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Moved page from wikipedia:en:Tension (physics) (history)
此词条暂由彩云小译翻译，翻译字数共1058，未经人工整理和审校，带来阅读不便，请见谅。
{{Short description|Pulling force transmitted axially – Opposite of compression}}
In [[physics]], '''tension''' is described as the pulling [[force]] transmitted axially by the means of a string, a cable, chain, or similar object, or by each end of a rod, [[truss]] member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of [[compression (physics)|compression]].
In physics, tension is described as the pulling force transmitted axially by the means of a string, a cable, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of compression.
在物理学中，张力被描述为通过弦、电缆、链条或类似物体，或杆、桁架构件或类似三维物体的每一端传递的轴向拉力; 张力也可以被描述为作用于所述元素的每一端的作用力-反作用力对。张力可能是压力的反义词。
At the atomic level, when atoms or molecules are pulled apart from each other and gain [[potential energy]] with a [[restoring force]] still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.
At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.
在原子水平上，当原子或分子彼此拉开并获得势能时，恢复力仍然存在，恢复力可能产生也称为张力的东西。在这种张力下，绳子或杆的每一端都可以拉住它所附着的物体，以便使绳子或杆恢复到松弛的长度。
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in [[newton (unit)|newtons]] in the [[International System of Units]] (or [[pounds-force]] in [[Imperial units]]). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings:<ref name="Physics">''[https://books.google.com/books?id=xz-UEdtRmzkC&printsec=frontcover#v=onepage&q=Tension&f=false Physics for Scientists and Engineers with Modern Physics]'', Section 5.7. Seventh Edition, Brooks/Cole Cengage Learning, 2008.</ref> either [[acceleration]] is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a [[net force]] is present in the system.
[[File:Tug Of War Tension.png|thumb|Nine men at the Irish champion tug of war team pull on a rope. The rope in the photo extends into a drawn illustration showing adjacent segments of the rope. One segment is duplicated in a free body diagram showing a pair of action-reaction forces of magnitude T pulling the segment in opposite directions, where '''T''' is transmitted axially and is called the tension force. This end of the rope is pulling the [[tug of war]] team to the right. Each segment of the rope is pulled apart by the two neighboring segments, stressing the segment in what is also called tension, which can change along the two football field's members.]]
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings:Physics for Scientists and Engineers with Modern Physics, Section 5.7. Seventh Edition, Brooks/Cole Cengage Learning, 2008. either acceleration is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a net force is present in the system.
张力(作为一个传递力，作为一个作用力-反作用力对，或作为一个恢复力)在国际单位制中以牛顿计量(或在帝国单位中以磅力计量)。传递张力的绳子或其他物体的末端会对与绳子或杆子相连的物体施加力，力的方向是连接点处的绳子。这些由于张力而产生的力也称为“被动力”。有两种基本的可能性，物体系统由弦持有: 物理科学家和工程师与现代物理，第5.7节。第七版，布鲁克斯/科尔圣智学习出版公司，2008年。要么加速度为零，因此系统处于平衡状态，要么存在加速度，因此系统中存在净力。
==Tension in one dimension==
[[Image:Tension figure.svg|right|350px|The tension in a tetherball rope.]]
Tension in a string is a non-negative [[scalar (physics)|vector quantity]]. Zero tension is slack. A string or rope is often idealized as one dimension, having length but being massless with zero [[cross section (geometry)|cross section]]. If there are no bends in the string, as occur with [[vibration]]s or [[pulley]]s, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string. By [[Newton's third law]], these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are [[mass]]less and [[friction]]less. A [[vibrating string]] vibrates with a set of [[frequencies]] that depend on the string's tension. These frequencies can be derived from [[Newton's laws of motion]]. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string.
right|350px|The tension in a tetherball rope.
