1. SURFACE TENSION
Lecture 1
By Vidyaraashi
Have you ever thought about
why can a steel needle float but a larger piece of steel sink?
why can inscet walks on water ?
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The Surface of any liquid behaves as though it is covered by a
streched membreane. small insects can walk on water without
getting wet. the membrane is obviosly quite strong.... It will
support dense objects, provided they are small in size and of
right shape --- a needle, a small square of alluminium sheet, a
razor blade, a container made of fine wire gauge and small
insects.
The strenght of the surface tension on the membrane can be
imagined to arise from a set of forces acting at each point of the
surface parallel to the surface, like the skin of a drum.
The cohessive force acts between the molecules of the substance
without chemical bonding.
cohessive :- attaractive forces between "like" molecules

2. T
he surface of a liquid behaves as am elastic rubber
membrane(spring). If you try to pull a molecule from the surface
an attractive restoring force due to cohessive forces acts on the
molecule. If a surface molecule is depressed slightly into the
liquid, then molecule experiences a repulsive restoring force.
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why are soap bubbles spherical?
How do you make lead shots(small spherical balls of lead)
what is the difference between wet and dry hair on a brush?
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3. surface of a liquid acts like an elastic skin minimum
surface energy minimum surface area of a given volume.
generally, a system under the influence of forces movesd towards
as equilibrium configuration that corresponds to minimum
potential energy. The spehere contains the most volume for the
least area minimum surface potential energy, there are no
cubic rain drops.
The force a liquid surface exerts on an object that is in
intimate contact with it is directly proportional to the length of
the line of contact L. The constant of proportionality is T is
called the coefficient of surface tension of the liquid.
Hence the coefficient of surface tension can be expressed as

4. Floating Needle (Not a buoyancy phenomenon)
why is it better to use hot soapy water to wash clothes ?
The strenght of the membrane varies for different liquids, eg it
is much less for soapy solution than pure water. Substances that
reduce surface tension of a liquid are called surfactants. Adding
soap or detergent to water reduces the surface tension.
Liquids Surface tension
1) water(20 degree C) 0.073
2) Water (100 degree C) 0.059

5. 3) Soapy Water solution (20 degree C) 0.025
Concepts through Problems
Type 1 :-
A thin circular wire of diameter D and total mass M is gently
pulledvertically from a water surface by a sensitive spring (K).
when the spring is streched by X from its equilibrium position in
air, the ring is on the verge of being pulled free from the water
surface. Find the coefficient of surface tension T of the water.
Neglect the mass of the water lifted.
The

6. lenght of contact L with the water surface is twice the
circumference of the ring since there is water on both sides of
the ring.
Type 2 :-
The base of an insects leg is approximately spherical in shape
with a radius R. The mass of the insect is M and is supported
equally by six legs. Calculate the contact angle theta as shown in
the diagram. The coefficient of surface tension T.
Assumption :- The surface tension acts around ther circle of
radius R, where R is the radius of a leg. This is not accurate,
since the radius of the surface depression is not precisely the
radius of the leg.
Type 3 :-

7. A thin metal disc of radius R floats on water surface and bends
the surface downwards along the perimeter making an angle
theta with the verticle edge of the disc. If the disc displaces a
weight of water W and surface tension of the water is T , then
the weight of the metal disc is ?
Type 4 :-
There is a horizontal film of soap solution. On it a thread is
placed in the form of a loop. The film is pierced inside the loop
and the thread becomes a cirular loop of radius R. If the surface
tension of the loop be T, then what will be the tension in the
thread?

8. Type 5 :-
A liquid is filled into a tube with semi- elliptical cross- section as
shown. The ratio of the surface tension forces on the curved part
and the plane part of the tube is verticle postion will be ?
Some types of surfaces discussed below
a) Needle

9. b) Hollow Disc
c) Thin ring

10. d) Circular Plate
e) Square frame

11. f) Square plate
Factors
affecting the Surface Tension
Temperature :-
The surface tension of the liquid decreases with the rise in
temperature

12. Surface Energy
The molecule on the liquid surface experiences net downward
force. so to bring a molecule from the interior of the liquid to
the free surface, some work is required to be done against the
intermolecular force of attraction, which will ne stored as
potential energy of the molecule on the surface. The potential
energy of the surface molecules per unit area of the surface is
called surface energy.
Unit :-
Dimension :-
If a rectangular wire frame say ABCD, equipped with a sliding
wire LM dipped in soap solution, a film is formed over the frame.
due to the surface tension, the film will have a tendency to shrink
and therby the sliding wire LM will be pulled inward direction.
However the sliding wire can be held in this position under a

13. force F, which is equal and opposite to the force acting on the
sliding wire LM all along its length due to surface tension in the
soap film.
If T is the force due to the surface tension per unit length, then
Here L, is the length of the sliding wire LM. The length of the
sliding wire has been taken as 2L, why because the film has got
two free surfaces.
Suppose that the sliding wire LM is moved through a small
distance X, so as to take the position . In this process,
the area of the film increases by

14. to do so the amount of work done will be
Now if the temperature of the film remains constant in this
process, this work done is stored in the film as its surface energy,
from the above equation we have
so the surface tension may be defined as the amount of work
done in increasing the area of the liquid surface by unity against
the force of surface tension at constant temperature.