Tension Force

In general, tension refers to the force transmitted when a cable, rope, wire, or string is tethered by forces acting on opposite ends. The cable is directed in one direction along its length and pulls equally on objects on either end of the cable.

The term  tension may also be used to describe the action-reaction forces affecting each end of the two elements. In other words, tension is the opposite of compression.

Physical objects are forced to exert some force upon each other when they are in contact. In accordance with the kind of object, each of these contact forces will be assigned a unique name. Cables, chains, or ropes exert tension on objects when they are being pulled.

It is possible to transfer force - over a specified distance with ropes and cables, since they are efficient at transferring force. Pulling force originates from tension since ropes cannot push effectively. When a rope is pushed, it will become slack and lose tension, thus it will no longer be able to pull in its original position.

The Formula of Tension

The tension is equal to the mass of the object × gravitational acceleration for suspended objects which are in equilibrium.

T= mg 

T= tension, N, kg-m/s2

m= mass, kg

g= gravitational force,

Newton's Laws and Tension Force

Newton's law is applied to tension in the final application. Cables and rope are usually used to transmit force, which causes tension. For example, let's consider a rope pulling a block. People pulling at one end of the rope cannot exert direct force on the block at the other end as they are not in contact with the block. So the rope exerts a force on the block which is transmitted to the block by the rope. An object experiencing tension force is a block.

Massless ropes or cables are the basis of classical mechanics. A massless cable or rope transmits force equally from one end to the other. By using the massless rope as an example, a person pulling a massless rope with the force 30 N then the pull experienced by the block will be the same 30 N. 

The total force on a massless rope should always be zero. This can be proven using Newton’s second law. The mass of a massless rope equals the force acting upon it, so a net force on a rope causes infinite acceleration A=F/m and zero mass.

It is physically impossible to experience the net force in the situation described above, so the massless rope cannot experience it.

Consequently, all of the massless ropes will undergo equal and opposite tension forces. When a man pulls a block with a rope, the rope experiences tension from the pull in one direction, and tension from the reactive force of the block in the opposite direction.

The Tension in One Dimension

In one dimension string, the tension is a scalar quantity. The tension is not negative. When the tension is zero, the string is loose. Unlike ropes and strings, which have a dimension of length yet no cross-section, ropes and strings are massless. Since the tension is constant along the string, there will be no bends not caused by vibrations and pulleys, as they occur with vibrations and pulleys. 

According to Newton's third law, these are the forces applied on the ends of the string or rope by the objects to which the ends are attached. When a string vibrates, the frequencies it produces are determined by its tension. These frequencies are derived from Newton's law of motion.

Three Dimensions of Tension

In addition, tension is also used to describe a force that is generated by the ends of three-dimensional continuous material, such as truss and rods. Such rods swell under tension. 

Stress=axial force/cross-sectional area

So failure is caused by both the lengthening and the load, as both are determined by the force per cross-sectional area rather than the force alone. Stress is a 3×3 matrix. It is called a tensor.