Tension in a string is a non-negative vector quantity. Zero tension is slack. A string or rope is often idealized as one dimension, having length but being massless with zero cross section. If there are no bends in the string, as occur with vibrations or pulleys, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string. By Newton's third law, these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are massless and frictionless. A vibrating string vibrates with a set of frequencies that depend on the string's tension. These frequencies can be derived from Newton's laws of motion. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string.
= = 一维中的张力 = = right | 350px | 绳索中的张力。字符串中的张力是一个非负向量。零张力就是松弛。绳子通常被理想化为一维，有长度但无质量，横截面为零。如果在弦中没有弯曲，就像振动或滑轮一样，那么沿着弦的张力是一个常数，等于弦两端施加的力的大小。根据牛顿第三定律，这些力与两端相连的物体对绳子两端施加的力是一样的。如果绳子绕着一个或多个滑轮弯曲，在滑轮无质量无摩擦的理想情况下，沿着它的长度仍然有恒定的张力。振动弦的振动频率取决于弦的张力。这些频率可以从牛顿运动定律推导出来。弦的每一个微观部分都被它的相邻部分拉扯着，拉力等于沿着弦的那个位置的张力。
If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a [[net force]] on that segment of the string, causing an acceleration. This net force is a [[restoring force]], and the motion of the string can include [[transverse wave]]s that solve the equation central to [[Sturm–Liouville theory]]:
<math display="block">-\frac{d}{dx} \bigg[ \tau(x) \frac{d\rho(x)}{dx} \bigg]+v(x)\rho(x) = \omega^2\sigma(x)\rho(x)</math>
where <math>v(x)</math> is the force constant per unit length [units force per area] and <math>\omega^2</math> are the [[eigenvalue]]s for resonances of transverse displacement <math>\rho(x)</math> on the string,<ref>A. Fetter and J. Walecka. (1980). [https://books.google.com/books?id=n54oAwAAQBAJ&printsec=frontcover#v=onepage&q=Tension&f=false Theoretical Mechanics of Particles and Continua]. New York: McGraw-Hill.</ref> with solutions that include the various [[scale of harmonics|harmonics]] on a [[stringed instrument]].
If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a net force on that segment of the string, causing an acceleration. This net force is a restoring force, and the motion of the string can include transverse waves that solve the equation central to Sturm–Liouville theory:
-\frac{d}{dx} \bigg[ \tau(x) \frac{d\rho(x)}{dx} \bigg]+v(x)\rho(x) = \omega^2\sigma(x)\rho(x)
where v(x) is the force constant per unit length [units force per area] and \omega^2 are the eigenvalues for resonances of transverse displacement \rho(x) on the string,A. Fetter and J. Walecka. (1980). Theoretical Mechanics of Particles and Continua. New York: McGraw-Hill. with solutions that include the various harmonics on a stringed instrument.
如果弦具有曲率，那么两个相邻的两个力就不会加到零，那么弦的那个部分就会受到一个净力，从而产生加速度。这个净力是一个恢复力，弦的运动可以包括解决 Sturm-Liouville 理论中心方程的横波:-frac { d }{ dx } bigg [ tau (x) frac { d rho (x)}{ dx } bigg ] + v (x) rho (x) = omega ^ 2 sigma (x) rho (x) ，其中 v (x)是单位长度上的力常数[单位面积上的力] ，omega ^ 2是弦上横向位移 rho (x)共振的特征值。Fetter 和 J. Walecka。(1980).粒子理论力学和连续介质。纽约: 麦格劳-希尔。包括弦乐器上的各种谐波的解决方案。
==Tension of three dimensions==
Tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or [[truss]] member. In this context, tension is analogous to [[Pressure#Negative pressures|negative pressure]]. A rod under tension elongates. The amount of elongation and the [[structural load|load]] that will cause failure both depend on the force per cross-sectional area rather than the force alone, so [[stress (mechanics)|stress]] = axial force / cross sectional area is more useful for engineering purposes than tension. Stress is a 3x3 matrix called a [[tensor]], and the <math>\sigma_{11}</math> element of the stress tensor is tensile force per area, or compression force per area, denoted as a negative number for this element, if the rod is being compressed rather than elongated.
Tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or truss member. In this context, tension is analogous to negative pressure. A rod under tension elongates. The amount of elongation and the load that will cause failure both depend on the force per cross-sectional area rather than the force alone, so stress = axial force / cross sectional area is more useful for engineering purposes than tension. Stress is a 3x3 matrix called a tensor, and the \sigma_{11} element of the stress tensor is tensile force per area, or compression force per area, denoted as a negative number for this element, if the rod is being compressed rather than elongated.
张力也用来描述三维连续材料如杆或桁架构件的两端所施加的力。在这种情况下，紧张类似于负面压力。拉力下的杆伸长。延伸量和将导致破坏的载荷都取决于每个截面积的力，而不是单独的力，所以应力 = 轴向力/截面积对于工程目的比张力更有用。应力是一个称为张量的3x3矩阵，而应力张量的 sigma _ {11}元素是每个面积的拉力，或每个面积的压缩力，如果杆被压缩而不是拉长，则表示为该元素的负数。
Thus, one can obtain a scalar analogous to tension by taking the [[trace (linear algebra)|trace]] of the stress tensor.
Thus, one can obtain a scalar analogous to tension by taking the trace of the stress tensor.
因此，我们可以通过追踪应力张量得到一个类似于张力的标量。
==System in equilibrium==
A system is in equilibrium when the sum of all forces is zero.<ref name="Physics"/>
<math display="block">\sum \vec{F} = 0</math>
A system is in equilibrium when the sum of all forces is zero.
\sum \vec{F} = 0
= = 系统处于平衡状态 = = 当所有力之和为零时，系统处于平衡状态。Sum vec { F } = 0
For example, consider a system consisting of an object that is being lowered vertically by a string with tension, ''T'', at a constant [[velocity]]. The system has a constant velocity and is therefore in equilibrium because the tension in the string, which is pulling up on the object, is equal to the [[weight]] [[force]], mg ("m" is mass, "g" is the acceleration caused by the [[gravity of Earth]]), which is pulling down on the object.<ref name="Physics"/>
<math display="block">\sum \vec{F} = \vec{T} + m\vec{g} = 0</math>
For example, consider a system consisting of an object that is being lowered vertically by a string with tension, T, at a constant velocity. The system has a constant velocity and is therefore in equilibrium because the tension in the string, which is pulling up on the object, is equal to the weight force, mg ("m" is mass, "g" is the acceleration caused by the gravity of Earth), which is pulling down on the object.
\sum \vec{F} = \vec{T} + m\vec{g} = 0
例如，考虑一个由一个物体组成的系统，该物体被一根张力为 T 的弦垂直放下，速度恒定。这个系统有一个恒定的速度，因此处于平衡状态，因为绳子的张力，在物体上拉起，等于重力，mg (“ m”是质量，“ g”是地球引力引起的加速度) ，在物体上拉下。Sum vec { F } = vec { T } + m vec { g } = 0
==System under net force==
A system has a net force when an unbalanced force is exerted on it, in other words the sum of all forces is not zero. Acceleration and net force always exist together.<ref name="Physics"/>
<math display="block">\sum \vec{F} \ne 0</math>
A system has a net force when an unbalanced force is exerted on it, in other words the sum of all forces is not zero. Acceleration and net force always exist together.
\sum \vec{F} \ne 0
在净力作用下的系统 = = 当一个不平衡力作用在一个系统上时，系统有一个净力，换句话说，所有力的总和不等于零。加速度和净力总是同时存在。求和与{ F } ne 0
For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards (positive acceleration) therefore there exists a net force somewhere in the system. In this case, negative acceleration would indicate that <math>|mg| > |T|</math>.<ref name="Physics"/>
<math display="block">\sum \vec{F} = \vec{T} - m\vec{g} \ne 0</math>
For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards (positive acceleration) therefore there exists a net force somewhere in the system. In this case, negative acceleration would indicate that |mg| > |T|.
