Tension Force

What is Tension Force | Definition and Examples

Introduction:

Force:

Force is an action that causes a free object with finite mass to accelerate, relative to a non-accelerating frame of reference.
The force can be divided into two types namely- Contact force and Non-contact force.

Contact forces are those requiring contact with the other object. All mechanical forces are contact forces. Contact forces can be divided into following types- muscular force, frictional force, normal force, applied force, tension force, spring force, and air resisting force.

Likewise, the non-contact forces can be exerted without any contact with any of the object. They are divided into gravitational force, magnetic force and electrostatic force.

Now we will look after the detailed description of the Tension force which is a contact force.

Tension force:

The tension force is the force that is transmitted through a cable, rope, wire or string when it is pulled tight by forces acting from opposite ends. It is directed along the length of the cable and pulls equally on the objects on the opposite ends of the wire.

Tension may also be described as the action-reaction pair of forces acting at each end of the said elements. Tension could be the opposite of compression.

Every physical object which is in contact applies some force on one another. These contact forces will be assigned with names based on the kind of objects. If one of the forces exerting object is a cable, chain or rope then it is called as tension.

Cables and ropes can be used for exerting forces since they can transfer force over a specific distance efficiently. Tension is the pulling force since the ropes cannot push effectively. Pushing with a rope causes the rope to go slack and lose tension that allowed it to pull it in the original place.

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,

What is tension force equal to?

The system has a constant velocity and there is an equilibrium because the tension in the cable/string, which is pulling up the object, is equal to the weight force, i.e. mg. where m is a mass and g is the acceleration caused by the gravity which is pulling down the object.

Does tension do work?

It is quite simple that tension never applies on its own. The tension has to be put on the system and tension is always pulling force, so it pulls from both ends no how complex is the system, making the network zero. Tension does not work on its own but only transfer.

Why is tension force important?

All physical objects that are in contact can apply/exerts forces on each other. It is important to note that tension is a pulling force since ropes simply can’t push effectively. Trying to push with a rope causes the rope to go slack and lose the tension that allowed it to pull in the first place.

Why tension constant in a massless string?

The concept of tension in a string can be difficult to grasp because a string is extended and non- rigid so that the tension exists throughout the string rather than applied at the single point.

Does tension depend on mass?

If weight is hanged from a cable or wire from a fixed point, the wire or cable would be under tension proportional to the mass of the object. The wire is under tension proportional to the force of pulling.

Tension force and Newton’s Laws:

The final application of Newton’s law deals with the tension. Tension usually arises in the use of cables, rope to transmit a force. Let’s consider a block being pulled by a rope. The person pulling at one end of the rope is not in contact with the block in the other end and cannot exert the direct force on the block. So, the force is exerted on the rope, which transmits the force to the block. The force that is experienced by the block from the rope is called the tension force.

The classical mechanics deal with massless ropes or cables. If a cable or rope is massless, then it perfectly transmits the force from one end to another end. For example, if a man pulls the massless rope with a force of 30 N then the block will also experience the force of 30 N only.

An important property of the massless rope should be that the total force on the rope must be zero at all times. To prove this, we look at Newton’s second law. If a net force acts upon a massless rope, then it would cause infinite acceleration A=F/m and mass of the rope is zero.

The situation mentioned above is not physically possible and consequently, the massless rope can never experience the net force.
Thus, all the massless rope will experience the two equal and opposite tension forces. In case a man is pulling the block with a rope/string, the rope experiences tension in one direction from the pull and tension in the other direction from the reactive force of the block.

Tension and pulleys:

The dynamics of a single rope is quite simple and easy as it transmits the applied force. But when pulleys are used instead of ropes then the complications arise. In the dynamical sense, the pulleys act to change the direction of the rope and they do not change the magnitude of the forces on the rope.



The diagram which is given above represents a small block on the left and it is lifted by the larger block on the right. Notice the forces T and -T in the figure. Even when the pulleys are used the rope must experience the two equal and opposite tension forces. In the figure above the rope actually experiences the two forces in the same direction, making the situation impossible. 
The presence of the pulley changes the situation to make it physically sustainable.

When rope and pulley are taking into existence it is useful to define a direction not in terms of up and down but in terms of the shape of the rope. In the above situation, we can define the positive direction on the rope as pointing up on the left side and pointing down on the right side of the pulley. When the direction is defined in the way mentioned above the rope does actually experience the two equal and opposite force.

If the string curves around one or more pulleys it will have constant tension along its length in the situation that the pulleys are frictionless and massless.

The Tension in one dimension:

The tension in the one-dimension string is a scalar quantity. It is non-negative. Zero tension is loose/slack. The rope or string is one dimension having length but is massless with zero cross-sections. If there are no bends in the rope/string as they occur with the vibrations and the pulleys then the tension will be constant along the string, equal to the magnitude of the forces applied by the end of the string.

By 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. A vibrating string will vibrate with the set of frequencies that depend on the strings tension. These frequencies can be derived from Newton’s law of motion. 




The Tension in three dimensions:

Tension is also used to describe the force applied by the ends of a three-dimensional continuous material like the truss and rods. Such rods elongate under tension. The amount of lengthening and the load will cause failure, and both will depend on the force per cross-sectional area rather than the force alone, so stress=axial force/cross-sectional area. Stress is a 3×3 matrix. It is called a tensor.




Direction of Tension:

The direction of tension is the pull which is given the name tension. Thus, the tension will point away from the mass in the direction of the string/rope. In case of the hanging mass, the string pulls it upwards, so the string/rope exerts an upper force on the mass and the tension will be in the upper side.

The ends of a string or other object transmitting tension will apply forces on the objects to which the string is connected, in the direction of the rod/string at the point of attachment. The forces due to the tension are called passive forces. There are two chances for the objects held by strings/rods: either acceleration is zero and the system is therefore in equilibrium or there is acceleration and the net force is present in the system.

The system will be in equilibrium when the sum of all forces is zero.
∑ F = 0
The System under net force:
A system has a net force when an unbalanced force is exerted on it; i.e. the sum of all forces is not zero. Acceleration and net force always exist together.
∑ F ≠ 0.