Tension is a force, and therefore, a vector. It points towards the point of suspension, which, in the case of the Atwood Machine, happens to be the pulley.
In some cases we hear that tension has no definite direction. How is it so that it is vector, I am a little bit confused is it purelu vector or scalar in some cases and vector in some.
Lets imagine a case where a pendulum bob is suspended by a thin string. As usual, you may draw an arrow upward at the point of oscillation to represent a force balancing the weight of bob. You may say this force as TENSION on the string. Now go upward and add an arrow to represent the force exerted by the string on the point of suspension(pivot). Will you give the direction again upward to represent the TENSION? No! certainly, you will draw a downward arrow. But the question is, if the upward force is tension, what is the downward force at the pivot?
Did you get me? The reason why we add these arrows is to represent the FORCES at the end points which are due to the tension on the string and are now indeed vectors. But the tension?? Its scalar giving only the magnitude of the pulling force.
We are addicted to the calculations done mainly during our Higher Secondary level and Bachelors where we always added an arrow (in free body diagram involving tension) to tension without any reasoning. Have we ever read a proper definition of the word TENSION?
"Tension is the magnitude of pulling force exerted by a stretched string on objects attached on its both ends."
By the way, 'the attached objects on the ends' don't excludes the molecules of the string itself.
I agree with everything Gyanendra Dai said. But I do think that there is a crucial point that was missed in the discussion above. The 'pivot' and the 'bob' are interchangeable (albeit this is a little counter-intuitive because are used to thinking of the pivot as something like a nail hanging on to the wall, and the bob as something that's hanging in the air.) When you are drawing the free body diagram for the 'pivot', wouldn't the center of suspension be the center of mass of the 'bob'? So where is the inconsistency in the statement that tension is always directed towards the center of suspension?
Bijay! I haven't forgotten the fact you pointed. As you said, the pivot and the bob are always interchangeable. But you are misinterpreting something really! The forces you are explaining are the forces acting on the bodies (pivot and ball) but not the TENSION on the string. Some physicist say this force as "TENSION FORCE"(I had never used the term, but now using), and I agree, these are vectors pointing toward the point of suspension (interchangeable), and you are right up to that level. But if you say the tension is directed toward the point of suspension, it will be wrong.
Bijay! You say “TENSION on string” and deal with the “force on the objects”. Doesn’t it sound silly? TENSION measures the amount of elastic energy stored per unit length of extension. (Extension should not be strictly along a straight line). How can you say the "SAME TENSION" on "SAME STRING" (if vector) reverses its direction as we go from one end to another (at least in this case) without any external cause that can change the direction?
As a correction, you can say the direction of the "TENSION FORCE" is along the direction of tangent drawn on the string at that point where we are interested. (Imagine a string rolled over a pulley and find the direction of the tension force on the curved portion, you will see my points.) The TENSION FORCE keeps changing (in direction) as we change the points but the TENSION on the string remains same. Isn’t it? You may say that we are discussing the word meaning of "TENSION" but not physics about it, but don’t think so. Again, I strongly recommend having a look on some books by well known writers.
The conclusion is TENSION is the property of string and is equally distributed over the length (as like liquid pressure in a squeezed balloon, which doesn’t have any fixed direction). And, TENSION, being the magnitude of the force a stretched string exerts on an object attached to it, is a scalar quantity, without any doubt.
Yes, you're right! This clears up everything. my tension = your 'tension force' i should have defined my terms before initiating the conversation.....poor Voltaire must be cringing in his grave
At least, whatever be the reason, we concluded the topic. Although physics deals with fact (in most cases), its perception relies on the explanations one has made.
I said "TENSION FORCE" and you said "TENSION" for same (physical quantity). In perception, both are right and no one does wrong in any calculations involving tension. But 'words' have certain significant meanings and physics can not ignore these.
An interesting example in the above discussion would be, If you and your friend see a stretched power cable over you but not the poles (very far) where the cable is attached, and your friend asks you, what is the direction of tension on the cable?
A vector is identified by its unique direction at a point of consideration (wherever). But in the above example...?? You have two options to answer your friend: 1. Let me reach to the pole and I will show the direction, 2. Tension is scalar quantity and doesn't have direction.
(ha ha ha... I am not forcing, you may choose third option).
