# Tension

## Tension

The most important application of Newton’s motion Laws is the explanation of tension. Ropes and strings are very useful in machines and mechanical systems. These are used to push or pull heavy loads. We can see the tension in using of ropes or cables. If we consider a load which is pulled by a rope, a person is exerting a force at one end of the rope who is not directly in the contact of the block. Thus, the force which is felt by block through the use of rope is called tension force.

What is Tension?

When a string or rope is tugged on the force that is applied on it when it is tugged on is termed as tension. The tension force is felt be every section of the rope in both the directions, apart from the end points. The end points experience tension on one side and the force from the weight attached. Throughout the string the tension varies in some circumstances.

“Tension is a pulling force applied by a string or chain on another body”.

Assumptions:

• The rope strings and cables have no mass.
• The tension remains same throughout the rope.

Tension Formula:

Tension \left( T \right)\,\,=\,\,\left( \frac{2{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)g\].

Law of Tension: The frequency of transverse vibration of a strained string is proportional to the square root of the tension (T) exerted on the string provided the vibrating length l and mass per unit length mm are kept constant.

v α √T, if l and m are constant.

How to find the Tension?

Problem: There are two books of mass 5kg and 2kg is tied to the two end of the string. Find the tension in the string if the system is free?

Solution: Given,

Mass (m₁) = 5 kg

Mass (m₂) = 2 kg

Acceleration due to gravity (g) = 9.8 m/ sec²

Tension (T) =?

We know that:

Tension \left( T \right)\,\,=\,\,\left( \frac{2{{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right)g\],

T\,\,=\,\,\left( \frac{2\times 5\times 2}{5+2} \right)\times 9.8\,\,=\,\,28N\],

Therefore, the tension in the spring is 28N.