Tension Formula: Explanation and Solved Examples

The Tension Formula is commonly used to calculate the tension force exerted on any object.

• Push, pull, thrust, lift, weight, friction, and tension are all names for forces.
• Tension is the pulling force that is transmitted along the length of a flexible object, such as a string, cable, or chain.
• It can also be described as the force that is exerted on each end of a rigid object, such as a rod or beam.
• In both cases, tension is an action-reaction pair of forces, meaning that the force exerted on one end of the object is equal and opposite to the force exerted on the other end.

Key Terms: Tension, Force, Gravitational force, Action-reaction force, Tension force formula, Weight, Push or pull

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Tension

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The pulling force transmitted axially by a string, rope, chain, or similar objects, or by each end of a rod, truss member, or similar three-dimensional object, is referred to as tension.

• In Latin, the word "tension" means "stretching".
• All physical things that come into contact with one another can exert forces on one another.
• Depending on the types of objects in touch, we call these contact forces by different names.
• The force tension is what we call it when one of the things applying the force is a rope, string, chain, or cable.
• It is essential to know that tension is a pulling force because ropes cannot effectively push.
• When you try to pull anything with a rope, it becomes slack and loses the tension that allowed it to pull in the first place.
• This may seem self-evident, but when drawing the forces acting on an object, students frequently draw the force of tension in the wrong direction.
• Remember that tension can only pull on an object.

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Tension Formula

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Tension is a force acting along the length of a medium, particularly one that is flexible, such as a rope or cable.

The formula of tension is given by

\(T=mg\pm ma\)

Where

• T is the tension force
• m is the mass of the body
• g is the acceleration due to gravity
• a is the acceleration of the moving body
• mg = W is the weight of the body

Cases:

• When the body is moving upward, then the tension will be T = mg + ma
• When the body is moving downward, then the tension will be T = mg – ma
• When the tension is equivalent to the weight of the body T = mg.

Also Read: 

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Solved Examples

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Ques. A light and inextensible string supports a body of mass of 25 kg hanging from its lower end. If the upper end of the string is firmly attached to a hook on the roof, then what is the tension in the string?

Ans. Since the mass attached to the string is not moving, therefore the tension on the string is given by

T = mg

Given the mass of the body, m = 25 kg

⇒ T = 25 x 9.8 = 245 N

Ques. A body of mass 10 kg is dangling at the end of a string. If the acceleration of the body is

1. 5 m/s² in the upward direction
2. 5 m/s² in a downward direction

Find the tension in the string.

Ans. Given, the mass of the body, m = 10 kg

1. If the body moves in the upward direction, then tension in the string is given by

T = mg + ma

⇒ T = (10 x 9.8) + (10 x 5) = 148 N

2. If the body moves in the downward direction, then tension in the string is given by

T = mg - ma

⇒ T = (10 x 9.8) - (10 x 5) = 48 N

Also Read: 

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Things to Remember

• Tension is a force acting along the length of a medium, particularly one that is flexible, such as a rope or cable.
• Tension force is always a pulling force.
• The net force acting on an object can be calculated as F_net = T − W = 0
• The formula of tension force is given by T = W ± ma = mg ± ma
• If the body is moving upward, the tension will be T = W + ma. 
• When the body is moving downward, the tension equals T = W – ma. 
• T = W if the tension is equal to the weight of the body.