Tension Formula

Definition of Tension: Tension is defined as the force exerted by a rope, string, or cable when forces are acting to pull it tight at either end. It is practically a pulling force acting along the length of the object. It is denoted by T (sometimes also symbolized as Ft).

Formula For Tension

The most basic formula for tension (T) Newton's second law can be used to determine the tension in a rope,

             T=mg+ma

Where,

• T= tension

• g = acceleration due to gravity

• m =Mass of the body

• a = Acceleration of the moving body

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

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

When the tension is equal to the weight of body T = mg

Tension Solved Examples

Problem: An 8 Kg mass is hanging at the end of a string. If the acceleration of the mass is

Determine the tension in the string.

Solution :

Given,

 m (Mass of the hanging body) = 8 Kg,

(a) When the body is going upwards. Then the expression of tension force will be like 

              T = mg + ma = 8 × 9.8 + 8 × 3 = 102.4 N

(b) If the body is in downward then the expression of tension force becomes

             T= mg – ma = 8 × 9.8 – 8 × 3=54.4 N

 

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