Answer: Choose which pole you want to call Bob, and then I'll tell you the direction. I realize the importance of being precise with the choice of words for a meaningful conversation, but IMHO, being too fastidious is no better. It will get us lost in a maze of words and make physicists look as dopey as philosophers. "We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: 'you don't know what you are talking about!'. The second one says: 'what do you mean by talking? What do you mean by you? What do you mean by know?' Richard P Feynman
But your friend had asked the direction of tension in the middle part of the cable which he was watching, not on the either ends.
Bijay! Can you give me some examples of vector field that have directions only in the end points? I am amazed with your response. Why can't you say the direction at a point exactly in between the two poles?
Perhaps I am not so precise in using words that could clear everything. The problem might be in the reasoning I presented and the language I used. Better would be that if I had presented some lines from some book that forces you to believe. After all, we are trained to believe what is written, not on the personal experiences and logic.
"When a rope attached to an object is pulling on the object, the rope exerts a force \vec{T} on the object, and the magnitude \emph{T} of that force is called tension in the rope. Because it is the magnitude of a vector quantity, tension is a scalar quantity."
page 122, Physics for Scientists and Engineers 6th Editioin, -Serway and Jewett.
This is just one of many that you can get when search. just googling about it gives more than we need, but have to filter, which one is the best.
If I had already written this, probably, there wouldn't be the discussion. Just I was trying someone to convince about a fact that we have always ignored. But in this case, I failed, completely lost.
Bijay! We had that discussion long before (1 year ago when Anup has to teach "perhaps simple pendulum") in our college, and after some time, we had visualized Tension as scalar without any written evidence.
I am here again. Proving something just by saying someone's statement seems to work here. Although a statement is right, I don't think that believing someone's statement by force without making a concept is good for physics students. Rather it creates a tendency to search for a book that denies with the previous one.
I don't know whether the example that I am going to present will make the concept clear or not, I think its not very bad, too.
Consider a thin rubber band (say a circular ring of rubber). Fix the band over the rim of a thick circular disc larger in radius than the rubber band by stretching it. As there is neither start or end of the rubber band, we don't have to search for the end points (like pivot and bob in simple pendulum) to stretch the rubber.
Now, who is going to say the direction of the the tension in the stretched circular band of rubber? There is nothing that the rubber can pull along its length except the molecules within it and each molecule is pulled equally in both directions along the length. One possibility is to say that the tension in this case is directed towards the center of the disc as the rubber exerts a compressing force to the disc rim directed towards the center. But a physicist doesn't give this answer certainly.
So tension is something related to the potential energy stored in the stretched material. The magnitude and direction of the force the material exerts depends upon where and in which direction something is attached to it. Although its unit is Newton, its a scalar.
If someone really takes tension as a vector, he is left with only an answer in the above example, that is: "In this case, the rubber band is not in tension." or even a worst one...
if you define tension as the force that acts towards the point of suspension(like i did), then the rubber band is not in tension...surely there is energy stored per unit length of the stretched band....but i would have to call it something else (you'd call it tension)...i admit this is unconventional...but in what way is it bad?....i quoted Feynman because i wanted to make the point that it it more important to understand things than to know their names....to communicate our ideas, however, it is important to declare our definitions and notations first (something that we did not do in this post!)....might be irrelevant but certainly interesting: "If you wish to converse with me, define your terms first!" : Voltaire
I was not saying anything else about Feynmann's quotation Bijay. Rather, I was talking about myself. In the previous comment, I had placed a statement from a book that clearly says tension as a scalar quantity (please read it). What I meant was, proving my side of discussion by giving someone's statement is not good if the main concept is not clear. Thats why I presented the example of rubber band.
I don't say you are wrong. But its hard to follow what you said, too. Physics is not like what Voltire said. Defining everything according to your needs that completely change the meaning what others know doesn't make you unconventional, it leads you in wrong way. The proof is, you said that the rubber band is not in tension. Your response is not unconventional, its wrong, i need to say.
Tension and Tension force are well defined terms with clear meanings. The problem is many of us don't know them. In spite of using them correctly, we want to prove what we say. I see a positive point on Voltire's quotation, if you define something wrong before starting conversation, there will be enough room for the correction.
Any way, the conversation was not so bad. Had a good time here talking with you.
You know what you’re talking about, why waste your intelligence on just posting videos to your blog when you could be giving us something enlightening to read? iosh course in chennai
Tension is a force, and therefore, a vector. It points towards the point of suspension, which, in the case of the Atwood Machine, happens to be the pulley.
