## Wednesday, December 17, 2014

### Surface Tension and Concept Related Problems

Surface tension is the property of a liquid because of which the surface behaves like a stretch the elastic membrane. Surface tension is due to the inter molecular force of attraction between the molecules of the liquid. The molecular force is always an attractive force. The molecular force of attraction between the similar kind of molecules is called a cohercive force and the molecular force of attraction between the different kinds of molecules is called as an adhesive force. Both of them are  always an attractive forces.

Each molecule can influence the surrounding molecules up to certain distance and this particular distance is called as a molecular range. Taking the molecule as the centre and the molecular range is a radius if a sphere is drawn,then that is called a sphere of influence. Within the sphere of influence, the given molecule can influence the surrounding molecules.

Surface tension is defined as a tangential force acting per unit length at right angles to the either side of the imagined line drawn on the free liquid Surface of  the liquid in the equilibrium state.

To understand the direction of the surface tension force,we shall imagine a line  on the surface of the liquid.  At right angles to the either side of the line if you draw a tangential line, it gives the direction of the force and the direction of the surface tension. This is treated as  a scalar physical quantity.

A small needle is able to float on the surface of the liquid because of the surface tension force.

A small insect is able to walk on the surface of the water due to the surface tension. Here the weight of the small insect is able to be compensated by the force due to the surface tension in the opposite direction , therefore it is not sinking down.

When we are using  the length in the definition of the surface tension we shall write the free length of the surface. Under different circumstances the length of the free surface will change and correspondingly the force due to the surface tension also change as shown below. When you are dealing with the wire it will how two free surfaces where as when we are dealing with a closed body like a metal body it will have only one free surface.

Problem and solution

When a wire of length l and a cross-sectional radius r is floating on the surface of the liquid, find the minimum surface of the wire such that it may not sink ?

While we are solving this problem, we shall consider that the weight is acting in the downward direction and is compensated by the force due to the surface tension. Therefore at the equilibrium state we can just equate this two forces.

Problem and solution

A liquid is contained in a vertical Tube of a semicircular cross-section find the ratio of the force of surface tension on the circular part as well as the flat part?

In solving this problem we have to count the surface length of the liquid bit carefully. The 1st case it is half of the circumference of the circle it is in the second case it the  flat part  and is nothing but the diameter of the circle.

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