Dimension of Tension & its Derivation

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Dimension of Tension: Tension is a pulling force that acts along a medium that is being applied an external force. This tension acts axially i.e. along with length. The action-reaction pair of forces that are present at each end of the element can also be referred to as tension. The opposite of compression might be tension. Tension Dimensional Formula is

M¹L¹T ^-2

In this article, we obtain the Dimension of Tension along with its derivations.

Dimension of Tension and Its Derivation

Since Surface Tension is a type of Force, the Dimension of Tension is equal to the Dimension of Force

$~=~{M^1L^1T^{-2}}$

Derivation of Dimension of Tension

The Dimensional Formula is written as follows.

$~=~{M^{a}L^{b}T^{~c}}$

Where,

M represents Mass

L represents Length

T represents Time

and a, b and c are the powers of M, L and T respectively

Dimension of Mass = M¹L⁰T⁰

Dimension of Distance = M⁰L¹T⁰

Dimension of Time = M⁰L⁰T¹

Dimension of Velocity = M⁰L¹T^-1 (obtained by dividing Dimension of Distance by Dimension of Time)

Since we know that

Hence

$~=~{M^0L^1T^{-1}}/{M^0L^0T^{1}}$

$~=~{M^0L^1T^{-2}}$

Also, we know that

$~=~{M^1L^0T^{0}}~*~{M^0L^1T^{-2}}$

$~=~{M^1L^1T^{-2}}$

What is Tension?

When you pull a rope or any similar object so that it fully stretches, then the force that is transmitted through it is called Tension. It is defined as the stretching force transmitted axially in a rope, string or any similar object. Being a type of force, it is measured in Newton.

Tension Force in a stretched string is a result of the intermolecular forces. When the rope is stretched, the molecules that are bound together are pulled away from each other. The force molecules pull each other back, thus resulting in Tension force.

The existence of Tension force can also be explained using Newton’s Third Law of Motion. Newton’s Third Law of Motion states that every action has an equal and opposite reaction. Thus, if a force is applied to a rope or string, an equal and opposite force will be produced. This force is tension.

Tension in Everyday Life

We may not realize it at first, but tension force is extremely important in everyday life. It is the force that prevents an object from falling when it is suspended from a string. Some examples in everyday life related to tension force are as follows:

Suspension Bridge: In a suspension bridge, the road is suspended by a series of cables. The bridge exerts its weight on the cables and in return, the tension force in the cables exerts a pull force on the bridge, thus keeping it stable.
Elevators: In the elevator system, the elevator cabin is suspended through a cable which exerts an equal and opposite force when the elevator is at rest. When the elevator moves, the tension in the cable changes accordingly.
Brakes: In the cycle, the brake wire exerts tension as soon as you press the brake lever. The tension force is then transmitted to the brake shoe through the cable.
Pulleys: Perhaps the best example to demonstrate tension is through the use of pulleys. When you hold a bucket using a pulley, the weight of the bucket (and the water in it, if any) pulls the rope down. But an equal and opposite force is experienced by the bucket which is transmitted through the rope. This happens when the bucket is at rest. However, if you pull it up, you give it acceleration against gravity. Thus, in this case, the tension force increases. If you let the bucket fall, the tension becomes zero and there is no force to balance the force out.
Trampoline: Trampoline is also a good example of tension in our everyday life. The weight of your body in a trampoline is supported by the tension force in the fabric. When you jump, the tension force exerts an equal and opposite force, making you bounce back.

Hence, proved that the Dimension of Tension is M¹L¹T^-2

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Dimension of Tension and Its Derivation

Derivation of Dimension of Tension

What is Tension?

Tension in Everyday Life

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