ReplyDeleteIn some cases we hear that tension has no definite direction. How is it so that it is vector, I am a little bit confused is it purelu vector or scalar in some cases and vector in some.
DeleteThis comment has been removed by the author.
ReplyDeleteLets imagine a case where a pendulum bob is suspended by a thin string. As usual, you may draw an arrow upward at the point of oscillation to represent a force balancing the weight of bob. You may say this force as TENSION on the string. Now go upward and add an arrow to represent the force exerted by the string on the point of suspension(pivot). Will you give the direction again upward to represent the TENSION? No! certainly, you will draw a downward arrow. But the question is, if the upward force is tension, what is the downward force at the pivot?
ReplyDeleteDid you get me? The reason why we add these arrows is to represent the FORCES at the end points which are due to the tension on the string and are now indeed vectors. But the tension?? Its scalar giving only the magnitude of the pulling force.
We are addicted to the calculations done mainly during our Higher Secondary level and Bachelors where we always added an arrow (in free body diagram involving tension) to tension without any reasoning. Have we ever read a proper definition of the word TENSION?
"Tension is the magnitude of pulling force exerted by a stretched string on objects attached on its both ends."
By the way, 'the attached objects on the ends' don't excludes the molecules of the string itself.
I agree with everything Gyanendra Dai said. But I do think that there is a crucial point that was missed in the discussion above. The 'pivot' and the 'bob' are interchangeable (albeit this is a little counter-intuitive because are used to thinking of the pivot as something like a nail hanging on to the wall, and the bob as something that's hanging in the air.) When you are drawing the free body diagram for the 'pivot', wouldn't the center of suspension be the center of mass of the 'bob'? So where is the inconsistency in the statement that tension is always directed towards the center of suspension?
ReplyDeleteBijay! I haven't forgotten the fact you pointed. As you said, the pivot and the bob are always interchangeable. But you are misinterpreting something really! The forces you are explaining are the forces acting on the bodies (pivot and ball) but not the TENSION on the string. Some physicist say this force as "TENSION FORCE"(I had never used the term, but now using), and I agree, these are vectors pointing toward the point of suspension (interchangeable), and you are right up to that level. But if you say the tension is directed toward the point of suspension, it will be wrong.
ReplyDeleteBijay! You say “TENSION on string” and deal with the “force on the objects”. Doesn’t it sound silly? TENSION measures the amount of elastic energy stored per unit length of extension. (Extension should not be strictly along a straight line). How can you say the "SAME TENSION" on "SAME STRING" (if vector) reverses its direction as we go from one end to another (at least in this case) without any external cause that can change the direction?
As a correction, you can say the direction of the "TENSION FORCE" is along the direction of tangent drawn on the string at that point where we are interested. (Imagine a string rolled over a pulley and find the direction of the tension force on the curved portion, you will see my points.) The TENSION FORCE keeps changing (in direction) as we change the points but the TENSION on the string remains same. Isn’t it? You may say that we are discussing the word meaning of "TENSION" but not physics about it, but don’t think so. Again, I strongly recommend having a look on some books by well known writers.
The conclusion is TENSION is the property of string and is equally distributed over the length (as like liquid pressure in a squeezed balloon, which doesn’t have any fixed direction). And, TENSION, being the magnitude of the force a stretched string exerts on an object attached to it, is a scalar quantity, without any doubt.
Yes, you're right! This clears up everything.
ReplyDeletemy tension = your 'tension force'
i should have defined my terms before initiating the conversation.....poor Voltaire must be cringing in his grave
At least, whatever be the reason, we concluded the topic. Although physics deals with fact (in most cases), its perception relies on the explanations one has made.
ReplyDeleteI said "TENSION FORCE" and you said "TENSION" for same (physical quantity). In perception, both are right and no one does wrong in any calculations involving tension. But 'words' have certain significant meanings and physics can not ignore these.
An interesting example in the above discussion would be, If you and your friend see a stretched power cable over you but not the poles (very far) where the cable is attached, and your friend asks you, what is the direction of tension on the cable?
A vector is identified by its unique direction at a point of consideration (wherever). But in the above example...?? You have two options to answer your friend:
1. Let me reach to the pole and I will show the direction,
2. Tension is scalar quantity and doesn't have direction.
(ha ha ha... I am not forcing, you may choose third option).
Answer: Choose which pole you want to call Bob, and then I'll tell you the direction.
ReplyDeleteI realize the importance of being precise with the choice of words for a meaningful conversation, but IMHO, being too fastidious is no better. It will get us lost in a maze of words and make physicists look as dopey as philosophers.