\sum \vec{F} = \vec{T} - m\vec{g} \ne 0
例如，考虑与上面相同的系统，但假设物体现在随着向下增加的速度(正加速度)而下降，因此在系统的某处存在一个净力。在这种情况下，负加速度表明 | mg | > | T | 。Sum vec { F } = vec { T }-m vec { g } ne0
In another example, suppose that two bodies A and B having masses <math>m_1</math> and <math>m_2</math>, respectively, are connected with each other by an inextensible string over a frictionless pulley. There are two forces acting on the body A: its weight (<math>w_1=m_1g</math>) pulling down, and the tension <math>T</math> in the string pulling up. Therefore, the net force <math>F_1</math> on body A is <math>w_1-T</math>, so <math>m_1a=m_1g-T</math>. In an extensible string, [[Hooke's law]] applies.
In another example, suppose that two bodies A and B having masses m_1 and m_2, respectively, are connected with each other by an inextensible string over a frictionless pulley. There are two forces acting on the body A: its weight (w_1=m_1g) pulling down, and the tension T in the string pulling up. Therefore, the net force F_1 on body A is w_1-T, so m_1a=m_1g-T. In an extensible string, Hooke's law applies.
在另一个例子中，假设质量分别为 m _ 1和 m _ 2的两个物体 A 和 B 通过无摩擦滑轮上的一根不可伸缩的弦相互连接。有两个力作用在物体 A 上: 它的重量(w _ 1 = m _ 1g)向下拉，和绳子中的张力 T 向上拉。因此，物体 A 上的净作用力 F _ 1为 w _ 1-T，所以 m _ 1a = m _ 1g-T。在可扩展的字符串中，胡克定律适用。
==Strings in modern physics==
String-like objects in [[special relativity|relativistic]] theories, such as the [[QCD string|strings]] used in some models of interactions between [[quarks]], or those used in the modern [[string theory]], also possess tension. These strings are analyzed in terms of their [[world sheet]], and the [[energy]] is then typically proportional to the length of the string. As a result, the tension in such strings is independent of the amount of stretching.
String-like objects in relativistic theories, such as the strings used in some models of interactions between quarks, or those used in the modern string theory, also possess tension. These strings are analyzed in terms of their world sheet, and the energy is then typically proportional to the length of the string. As a result, the tension in such strings is independent of the amount of stretching.
现代物理学中的弦 = = 相对论理论中的弦状物体，如夸克之间相互作用模型中使用的弦，或现代弦理论中使用的弦，也具有张力。这些弦根据它们的世界表来分析，然后能量通常与弦的长度成正比。因此，这种弦的张力与拉伸的量无关。
==See also==
{{Portal|Physics}}
{{Commons category|Tension}}
{{wikiquote|Tension}}
* [[Continuum mechanics]]
* [[Fall factor]]
* [[Surface tension]]
* [[Tensile strength]]
* [[Hydrostatic pressure]]
* Continuum mechanics
* Fall factor
* Surface tension
* Tensile strength
* Hydrostatic pressure
= = 参见同样 = =
* 连续介质力学
* 跌落系数
* 表面张力
* 抗拉强度
* 静水压力
==References==
{{Reflist}}
{{Authority control}}
[[Category:Solid mechanics]]
Category:Solid mechanics
类别: 固体力学
<noinclude>
<small>This page was moved from [[wikipedia:en:Tension (physics)]]. Its edit history can be viewed at [[张力/edithistory]]</small></noinclude>
[[Category:待整理页面]]
{{Short description|Pulling force transmitted axially – Opposite of compression}}
In [[physics]], '''tension''' is described as the pulling [[force]] transmitted axially by the means of a string, a cable, chain, or similar object, or by each end of a rod, [[truss]] member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of [[compression (physics)|compression]].
In physics, tension is described as the pulling force transmitted axially by the means of a string, a cable, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as the action-reaction pair of forces acting at each end of said elements. Tension could be the opposite of compression.
