How to Calculate Tension Force? Check Formula and Examples

Tension force is the force applied from the opposite side when a string or wire is being pulled. The tension force is directed over the entire length of the string.

Apart from the strings or wires, cables and ropes can also be used to transmit force to the length of the rope or the cable. Tension force is always a pull force as pushing the rope will result in slacking of the rope that causes the rope to lose the tension force responsible to keep the rope intact to be able to pull. In general conditions, when the mass of the rope is not specified, it is considered to be negligible, and hence the force is transmitted perfectly from one end of the rope to the other.

Tension Force

Figure: Tension Force illustration

Tension Force: Formula

Tension force for any given condition can be calculated using the universal equation for tension:

Tension Force (T) = mg + ma

Where,

m is the mass in kg

a is the acceleration in m/s2

g is the gravitational force (~9.8m/s2)

Tension: Equations

As the Tension force is a pulling force on the body, the formula while the body is moved upwards or downwards can be as:

  1. If the body is moving upwards: T = W + ma
  2. If the body is moving downwards: T = W- ma

Tension Equations

Newton’s Laws in Tension Force

Newton’s 3rd law states that every action has an equal and opposite reaction. Hence, in the case of an object being pulled by a rope with a force F N, there will be an equal and opposite force applied by the body that pulls the rope from both ends. This proves that Newton’s 3rd law finds its application while determining the tension force of the string.

Tension Force: Daily Life Examples

In daily life, we come across various situations where the tension force is being used, but we are unaware of the term. A few daily life examples where the tension force is applied are discussed further:

  • Car Towing: When the towing vehicle applies force on the taut chain (the connecting link between the 2 vehicles), the force applied on the chain is known as the tension force. The force applied is through the engine of the towing vehicle that is transmitted through the chains to the vehicle being towed and once the force applied is sufficient to pull the vehicle, the vehicle is towed.

Car Towing

  • Tug of War: Many of us have played tug of war, where 2 teams compete by pulling the rope on their ends. The force applied by each team on their ends is a pull force and the force developed in the rope to resist until the tensile strength is reached is the tension force.

Tug of War

  • Cranes: Most of the construction sites use cranes to lift heavy slabs or materials. When the cranes make use of a hook and a rope arrangement to transfer the materials, the rope develops a tension force. The total load that a crane can carry is calculated based on the tensile strength of the rope being used and the strength of the hook. This is one of the major applications of the tension force in the industries.

Cranes

  • Elevators: When we use the elevators, either for going up or down the floors, the force by which the compartment of the elevators is suspended is the tension force. Now, while moving against the gravity i.e., moving up the floors, the tension force will be m(g+a), while moving in the direction of gravity, the tension force in the cable will be m(g-a).

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