Static Equilibrium problem
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I would like to ask about a part of a question I saw in an IG textbook, the question starts as "A smooth bead is threaded on a light inextensible string, the ends of the string are attached to the ceilling, the bead is acted on by a horizontal force F and the bead is in equilibrium..... ", the point is that the answer assumes that the tension on both sides of the string are equal, why is this true?
physics mathematical-physics classical-mechanics
asked Aug 25 at 2:15
saker jood
133
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up vote
1
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I would like to ask about a part of a question I saw in an IG textbook, the question starts as "A smooth bead is threaded on a light inextensible string, the ends of the string are attached to the ceilling, the bead is acted on by a horizontal force F and the bead is in equilibrium..... ", the point is that the answer assumes that the tension on both sides of the string are equal, why is this true?
physics mathematical-physics classical-mechanics
asked Aug 25 at 2:15
saker jood
133
why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I would like to ask about a part of a question I saw in an IG textbook, the question starts as "A smooth bead is threaded on a light inextensible string, the ends of the string are attached to the ceilling, the bead is acted on by a horizontal force F and the bead is in equilibrium..... ", the point is that the answer assumes that the tension on both sides of the string are equal, why is this true?
physics mathematical-physics classical-mechanics
asked Aug 25 at 2:15
saker jood
133
I would like to ask about a part of a question I saw in an IG textbook, the question starts as "A smooth bead is threaded on a light inextensible string, the ends of the string are attached to the ceilling, the bead is acted on by a horizontal force F and the bead is in equilibrium..... ", the point is that the answer assumes that the tension on both sides of the string are equal, why is this true?
physics mathematical-physics classical-mechanics
asked Aug 25 at 2:15
saker jood
133
asked Aug 25 at 2:15
saker jood
133
asked Aug 25 at 2:15
saker jood
133
asked Aug 25 at 2:15
saker jood
133
133
why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52
add a comment |Â
why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52
why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52
add a comment |Â
2 Answers
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0
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There are (possibly hidden) assumptions in the problem statement,
namely that there is no frictional force between the bead and the string
and the part of the string in contact with the bead has zero weight.
So although the string may bend around its region of contact with the bead,
the tension remains equal throughout that piece of the string;
there is no tangential component of any other force (from the bead or from gravity)
at any point along that part of the string's path.
If we allow the bead to exert a significant frictional force on the string then we are no longer justified in assuming the tension is equal on both sides.
Likewise if the part of the string in contact with the bead has significant weight.
The descriptions of the bead and string as "smooth" and "light" are presumably indicators that we are supposed to assume negligible friction and negligible weight of that portion of the string.
answered Aug 25 at 15:26
David K
48.9k340109
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
add a comment |Â
up vote
0
down vote
In the figure, point B shows the bead location threaded to the massless smooth string ABC.
In black is represented the bead weight, In blue the exerted horizontal force and in red the resultant force in equilibrium with the tension forces in green. The tension forces which are equal in modulus, have their resultant at the bisector dotted line.
answered Aug 25 at 13:48
Cesareo
5,8882412
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
accepted
There are (possibly hidden) assumptions in the problem statement,
namely that there is no frictional force between the bead and the string
and the part of the string in contact with the bead has zero weight.
So although the string may bend around its region of contact with the bead,
the tension remains equal throughout that piece of the string;
there is no tangential component of any other force (from the bead or from gravity)
at any point along that part of the string's path.
If we allow the bead to exert a significant frictional force on the string then we are no longer justified in assuming the tension is equal on both sides.
Likewise if the part of the string in contact with the bead has significant weight.
The descriptions of the bead and string as "smooth" and "light" are presumably indicators that we are supposed to assume negligible friction and negligible weight of that portion of the string.
answered Aug 25 at 15:26
David K
48.9k340109
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
add a comment |Â
up vote
0
down vote
accepted
There are (possibly hidden) assumptions in the problem statement,
namely that there is no frictional force between the bead and the string
and the part of the string in contact with the bead has zero weight.
So although the string may bend around its region of contact with the bead,
the tension remains equal throughout that piece of the string;
there is no tangential component of any other force (from the bead or from gravity)
at any point along that part of the string's path.
If we allow the bead to exert a significant frictional force on the string then we are no longer justified in assuming the tension is equal on both sides.
Likewise if the part of the string in contact with the bead has significant weight.
