# Tension Formula

Tension is nothing but the drawing force acting on the body when it is hung from objects like chain, cable, string etc. It is represented by **T **(occasionally also symbolized as **F _{t}**).

Tension formula is articulated as

Where,

The Weight of the body = W,

mass of the body = m,

acceleration of the moving body = a

If the body is traveling upward, the tension will be T = W + ma

If the body is traveling downward, the tension will be T = W – ma

If the tension is equivalent to the weight of body T = W.

The weight of the object can be articulated as **W = mg**. Therefore, tension formula can also be represented as:

Where,

m = mass of the body,

g = acceleration due to gravity,

a = acceleration of the moving body.

**Tension Formula** is made use of to find the tension force acting on any object. It is useful in problems. Tension is a force so it is expressed in **Newtons (N)**.

**Tension Solved Examples **

Underneath are questions based on tension which may be useful for you.

**Problem 1: **A 8 Kg mass is dangling at the end of a string. If acceleration of the mass is

- 3 m/s
^{2}in the upward direction

(b) 3 m/s^{2} in downward direction.

Find the tension in the string.

**Answer:**

Known:

m (Mass of the hanging body) = 8 Kg,

(a) If the body is traveling in the upward direction the tension force is articulated as

T = mg + ma = 8 × 9.8 + 8 × 1.5 = 90.4 N

(b) If the body is traveling in down direction, the tension force is articulated as

T = mg – ma = 8 × 9.8 – 8 × 1.5 = 66.4 N.

**Problem 2: **A 500 N man is standing on the floor of an elevator. The scale is keeping a watch on the force. What will be the force if the acceleration is

(a) 1.5 m/s^{2 }in upward direction

(b) 9.8 m/s^{2} in downward direction.

**Answer:**

Known:

Weight of the man W = 500 N,

- If the body is traveling in upward direction, the tension force is articulated as

T = W + ma = 500 + 51 × 5 = 500 – 76.5 = 423.5 N - If the body is traveling in down direction, the tension force is articulated as,

T = W – ma = 500N- 51.02× 9.8 = 500 N – 499.998N = 0 N.