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Tension

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Forces can be applied to solids. For rigid solids, forces can be applied in the form of compression or tension forces. Compression forces act to decrease the length of a solid, whereas tension forces act to increase the length. Tension forces, but not compression forces, can also be applied to non-rigid solids, such as a piece of elastic. 

What is Tension?

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Tension is defined as a kind of force which is responsible for the stretching of a material. Let us see some example of tension which are common in our day to day life.
  • Cable used in a crane
  • Stretched rubber band
  • A bolt, when the nut is tightened
A tensile force, that is, one producing tension increases the length of the material on which it acts. In the case of tension forces, a solid object usually has a limit of tolerance, known as the tensile limit, above which the material fractures.

Formula

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Tension can be represented by T, the formula for calculating the tension force is given as,

T = W + ma
or
T = mg + ma
T = m (g + a)
Where W = weight of a material
          m is the mass
          a is the acceleration

Surface Tension

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Surface tension is a characteristic property of a liquid. In this property, all liquids have a tendency to contract its surface in order to  acquire minimum surface area. So this surface appears like a stretched membrane. Quantitatively surface tension is,

T = $\frac{F}{l}$

Where F is the force acting on an imaginary line of length l, drawn tangentially to the liquid surface at rest.

Surface tension is also defined as the work done per unit area in increasing the area of the liquid film at constant temperature.

T = $\frac{Work\ done}{Expansion\ in\ area}$

How to Find Tension?

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Some solved problems of tension are given below:

Solved Examples

Question 1: An elevator of mass 500kg is hanging in a cable. Calculate the tension in the cable if  the elevator is moving with an upward acceleration of 2m/s2?

Solution:
 
Given parameters are,
m = 500kg, a = 2m/s2, g = 9.8m/s2
T = m (g + a)
T = 500 (9.8 + 2) = 5900N

 

Question 2: An object of mass 150kg is suspended in a rope, if that object is moving with a downward acceleration of 1.5m/s2, calculate its tension?

Solution:
 
Given that,
m = 150kg, a = -1.5m/s2, g = 9.8m/s2
T = m (g + a)
T = 150 (9.8 - 1.5) = 1245N