Things to Remember

• Tension is a force that works in medium lengths, especially those that are flexible, such as rope or cord.
• Tension force remains a gravitational force.
• Total energy can be calculated as: Fnet = T − W = 0
• T = W ± ma
• If the body is moving upwards then the tension will be referred to as the T = W + ma.
• When the body goes down, the thickness is the same as T = W – ma.
• T = W if the discomfort is equal to body weight.

At the atomic level, when atoms or molecules are pulled apart from each other and gain potential energy with a restoring force still existing, the restoring force might create tension. Each end of a string or rod under such tension could pull on the object it is attached to, in order to restore the string/rod to its relaxed length.

Tension can be easily explained in the case of bodies hung from chain, cable, string etc. It is represented by T (occasionally also, denoted as Ft).

If such a hung body moves vertically with an acceleration a, then; 

T = W ± ma

Where, W is the weight of the body and m is the mass of the body 

Case (i) If the body is moving upwards, with acceleration a, the tension; T = W + ma 

Case (ii) If the body is moving downwards, with acceleration a, the tension; T = W – ma

 Case (iii) If the body is just suspended (not moving), the tension; T = W.

Case (iv) If the body moves up or down with uniform speed, tension; T = W

The weight of the object is W = mg. 

Therefore, tension formula can be modified as:

T=m(g±a)

Where, m = mass of the body, g = acceleration due to gravity, a = acceleration of the moving body.

As tension is a force, its SI unit is newton (N).

Example:

A light and inextensible string support a body of mass of 15 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?

Solution:

As the body is not moving and just suspended, the tension in the string will be equal go the weight of the body. m = 15 kg

T = W = mg = 15 × 9.8 = 147 N

Example:

A monkey of mass 10 kg climbs up a light vertical string suspended from a hook with an acceleration of 2 m/s2. Find the tension in the string (take g = 10 m/s2)

Solution:

m = 10 kg, g = 10 m/s2, a = 2 m/s²

As the monkey moves up with an acceleration, the tension in the string will be equal to the apparent weight of the monkey.

i.e., T = m (g + a) = 10 (10 + 2) = 120 N

Question:

If M1 = 4 kg and M2 = 6 kg in the following figure, then T2 equals:

Options:

(a) 98 N

(b) 39.2 N

(c) 58.8 N

(d) 19.6 N

Answer: (c)

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