在物理学中，张力被描述为通过弦、电缆、链条或类似物体，或杆、桁架构件或类似三维物体的每一端传递的轴向拉力; 张力也可以被描述为作用于所述元素的每一端的作用力-反作用力对。张力可能是压力的反义词。
At the atomic level, when atoms or molecules are pulled apart from each other and gain [[potential energy]] with a [[restoring force]] still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.
At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create what is also called tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.
在原子水平上，当原子或分子彼此拉开并获得势能时，恢复力仍然存在，恢复力可能产生也称为张力的东西。在这种张力下，绳子或杆的每一端都可以拉住它所附着的物体，以便使绳子或杆恢复到松弛的长度。
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in [[newton (unit)|newtons]] in the [[International System of Units]] (or [[pounds-force]] in [[Imperial units]]). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings:<ref name="Physics">''[https://books.google.com/books?id=xz-UEdtRmzkC&printsec=frontcover#v=onepage&q=Tension&f=false Physics for Scientists and Engineers with Modern Physics]'', Section 5.7. Seventh Edition, Brooks/Cole Cengage Learning, 2008.</ref> either [[acceleration]] is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a [[net force]] is present in the system.
[[File:Tug Of War Tension.png|thumb|Nine men at the Irish champion tug of war team pull on a rope. The rope in the photo extends into a drawn illustration showing adjacent segments of the rope. One segment is duplicated in a free body diagram showing a pair of action-reaction forces of magnitude T pulling the segment in opposite directions, where '''T''' is transmitted axially and is called the tension force. This end of the rope is pulling the [[tug of war]] team to the right. Each segment of the rope is pulled apart by the two neighboring segments, stressing the segment in what is also called tension, which can change along the two football field's members.]]
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in newtons in the International System of Units (or pounds-force in Imperial units). The ends of a string or other object transmitting tension will exert forces on the objects to which the string or rod is connected, in the direction of the string at the point of attachment. These forces due to tension are also called "passive forces". There are two basic possibilities for systems of objects held by strings:Physics for Scientists and Engineers with Modern Physics, Section 5.7. Seventh Edition, Brooks/Cole Cengage Learning, 2008. either acceleration is zero and the system is therefore in equilibrium, or there is acceleration, and therefore a net force is present in the system.
张力(作为一个传递力，作为一个作用力-反作用力对，或作为一个恢复力)在国际单位制中以牛顿计量(或在帝国单位中以磅力计量)。传递张力的绳子或其他物体的末端会对与绳子或杆子相连的物体施加力，力的方向是连接点处的绳子。这些由于张力而产生的力也称为“被动力”。有两种基本的可能性，物体系统由弦持有: 物理科学家和工程师与现代物理，第5.7节。第七版，布鲁克斯/科尔圣智学习出版公司，2008年。要么加速度为零，因此系统处于平衡状态，要么存在加速度，因此系统中存在净力。
==Tension in one dimension==
[[Image:Tension figure.svg|right|350px|The tension in a tetherball rope.]]
Tension in a string is a non-negative [[scalar (physics)|vector quantity]]. Zero tension is slack. A string or rope is often idealized as one dimension, having length but being massless with zero [[cross section (geometry)|cross section]]. If there are no bends in the string, as occur with [[vibration]]s or [[pulley]]s, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string. By [[Newton's third law]], these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are [[mass]]less and [[friction]]less. A [[vibrating string]] vibrates with a set of [[frequencies]] that depend on the string's tension. These frequencies can be derived from [[Newton's laws of motion]]. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string.
right|350px|The tension in a tetherball rope.
