Tension Force Formula - How to calculate tension Force?

Tension is the pulling force transmitted along the length of a string, cable, chain, or similar one-dimensional object or at each end of a rod or similar three-dimensional object. It can also be described as the action-reaction force pair acting at both ends of these elements.

What is Tension Force?

Tension is the force transferred through a rope, string, or wire when it is pulled by forces from opposite directions. This force acts along the length of the wire, applying an equal pull on the objects at both ends.

• It is the external agent that is capable of changing the state of rest or motion of a particular object.

• Tension Force is transmitted through the rope or chain when they were pulled from either end or both ends together, which helps balance with the other forces in the system of containing ropes and chains. 

• The force that is transmitted through a rope, string, or wire when pulled by forces acting from the opposite side is called Tension force. For example: During the game of "Tug of War" both teams applied opposite forces to pull the rope.

• Towing cars and pulling buckets from wells are also examples of tension force. The tension force in a rope allows us to transfer our force through the rope to lift the object. Tension force is generally represented by "T".

Example of Tension Force

In daily life, there are various examples of tension force. Some of those examples are as follows:

• When a person pulls a sled using a rope, the rope experiences tension forces as it stretched tight between the sled and the other end.
• In hosting a flag, a rope is used to hold the flag in the air, which is pulled against a pully and creates tension.
• In the zipline, the weight of a person is supported by the tension of the zipline.
• Bungee jumping is also an example of tension force, where the difference between life and death is only supported by the tension in the bungee rope.
• Guitar strings are stretched between the bridge of the guitar and tuning pegs, which put these strings in tension and these tensed strings help the guitarist to create a symphony of music.

Tension force formula- Physics

The formula of tension in the string or the rope attached to a body is discussed below:

• T = W + ma     [When body is travelling upward]
• T = W - ma     [When body is travelling downward]
• T = W             [When tension is equivalent to body weight]

where,

• T  is Tension Force
• W is Weight of the body, (W = mg)
• a is acceleration
• m is mass

Unit and Dimension of Tension Force

• As tension is a force as well, it has the same unit and dimension as a force. The SI unit of Tension force is "Newton(N)" which can also be represented by Kgms^-2. Other than Newton, in the CGS system "dyne" is also a unit of tension force. 

• The dimension of Tension Force is [M¹L¹T^-2] where [M],[L], and [T] are the dimensions of mass, length, and time respectively.   

Applications of Tension Force

There are various applications of tension force in the life of a common being, some of these applications are as follows:

1. Crane Machine
2. Towing Vehicles
3. Pulling Water from Well
4. Tug of War

1. Crane Machine

The most useful application of tension force can be seen in the construction and logistic industries in the form of cranes. In the cranes, one of the balancing forces which counter the weight of the object is the tension force. 

2. Towing Vehicles

Towing vehicles is nothing but the mini crane on the back of a small utility vehicle, which helps us tow the other vehicles when they are immobile due to some maintenance issue or accident.

3. Weight Balance

Weight balance is a piece of equipment that helps us find the weight of the object by balancing it against the spring placed in the core of that equipment.

4. Pulling Water from Well

Pulling water from the well is the most used application of tension force, where the tension of the rope is distributed with the help of a pulley to bring out the water from the deep well, which otherwise is not easily possible.

5. Tug of War

Tug of War is a fun game in which two teams participate and pull a rope from both ends until they succeed in pulling the defined amount of the rope from the other team's side to their side, which is only possible due to the understanding of the tension force.

Solved Examples

1. A 2 kg box is being pulled across a frictionless surface by a rope. If the rope is being pulled with a force of 10 N, what is the tension in the rope?

Here, the forces acting on the box are its weight (W = mg) acting downwards, normal reaction acting in an upward direction, and the tension force (T) in the rope acting horizontally. 

As there is no friction, (surface is frictionless)

Thus, 

Tension Force on Rope = Force Applied on Rope = 10 N

Therefore, the tension in the rope is 10 N.

2. A body of 4 kg mass is hanging at the end of a thread. If the acceleration of the mass is acting as 7m/s²in the upward direction. Find the tension in the thread.

m = 4kg, a = 7m/s² and g = 9.8m/s².

Now, W = mg

⇒ W = 4×9.8

⇒ W = 39.2 N

As acceleration is in upward direction,

T = mg + ma

⇒ T = 39.2 + 4×7

⇒ T = 39.2 + 28

⇒ T = 67.2 N

Therefore, tension in thread will be 67.2 N  

3. A body of 9 kg mass is hanging at the end of the string. If the acceleration of the mass is 8m/s² in a downward direction. Calculate the tension in the thread.

Given,

• a = 8 m/s²
• m = 9 kg
• g = 9.8 m/s²

As the body is moving downward direction 

T = W - ma

⇒ T = mg - ma

⇒ T = (9×9.8) - (9×8)

⇒ T = 16.2 N

Therefore, tension will be 16.2 N

4. A light and indestructible string supports a body of mass 25kg hanging from its lower end. If the top end of the string is attached to the hook on the ceiling. What is the tension in the string?

Given,

• m = 25 kg 
• g = 9.8 m/s².

As the body is not moving 

T = W

⇒ T = mg

⇒ T = 25×9.8 N

⇒ T = 245 N

Therefore, tension will be 245 N

5. A squirrel of mass 500 g climbs up a light vertical string suspended from a hook with an acceleration of 9m/s². Find the tension on the string.

Given,

• m = 500 g = 0.5 kg
• a = 9 m/s²
• g = 9.8 m/s²

As squirrel is moving up 

T = W + ma

⇒ T = mg + ma 

⇒ T = (0.5×9.8) + (0.5×9)

⇒ T = 4.9 + 4.5

⇒ T = 9.4 N

Therefore, tension will be 9.4 N

Conclusion

The tension formula, written as T = mg ± ma, helps to find the force in a string or rope holding an object. Here, 'T' is the tension, 'm' is the object's mass, 'g' is the force of gravity (around 9.8 m/s²), and 'a' is how fast the object is speeding up or slowing down.If the object is moving up, you add the force from gravity and the extra force needed to lift the object (T = mg + ma). If the object is moving down, you subtract the extra force because gravity is already helping it fall (T = mg - ma).

Related Reads,

• Surface Tension
• Net Force
• Net Force Formula
• Gravity
• Exploring forces
• Interaction of forces