The descriptions of the bead and string as "smooth" and "light" are presumably indicators that we are supposed to assume negligible friction and negligible weight of that portion of the string.
answered Aug 25 at 15:26
David K
48.9k340109
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
add a comment |Â
up vote
0
down vote
accepted
up vote
0
down vote
accepted
There are (possibly hidden) assumptions in the problem statement,
namely that there is no frictional force between the bead and the string
and the part of the string in contact with the bead has zero weight.
So although the string may bend around its region of contact with the bead,
the tension remains equal throughout that piece of the string;
there is no tangential component of any other force (from the bead or from gravity)
at any point along that part of the string's path.
If we allow the bead to exert a significant frictional force on the string then we are no longer justified in assuming the tension is equal on both sides.
Likewise if the part of the string in contact with the bead has significant weight.
The descriptions of the bead and string as "smooth" and "light" are presumably indicators that we are supposed to assume negligible friction and negligible weight of that portion of the string.
answered Aug 25 at 15:26
David K
48.9k340109
There are (possibly hidden) assumptions in the problem statement,
namely that there is no frictional force between the bead and the string
and the part of the string in contact with the bead has zero weight.
So although the string may bend around its region of contact with the bead,
the tension remains equal throughout that piece of the string;
there is no tangential component of any other force (from the bead or from gravity)
at any point along that part of the string's path.
If we allow the bead to exert a significant frictional force on the string then we are no longer justified in assuming the tension is equal on both sides.
Likewise if the part of the string in contact with the bead has significant weight.
The descriptions of the bead and string as "smooth" and "light" are presumably indicators that we are supposed to assume negligible friction and negligible weight of that portion of the string.
answered Aug 25 at 15:26
David K
48.9k340109
answered Aug 25 at 15:26
David K
48.9k340109
answered Aug 25 at 15:26
David K
48.9k340109
answered Aug 25 at 15:26
David K
48.9k340109
48.9k340109
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
add a comment |Â
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
Those considerations are relevant but they do not help us solve the problem.
– Cesareo
Aug 25 at 16:34
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
@Cesareo If you don't have a reason to say the tension is equal then the problem does not have a unique solution.
– David K
Aug 25 at 16:44
add a comment |Â
up vote
0
down vote
In the figure, point B shows the bead location threaded to the massless smooth string ABC.
In black is represented the bead weight, In blue the exerted horizontal force and in red the resultant force in equilibrium with the tension forces in green. The tension forces which are equal in modulus, have their resultant at the bisector dotted line.
answered Aug 25 at 13:48
Cesareo
5,8882412
add a comment |Â
up vote
0
down vote
In the figure, point B shows the bead location threaded to the massless smooth string ABC.
In black is represented the bead weight, In blue the exerted horizontal force and in red the resultant force in equilibrium with the tension forces in green. The tension forces which are equal in modulus, have their resultant at the bisector dotted line.
answered Aug 25 at 13:48
Cesareo
5,8882412
add a comment |Â
up vote
0
down vote
up vote
0
down vote
In the figure, point B shows the bead location threaded to the massless smooth string ABC.
In black is represented the bead weight, In blue the exerted horizontal force and in red the resultant force in equilibrium with the tension forces in green. The tension forces which are equal in modulus, have their resultant at the bisector dotted line.
answered Aug 25 at 13:48
Cesareo
5,8882412
In the figure, point B shows the bead location threaded to the massless smooth string ABC.
In black is represented the bead weight, In blue the exerted horizontal force and in red the resultant force in equilibrium with the tension forces in green. The tension forces which are equal in modulus, have their resultant at the bisector dotted line.
answered Aug 25 at 13:48
Cesareo
5,8882412
edited Aug 26 at 14:58
answered Aug 25 at 13:48
Cesareo
5,8882412
answered Aug 25 at 13:48
Cesareo
5,8882412
answered Aug 25 at 13:48
Cesareo
5,8882412
5,8882412
add a comment |Â
add a comment |Â
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why do you think the tension should not be equal on both side. Here given string has the same density all over the rope.
– Deepesh Meena
Aug 25 at 2:31
James, usually a typical question of this sort assumes that we have two tentional forces T1 and T2 in both sections of the string and asks to find the values of both, but there the particle is not a bead that is threaded, but an object that is attachedto the ends of two different ropes, so I am trying to figure out the very difference between the two situations that led to the assumption that they are equal in the case of the bead.
– saker jood
Aug 25 at 6:52