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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 Ft).

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/s2in the upward direction

(b) 3 m/s2 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/sin upward direction
(b) 9.8 m/s2 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.
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