Tension in a string is a non-negative vector quantity. Zero tension is slack. A string or rope is often idealized as one dimension, having length but being massless with zero cross section. If there are no bends in the string, as occur with vibrations or pulleys, then tension is a constant along the string, equal to the magnitude of the forces applied by the ends of the string. By Newton's third law, these are the same forces exerted on the ends of the string by the objects to which the ends are attached. If the string curves around one or more pulleys, it will still have constant tension along its length in the idealized situation that the pulleys are massless and frictionless. A vibrating string vibrates with a set of frequencies that depend on the string's tension. These frequencies can be derived from Newton's laws of motion. Each microscopic segment of the string pulls on and is pulled upon by its neighboring segments, with a force equal to the tension at that position along the string.
= = 一维中的张力 = = right | 350px | 绳索中的张力。字符串中的张力是一个非负向量。零张力就是松弛。绳子通常被理想化为一维，有长度但无质量，横截面为零。如果在弦中没有弯曲，就像振动或滑轮一样，那么沿着弦的张力是一个常数，等于弦两端施加的力的大小。根据牛顿第三定律，这些力与两端相连的物体对绳子两端施加的力是一样的。如果绳子绕着一个或多个滑轮弯曲，在滑轮无质量无摩擦的理想情况下，沿着它的长度仍然有恒定的张力。振动弦的振动频率取决于弦的张力。这些频率可以从牛顿运动定律推导出来。弦的每一个微观部分都被它的相邻部分拉扯着，拉力等于沿着弦的那个位置的张力。
If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a [[net force]] on that segment of the string, causing an acceleration. This net force is a [[restoring force]], and the motion of the string can include [[transverse wave]]s that solve the equation central to [[Sturm–Liouville theory]]:
<math display="block">-\frac{d}{dx} \bigg[ \tau(x) \frac{d\rho(x)}{dx} \bigg]+v(x)\rho(x) = \omega^2\sigma(x)\rho(x)</math>
where <math>v(x)</math> is the force constant per unit length [units force per area] and <math>\omega^2</math> are the [[eigenvalue]]s for resonances of transverse displacement <math>\rho(x)</math> on the string,<ref>A. Fetter and J. Walecka. (1980). [https://books.google.com/books?id=n54oAwAAQBAJ&printsec=frontcover#v=onepage&q=Tension&f=false Theoretical Mechanics of Particles and Continua]. New York: McGraw-Hill.</ref> with solutions that include the various [[scale of harmonics|harmonics]] on a [[stringed instrument]].
If the string has curvature, then the two pulls on a segment by its two neighbors will not add to zero, and there will be a net force on that segment of the string, causing an acceleration. This net force is a restoring force, and the motion of the string can include transverse waves that solve the equation central to Sturm–Liouville theory:
-\frac{d}{dx} \bigg[ \tau(x) \frac{d\rho(x)}{dx} \bigg]+v(x)\rho(x) = \omega^2\sigma(x)\rho(x)
where v(x) is the force constant per unit length [units force per area] and \omega^2 are the eigenvalues for resonances of transverse displacement \rho(x) on the string,A. Fetter and J. Walecka. (1980). Theoretical Mechanics of Particles and Continua. New York: McGraw-Hill. with solutions that include the various harmonics on a stringed instrument.
如果弦具有曲率，那么两个相邻的两个力就不会加到零，那么弦的那个部分就会受到一个净力，从而产生加速度。这个净力是一个恢复力，弦的运动可以包括解决 Sturm-Liouville 理论中心方程的横波:-frac { d }{ dx } bigg [ tau (x) frac { d rho (x)}{ dx } bigg ] + v (x) rho (x) = omega ^ 2 sigma (x) rho (x) ，其中 v (x)是单位长度上的力常数[单位面积上的力] ，omega ^ 2是弦上横向位移 rho (x)共振的特征值。Fetter 和 J. Walecka。(1980).粒子理论力学和连续介质。纽约: 麦格劳-希尔。包括弦乐器上的各种谐波的解决方案。
==Tension of three dimensions==
Tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or [[truss]] member. In this context, tension is analogous to [[Pressure#Negative pressures|negative pressure]]. A rod under tension elongates. The amount of elongation and the [[structural load|load]] that will cause failure both depend on the force per cross-sectional area rather than the force alone, so [[stress (mechanics)|stress]] = axial force / cross sectional area is more useful for engineering purposes than tension. Stress is a 3x3 matrix called a [[tensor]], and the <math>\sigma_{11}</math> element of the stress tensor is tensile force per area, or compression force per area, denoted as a negative number for this element, if the rod is being compressed rather than elongated.
