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# Tension Formula

Forces are given many names which are like push, pull, thrust, lift, weight, friction, and tension. Traditionally, we may group these forces into several categories and given names relating to their source, like how they are transmitted, or their effects. The most important of these categories will be discussed in this section with some interesting applications. Further examples of forces will also be discussed. The student will learn one particular kind of force which is tension with tension formula. The word “tension” comes from a Latin word meaning “to stretch.” Let us learn it!

Source:en.wikipedia.org

## Tension Formula

### Definition of tension formula

Tension is a force working along the length of a medium, especially this force is carried by a flexible medium, like a rope or cable.  The flexible cords which carry muscle forces to other parts of the body are known as tendons.

Any flexible connector like a string, rope, chain, wire, or cable, can exert pulls only parallel to its length. Therefore, a force carried by a flexible connector is a tension with a direction parallel to the connector.

It is important to understand that tension is a pull in the connector. The tension force pulls outward along the two ends of the string. This Tension in the rope must equal to the weight of the supported mass, which can be easily proved using Newton’s second law. Here, the only external forces acting on the mass will be its weight W and the tension T supplied by the rope. Thus,

Net force = $$F_{net} = T − W = 0$$,

where T and w are the magnitudes of the tension and weight and their signs indicate a direction, with up being positive here. Thus, just as we may expect, the tension equals the weight of the supported mass.

### The formula for Tension

Since tension is nothing but the drawing force acting on the body while in hanging state. Then,  its formula will be:

T = $$W \pm ma$$

Where,

 W The Weight of the body a Acceleration of the moving body m Mass of the body

Obviously, if the body is traveling upward, then the tension will be T = W + ma

And, if the body is traveling downward, then the tension will be T = W – ma

Therefore, if the tension is equivalent to the weight of body T = W.

Tension Formula is useful for finding the tension force acting on any object. It is useful in many mechanical problems. As tension is a force so its unit will be Newton (N).

## Solved Examples

Q.1: A 8 Kg mass is dangling at the end of a thread. If the acceleration of the mass is acting as:

(a) 3 m $$s^{-2}$$ in the upward direction.

(b) 3 m $$s^{-2}$$ in the downward direction.

Then determine the tension in the thread.

Solution:

Known parameters are:

Mass of the hanging body, m = 8 Kg,

g = 9.8 m $$s^{-2}$$

(a) Given as a = 3 m $$s^{-2}$$

If the body is traveling in the upward direction the tension force is:

T = mg + ma

= $$8 \times 9.8 + 8 \times 1.5$$

= 90.4 N

(b) Given as a = 3 m $$s^{-2}$$

If the body is traveling in down direction, the tension force is:

T = mg – ma

= $$8 \times 9.8 – 8 \times 1.5$$

= 66.4 N.

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