Tension (physics)
In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, 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.
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.
Tension (as a transmitted force, as an action-reaction pair of forces, or as a restoring force) is measured in
Tension in one dimension
Tension in a string is a non-negative
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:
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
Thus, one can obtain a scalar analogous to tension by taking the trace of the stress tensor.[3]
System in equilibrium
A system is in equilibrium when the sum of all forces is zero.[1]
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.[1]
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.[1]
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 .[1]
In another example, suppose that two bodies A and B having masses and , 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 () pulling down, and the tension in the string pulling up. Therefore, the net force on body A is , so . In an extensible string, Hooke's law applies.
Strings in modern physics
String-like objects in
See also
- Continuum mechanics
- Fall factor
- Surface tension
- Tensile strength
- Traction (mechanics)
- Hydrostatic pressure
References
- ^ a b c d e Physics for Scientists and Engineers with Modern Physics, Section 5.7. Seventh Edition, Brooks/Cole Cengage Learning, 2008.
- ^ A. Fetter and J. Walecka. (1980). Theoretical Mechanics of Particles and Continua. New York: McGraw-Hill.
- ^ Jayachandran, Arul. Design of Tension Members: Mechanical Properties and Block Shear Failure, Exercises of Civil Engineering April 9, 2014. Illinois Institute of Technology