Tension is also used to describe the force exerted by the ends of a three-dimensional, continuous material such as a rod or truss member. In this context, tension is analogous to negative pressure. A rod under tension elongates. The amount of elongation and the load that will cause failure both depend on the force per cross-sectional area rather than the force alone, so stress = axial force / cross sectional area is more useful for engineering purposes than tension. Stress is a 3x3 matrix called a tensor, and the \sigma_{11} element of the stress tensor is tensile force per area, or compression force per area, denoted as a negative number for this element, if the rod is being compressed rather than elongated.
张力也用来描述三维连续材料如杆或桁架构件的两端所施加的力。在这种情况下，紧张类似于负面压力。拉力下的杆伸长。延伸量和将导致破坏的载荷都取决于每个截面积的力，而不是单独的力，所以应力 = 轴向力/截面积对于工程目的比张力更有用。应力是一个称为张量的3x3矩阵，而应力张量的 sigma _ {11}元素是每个面积的拉力，或每个面积的压缩力，如果杆被压缩而不是拉长，则表示为该元素的负数。
Thus, one can obtain a scalar analogous to tension by taking the [[trace (linear algebra)|trace]] of the stress tensor.
Thus, one can obtain a scalar analogous to tension by taking the trace of the stress tensor.
因此，我们可以通过追踪应力张量得到一个类似于张力的标量。
==System in equilibrium==
A system is in equilibrium when the sum of all forces is zero.<ref name="Physics"/>
<math display="block">\sum \vec{F} = 0</math>
A system is in equilibrium when the sum of all forces is zero.
\sum \vec{F} = 0
= = 系统处于平衡状态 = = 当所有力之和为零时，系统处于平衡状态。Sum vec { F } = 0
For example, consider a system consisting of an object that is being lowered vertically by a string with tension, ''T'', at a constant [[velocity]]. The system has a constant velocity and is therefore in equilibrium because the tension in the string, which is pulling up on the object, is equal to the [[weight]] [[force]], mg ("m" is mass, "g" is the acceleration caused by the [[gravity of Earth]]), which is pulling down on the object.<ref name="Physics"/>
<math display="block">\sum \vec{F} = \vec{T} + m\vec{g} = 0</math>
For example, consider a system consisting of an object that is being lowered vertically by a string with tension, T, at a constant velocity. The system has a constant velocity and is therefore in equilibrium because the tension in the string, which is pulling up on the object, is equal to the weight force, mg ("m" is mass, "g" is the acceleration caused by the gravity of Earth), which is pulling down on the object.
\sum \vec{F} = \vec{T} + m\vec{g} = 0
例如，考虑一个由一个物体组成的系统，该物体被一根张力为 T 的弦垂直放下，速度恒定。这个系统有一个恒定的速度，因此处于平衡状态，因为绳子的张力，在物体上拉起，等于重力，mg (“ m”是质量，“ g”是地球引力引起的加速度) ，在物体上拉下。Sum vec { F } = vec { T } + m vec { g } = 0
==System under net force==
A system has a net force when an unbalanced force is exerted on it, in other words the sum of all forces is not zero. Acceleration and net force always exist together.<ref name="Physics"/>
<math display="block">\sum \vec{F} \ne 0</math>
A system has a net force when an unbalanced force is exerted on it, in other words the sum of all forces is not zero. Acceleration and net force always exist together.