"We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: 'you don't know what you are talking about!'. The second one says: 'what do you mean by talking? What do you mean by you? What do you mean by know?'
Richard P Feynman
But your friend had asked the direction of tension in the middle part of the cable which he was watching, not on the either ends.
ReplyDeleteBijay! Can you give me some examples of vector field that have directions only in the end points? I am amazed with your response. Why can't you say the direction at a point exactly in between the two poles?
Perhaps I am not so precise in using words that could clear everything. The problem might be in the reasoning I presented and the language I used. Better would be that if I had presented some lines from some book that forces you to believe. After all, we are trained to believe what is written, not on the personal experiences and logic.
"When a rope attached to an object is pulling on the object, the rope exerts a force \vec{T} on the object, and the magnitude \emph{T} of that force is called tension in the rope. Because it is the magnitude of a vector quantity, tension is a scalar quantity."
page 122, Physics for Scientists and Engineers 6th Editioin, -Serway and Jewett.
This is just one of many that you can get when search. just googling about it gives more than we need, but have to filter, which one is the best.
If I had already written this, probably, there wouldn't be the discussion. Just I was trying someone to convince about a fact that we have always ignored. But in this case, I failed, completely lost.
Bijay! We had that discussion long before (1 year ago when Anup has to teach "perhaps simple pendulum") in our college, and after some time, we had visualized Tension as scalar without any written evidence.
This comment has been removed by the author.
ReplyDeleteI am here again. Proving something just by saying someone's statement seems to work here. Although a statement is right, I don't think that believing someone's statement by force without making a concept is good for physics students. Rather it creates a tendency to search for a book that denies with the previous one.
ReplyDeleteI don't know whether the example that I am going to present will make the concept clear or not, I think its not very bad, too.
Consider a thin rubber band (say a circular ring of rubber). Fix the band over the rim of a thick circular disc larger in radius than the rubber band by stretching it. As there is neither start or end of the rubber band, we don't have to search for the end points (like pivot and bob in simple pendulum) to stretch the rubber.
Now, who is going to say the direction of the the tension in the stretched circular band of rubber? There is nothing that the rubber can pull along its length except the molecules within it and each molecule is pulled equally in both directions along the length. One possibility is to say that the tension in this case is directed towards the center of the disc as the rubber exerts a compressing force to the disc rim directed towards the center. But a physicist doesn't give this answer certainly.
So tension is something related to the potential energy stored in the stretched material. The magnitude and direction of the force the material exerts depends upon where and in which direction something is attached to it. Although its unit is Newton, its a scalar.
If someone really takes tension as a vector, he is left with only an answer in the above example, that is: "In this case, the rubber band is not in tension." or even a worst one...
if you define tension as the force that acts towards the point of suspension(like i did), then the rubber band is not in tension...surely there is energy stored per unit length of the stretched band....but i would have to call it something else (you'd call it tension)...i admit this is unconventional...but in what way is it bad?....i quoted Feynman because i wanted to make the point that it it more important to understand things than to know their names....to communicate our ideas, however, it is important to declare our definitions and notations first (something that we did not do in this post!)....might be irrelevant but certainly interesting:
ReplyDelete"If you wish to converse with me, define your terms first!" : Voltaire
This comment has been removed by the author.
ReplyDeleteI was not saying anything else about Feynmann's quotation Bijay. Rather, I was talking about myself. In the previous comment, I had placed a statement from a book that clearly says tension as a scalar quantity (please read it). What I meant was, proving my side of discussion by giving someone's statement is not good if the main concept is not clear. Thats why I presented the example of rubber band.
ReplyDeleteI don't say you are wrong. But its hard to follow what you said, too. Physics is not like what Voltire said. Defining everything according to your needs that completely change the meaning what others know doesn't make you unconventional, it leads you in wrong way. The proof is, you said that the rubber band is not in tension. Your response is not unconventional, its wrong, i need to say.
Tension and Tension force are well defined terms with clear meanings. The problem is many of us don't know them. In spite of using them correctly, we want to prove what we say. I see a positive point on Voltire's quotation, if you define something wrong before starting conversation, there will be enough room for the correction.
Any way, the conversation was not so bad. Had a good time here talking with you.
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ReplyDeleteYou know what you’re talking about, why waste your intelligence on just posting videos to your blog when you could be giving us something enlightening to read?
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