Tension (physics)

Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object.

In terms of force, it is the opposite of compression.

Tension might also be described as the action-reaction pair of forces acting at each end of an object.

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 newtons in the International System of Units (or pounds-force in Imperial units).

Tension in a string is a non-negative vector quantity.

A string or rope is often idealized as one dimension, having fixed length but being massless with zero cross section.

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.

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.

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:

are the eigenvalues for resonances of transverse displacement

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.

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

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.

Thus, one can obtain a scalar analogous to tension by taking the trace of the stress tensor.

[3] A system is in equilibrium when the sum of all forces is zero.

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.

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.

, respectively, are connected with each other by an inextensible string over a frictionless pulley.

In an extensible string, Hooke's law applies.

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.