\sum \vec{F} \ne 0
在净力作用下的系统 = = 当一个不平衡力作用在一个系统上时，系统有一个净力，换句话说，所有力的总和不等于零。加速度和净力总是同时存在。求和与{ F } ne 0
For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards (positive acceleration) therefore there exists a net force somewhere in the system. In this case, negative acceleration would indicate that <math>|mg| > |T|</math>.<ref name="Physics"/>
<math display="block">\sum \vec{F} = \vec{T} - m\vec{g} \ne 0</math>
For example, consider the same system as above but suppose the object is now being lowered with an increasing velocity downwards (positive acceleration) therefore there exists a net force somewhere in the system. In this case, negative acceleration would indicate that |mg| > |T|.
\sum \vec{F} = \vec{T} - m\vec{g} \ne 0
例如，考虑与上面相同的系统，但假设物体现在随着向下增加的速度(正加速度)而下降，因此在系统的某处存在一个净力。在这种情况下，负加速度表明 | mg | > | T | 。Sum vec { F } = vec { T }-m vec { g } ne0
In another example, suppose that two bodies A and B having masses <math>m_1</math> and <math>m_2</math>, respectively, are connected with each other by an inextensible string over a frictionless pulley. There are two forces acting on the body A: its weight (<math>w_1=m_1g</math>) pulling down, and the tension <math>T</math> in the string pulling up. Therefore, the net force <math>F_1</math> on body A is <math>w_1-T</math>, so <math>m_1a=m_1g-T</math>. In an extensible string, [[Hooke's law]] applies.
In another example, suppose that two bodies A and B having masses m_1 and m_2, respectively, are connected with each other by an inextensible string over a frictionless pulley. There are two forces acting on the body A: its weight (w_1=m_1g) pulling down, and the tension T in the string pulling up. Therefore, the net force F_1 on body A is w_1-T, so m_1a=m_1g-T. In an extensible string, Hooke's law applies.
在另一个例子中，假设质量分别为 m _ 1和 m _ 2的两个物体 A 和 B 通过无摩擦滑轮上的一根不可伸缩的弦相互连接。有两个力作用在物体 A 上: 它的重量(w _ 1 = m _ 1g)向下拉，和绳子中的张力 T 向上拉。因此，物体 A 上的净作用力 F _ 1为 w _ 1-T，所以 m _ 1a = m _ 1g-T。在可扩展的字符串中，胡克定律适用。
==Strings in modern physics==
String-like objects in [[special relativity|relativistic]] theories, such as the [[QCD string|strings]] used in some models of interactions between [[quarks]], or those used in the modern [[string theory]], also possess tension. These strings are analyzed in terms of their [[world sheet]], and the [[energy]] is then typically proportional to the length of the string. As a result, the tension in such strings is independent of the amount of stretching.
String-like objects in relativistic theories, such as the strings used in some models of interactions between quarks, or those used in the modern string theory, also possess tension. These strings are analyzed in terms of their world sheet, and the energy is then typically proportional to the length of the string. As a result, the tension in such strings is independent of the amount of stretching.
现代物理学中的弦 = = 相对论理论中的弦状物体，如夸克之间相互作用模型中使用的弦，或现代弦理论中使用的弦，也具有张力。这些弦根据它们的世界表来分析，然后能量通常与弦的长度成正比。因此，这种弦的张力与拉伸的量无关。
==See also==
{{Portal|Physics}}
{{Commons category|Tension}}
{{wikiquote|Tension}}
* [[Continuum mechanics]]
* [[Fall factor]]
* [[Surface tension]]
* [[Tensile strength]]
* [[Hydrostatic pressure]]
* Continuum mechanics
* Fall factor
* Surface tension
* Tensile strength
* Hydrostatic pressure
= = 参见同样 = =
* 连续介质力学
* 跌落系数
* 表面张力
* 抗拉强度
* 静水压力
==References==
{{Reflist}}
{{Authority control}}
[[Category:Solid mechanics]]
Category:Solid mechanics
类别: 固体力学
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<small>This page was moved from [[wikipedia:en:Tension (physics)]]. Its edit history can be viewed at [[张力/edithistory]]</small></noinclude>
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