The force that transmitted along the length of the flexible medium such as rope, cable, string etc. when it is pulled or hung by the force acting on the heavy object is known as **tension force**. In this article we are going to study **how to calculate tension force.**

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**Calculating the tension force**

Let us calculate the **tension force** by considering the mass of the object “m” and the object of acceleration “a”.

From **Newton’s second law of motion**, we know that

F=m*a

Here the force is called the **tension force** so that the equation becomes,

T=m*a

Case (i) : Let the weight of the object(w) acts downwards and the tension force(T) on the rope acting upwards and acceleration due to gravity is “g”.

Then the tension force will be calculated as

T = W

But we know W = m*g

i.e., T = m*g

Case (ii): When the object is with certain **acceleration** in downward direction, the weight of the object is greater than the tension, then the equation becomes,

W – T = ma

But W = m*g,

(m*g) – T = m*a

T = m*g – m*a

Or T = m (g – a)

Case (iii): Now the body is accelerating in upward direction and the weight must be lesser than the tension. Then the equation becomes,

T – W = m*a

T – (m*g) = m*a

T = m*g + m*a

Or T = m (g + a)

Case (iv): The **tension force** not only depends on the mass of the object and acceleration but also on the angle of suspension. When an object of mass “m” with suspended vertically with an angle θ, the tension force can be calculated as below.

Here there is only one string and the resolving force is in the Y direction.

T = m* g

T sin (θ) = m* g

Similarly ; when the object is clamped horizontally with the two masses and makes angle θ_{1} and θ_{2 }then the tension force will be

T_{1} cos (θ) = T_{2 }cos (θ)

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**Some solved examples**

**An object of mass 24 kg is hanging from the lower end of a light** **inextensible cable. If the upper end of the cable is attached to the roof with the help of a hook, then calculate the tension force acting on the cable?**

Solution:

Given: mass of the object = 24kg

Acceleration due to gravity = 9.8 m/s

As the object is just suspended by the roof and there is no movement of the object. Hence the tension force acting on the string is equal to the weight of the object.

T = W = mg = 24 × 9.8

= 235.20 N

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**Calculate the mass of the object when it is pulled by a rope and the object is moving in downward direction with the acceleration 8 m/s**^{2}. If the tension force acting on the rope is 286 N. (Take acceleration due to gravity as 10m/s^{2}).

^{2}. If the tension force acting on the rope is 286 N. (Take acceleration due to gravity as 10m/s

^{2}).

**Solution:**

** **Given: Tension force acting on the rope = 286N

Acceleration of the object acting in downward direction = 8m/s^{2}

Acceleration due to gravity = 10m/s^{2}

We know that for an object accelerating in downward direction the tension force is given by

T = mg – ma

To calculate the mass of the object; rearranging the equation we get

T = m (g – a)

**An object of mass 9kg is hung by a cable accelerating in upward direction. If the tension force acting on it is 143N then find out the acceleration of the object acting in upward direction. ( Take the acceleration due to gravity as 10m/s**^{2}).

^{2}).

Solution:

Given: mass of the object = 9kg

Tension force = 143N

Acceleration due to gravity = 10m/s^{2}

We know that the tension force acting on object when the it is accelerating in upward direction is

T = mg + ma

143N = (9kg × 10) + (9kg ×a)

143N = 90 + (9×a)

143 – 90 = 9a

53 = 9a

a = 5.888 m/s^{2}

**A string is attached to a kite it makes an angle of 35°. The string is neither pulled nor drag by anyone. The net force acting is 60N. calculate the tension on the string.**

Solution:

Given : angle of suspension = 35°

Net force = m * g = 60N

T sin(35) = 60

T (0.5735) = 60

T = 104.620 N

**Frequently Asked Questions : **

**Why the Work done by the tension is always zero explain?**

Answer : The work done by anything is given by

W = FS

Where F is the force and S is the displacement

This means that the work done depends on both force and the displacement. But tension is force where there will be no displacement.

i.e.; S = 0

W = F × 0

W = 0

Hence the work done by the tension force will always be zero.

** Tension force is a contact force explain?**

Answer : A contact force is a force exerted by the two object that are in contact with each other. In tension force the force is transmitted through a cable or rope or sting when it is tightly pulled by the forces acting opposite to each other. There is a contact between the transmitting medium and the object. So the tension force is a contact force.

**How does the gravity affect the tension force?**

Answer : Tension force always acts in the direction opposite to the gravitational pull. If an object is hanging it must be balanced by the tension force otherwise it must will accelerate in the downward direction due to the gravity.

**How does the tension depends on the mass?**

Answer: When an object is hung by a rope or a string or a cable then only tension will be produced. It is clear that when there is no object pulled by the rope there will be no tension acting on the rope. So the tension is always proportional to the mass of the object.

**When an object of certain mass m is pulled with a help of a rope by a person A. Person B pulls the same object in the opposite direction then what will the tension force acting on the rope of person A ?**

Answer : From the equation of tension force; the tension force acting on the side of person A is

T_{A} = m*a

The tension force from the side of person B is

T_{B} = m*a

The net force will be

F_{net }= T_{A }– T_{B}

Because the force T_{B }is acting in opposite direction of T_{B}_{}

Rearranging the above equation we get the tension on the rope A.

T_{A }= F_{net} + T_{B}