Surface Tension

 

We observe many things in our day-to-day life.Surface tension Phenomenon is one among them. Often we confuse the Phenomena of Surface tension with Buoyancy. Both the phenomena are entirely different to each other in the sense, in Buoyancy a portion of the body gets dipped in the liquid whereas in Surface tension the body will be remaining on the layer of water without getting wet.
Let us observe these leaves on the surface of water. We could see them moving in the water without getting wet.

For these leaves to be on the layer, there should be some force acted by the upward layer of water which keeps the leaf on the surface. This is nothing but the Surface tension.
Let us study more about the Surface tension in this section. 

What is Surface Tension?

The Surface tension is defined as:
The dragging force observed in the given liquid per unit length. It is given by the formula:

T = FL

where F = Force per unit length and
L = Length over which the force acts.
The Surface tension is expressed in Newton per meter.

What causes Surface Tension?

 

Surface tension is a physical property of water. Here the cohesive force keeps the water intact. Each molecule in the beaker is pulled in every direction equally by adjacent molecules.

Let us observe the following diagram:

The dragging force acts between the each molecules by the other molecule. Therefore the resulting net force is zero.
At the surface of water in a beaker, the water molecule does not have another water molecule around the sides of them. Therefore creation of internal pressure. Water molecules at the surface are pulled inwards. Top layer of liquid surface of beaker are compressed to minimum area.

Surface Tension formula

 

The Surface tension is expressed by the formula:

T = FL

Where F = Force per unit length and
L = Length over which the force acts.

To Calculate the tension we use the formula:

T = 12 ρ grh.

where h = h + r3.
Here
r = radius of the capillary tube at the liquid meniscus
h = height of the liquid in the capillary tube above the free surface of liquid in beaker.
ρ = Density of water (ρ = 1 × 10³ kg/m³ for water).

Capillarity

 

Capillarity is the phenomena observed in the capillary tube to draw the fluid upward against the force of gravity.

The Capillarity is given by the formula:

h = 2 T cosθρgr

Where h = height of liquid
σ = Surface tension
θ = Contact angle
ρ = Density of the liquid
g = acceleration due to gravity
r = radius of tube.

Examples of Surface Tension

Below are given some Illustration for Surface tension:

1. When a sewing needle or U-pin is gently placed on water surface , it floats. The water surface below the needle gets depressed slightly .The force of surface tension acts tangentially. The vertical component of the force of surface tension balances the weight of the needle or U-pin.
2. Impurities present in a liquid affects its surface tension. A highly soluble substance like salt increases the surface tension whereas sparingly soluble substances like soap decreases the surface tension.
3. When a small paper boat is placed in a glass jar containing water. Paper boat floats on the surface of water. When a drop of soap detergent is added to water. Soap molecules spreads on water surface which creates a reaction force which moves the small paper boat forward.

How to find Surface Tension

Tension is the magnitude of the pulling force exerted by a string, cable, chain, or similar object on another object.

Two masses M₁ and M₂ are attached to a string which passes over a pulley attached to the edge of a horizontal table. The mass M₁ lies on the frictionless surface of the table. Let the tension in the string be T and the acceleration of the system be a, then

T = M₁a

M₂g - T = M₂a

∴ a = M2gM1+M2

The Tension is given by:

T = M₁a = M1M2gM1+M2.

Below are given some problems Which are based on surface tension:

Solved Examples

Question 1: Three blocks masses 2kg, 3kg and 5kg are connected to each other with light strings and are then placed on a smooth frictionless surface. See fig. below. Let the system be pulled with a force F from the side of lighter mass so that it moves with an acceleration of 1ms^-2. T₁ and T₂ denote the tensions in the strings. Calculate the value of T₁ and T₂.
Solution:

Using the formula Tension T = Ma,
Where M = Mass and
           a = acceleration

For T₁ total effective mass is mass of block B₂ + mass of block B₁ and acceleration applied is of 1ms^-2.
therefore Tension T₁ = (3+5)kg × 1ms^-2 = 8 N
Similarly tension T₂ = 5kg × 1ms^-2 = 5N.

Question 2: A mass M is suspended by a rope from a rigid support at P as shown in the figure. Another rope is tied at the end Q, And it is pulled horizontally with a force F. If the rope PQ makes angle A with the vertical, then find the tension in the string PQ?
Solution:
In the triangle PLQ, QP =T, PL= mg, and LQ= F, (all are vectors ). The point Q is in equilibrium under the action of T, Mg and F.
Here, T = PQ = LQsinA
                   = FsinA.
The Tension is given by T = FsinA.