of such a string it'll stretch until the tension T cancels the weight W, ie T+W = 0, ie the resultant force is zero. We know T=-kx and we know W = Mg and so kx = Mg so $x = \frac{Mg}{k}$. Twice the mass will cause twice the stretch. Twice the gravity will cause twice the stretch. Double the string constant k and you'll halve the stretch.

Springs are exactly the same except you can allow for negative x, ie you compress it. Strings just go limp when you do that.

9. ### Aqueous Idflat Earth skepticValued Senior Member

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Consider a stringed instrument, such as a guitar, a violin, or even a piano. There is a tensioner (tuning machine, tuning peg, etc.) which increases or decreases the force applied in pulling the string away from its anchor at the far end. In a string the tension is proportional to the square of the frequency (pitch) so proper tension is necessary to be "in tune".

Another example along these lines is a rubber band. When you stretch a rubber band you are applying a force which places the rubber band in tension.

Besides the basic electromagnetic interactions explained above, materials will display a tendency to either stretch or break depending on their molecular geometry. Stiff materials may have a crystal shaped molecular structure, in which the electromagnetic force between crystals may fail along, say, a plane, on account of the regular repeating structure of a particular material's crystal structure. This is how metals tend to fail due to excess tension. On the other hand, something elastic, like rubber, is composed of molecules that are curled up and able to "uncurl" under the influence of tensile forces, stretching to a degree before they tear.

Human muscle tissue works like countless ratchets, something like a molecular winch (except it's a linear arrangement, not rotary). A better analogy is a turnbuckle. Upon the application of a chemical signal from the nerve that actuates a given bundle of fiber, the "ratchet" molecule - which is like an arm with a head joining the opposing fiber - will change the bond angle of the head (by gaining a phosphorus atom in the process during signaling from the nerve), drawing the two fibers closer to together, shortening their overall length. Of course this goes on in a chain millions of "molecular ratchets" long, so even though the distance in motion of the head is extremely small, there are so many of these in series that a muscle is able to contract in what amounts to a substantial fraction of its overall length. Here's an illustration, which speaks to the molecular biology, but depends entirely on the laws of physics to bring the fibers into tension. This is a rather unusual example of chemical energy being converted to mechanical energy, but one which living organisms have exploited well for billions of years.

When we speak of tension, compression or shear, we are talking about the distribution of force over the extensive network of molecules that comprise a material. It's the direction of the force - in opposite directions at each end of the material - that gives rise to the name tension. If the forces are directed toward each other, we call it compression. If the forces are in opposing directions laterally (sideways) from the longitudinal axis (as when chopping a blade of grass with a mower blade) then we call it shear. When used in this sense - acting on the particles of a material - we call them stress, as in shear stress or tensile stress - because we are concerning ourselves with the internal strength of the material, as in reliability testing of an aircraft wing.

But in the branch of physics we call Statics (as opposed to Dynamics) we call them force because we are concerned with the free body diagram which treats the object being subjected to force as an integrated body, and we want to solve the overall problem of force distribution at the interface between the free body and whatever apparatus produces the force. Thus, tension in a spring can be treated at the higher (system) level, without concerning ourselves with molecular interactions. In this case, we notice that the spring tension (force) or compression (force) is proportional to the distance that the spring has been stretched or compressed, and we see this without having to analyze the intermolecular forces that cause the spring to behave this way.

As you see it's partly language, partly the conventions used by scientists - and most importantly, the physical interpretation - which gives rise to this terminology.

10. ### ash64449Registered Senior Member

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790
In the case of Gravitation,it must be weight.($mg$) Right?

Then consider two masses $m_1$ and $m_2$ but mass of $m_1>m_2$. i tie both these masses with the help of two separate strings.

Then shouldn't the tensions developed in the strings different from $m_1$'s and $m_2$'s?

But i found that They are same... When my teacher derived the expressions of tensions in horizontally connected systems.

What is the reason?

11. ### AlphaNumericFully ionizedModerator

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It isn't clear what setup you're describing. If you suspect two masses from a table, each on a different string, then you'll get different tensions, $T = m_{1}g$ for one and $T = m_{2}g$ for the other. If you suspended the first mass from the table and then suspended the second mass from the first mass then you'll find that the tension in the string connected to the table is $T = (m_{1}+m_{2})g$, as the string has to counter the weight of both masses, while the tension in the second string, joining the two masses, will be $T = m_{2}g$ as it only have to hold up one mass.

12. ### Write4UValued Senior Member

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I think there are several types of tension.
There can be polarity tension, gravitational tension, electromagnetic tension.
Physical tension can be present 'up, down, sideways.

Stretch an elastic band and you will feel the tension increase as you pull. The next question is what are the properties of elastic for it to be able to stretch so easily? Stretching something is really a curious thing. What makes it want to return to its original shape (state)?

13. ### arfa branecall me arfValued Senior Member

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3,747
Then you must have made a mistake. Consider a spring that you attach the different masses to. Does the spring extend further with a larger mass? It should, you would think.
So the tension in the spring or string will be higher for a larger mass (in fact the tension is equal to mg at equilibrium), since the elasticity of strings or springs is constant (for small displacements).

14. ### eramSciengineerValued Senior Member

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Not sure what you mean. A diagram will be extremely helpful.

15. ### eramSciengineerValued Senior Member

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Lol. The question is pretty damn straightforward so even Tach couldn't say much.

Though I might add that the inter molecular forces may not be entirely electromagnetic in origin. Like Pauli repulsion.