UNIT- IV
PROPERTIES OF MATTER
Elasticity
Elasticity is the property of solid materials to return to their original shape and size after the forces
deforming them have been removed.
Ability of a deformed material body to return to its original shape and size when the forces causing
deformation are removed. Most solids show some elastic behaviour, but there is usually a limit—the
material's “elastic limit”—to the force from which recovery is possible. Stresses beyond its elastic
limit cause the material to yield, or flow, and the result is permanent deformation or breakage. The
limit depends on the material's internal structure; for example, steel, though strong, has a low elastic
limit and can be extended only about 1% of its length, whereas rubber can be elastically extended up
to about 1,000%. Robert Hooke, one of the first to study elasticity, developed a mathematical
relation between tension and extension.
Elastic limit:The ability of a solid to return to its original shape or form after being subject to strain. Most solid
materials display elasticity, up to a load point called the elastic limit; loads higher than this limit
cause permanent deformation of the material.
elastic limit, maximum stress or force per unit area within a solid material that can arise before the
onset of permanent deformation. When stresses up to the elastic limit are removed, the material
resumes its original size and shape. Stresses beyond the elastic limit cause a material to yield or
flow. For such materials the elastic limit marks the end of elastic behaviour and the beginning of
plastic behaviour. For most brittle materials, stresses beyond the elastic limit result in fracture with
almost no plastic deformation.
Plasticity:plasticity, ability of certain solids to flow or to change shape permanently when subjected to
stresses of intermediate magnitude between those producing temporary deformation, or elastic
behaviour, and those causing failure of the material, Plasticity enables a solid under the action of
external forces to undergo permanent deformation without rupture. Elasticity, in comparison, enables
a solid to return to its original shape after the load is removed. Plastic deformation is a property of
ductile and malleable solids. Brittle materials, such as cast iron, cannot be plastically deformed,
though at elevated temperatures some, such as glass, which is not a crystallized solid.
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Deforming Forces
External forces acting on a body, bring about a change in its state or configuration. The latter is
possible when the body is not free to move, but the molecules are compelled to change their
t
positions. Such forces are called deforming forces. These forces bring about a change in the length,
volume or shape. On applying the forces, the interatomic distance becomes more than ro, thus
increasing their potential energy (leading to instability
instability).
). On removing the forces, the system tends to
regain a minimum P.E. and as a result, attractive forces develop, restoring them to their original
shape. The same applies when a body is subjected to a compressional force, where repulsive forces
develop and restore the system to equilibrium.
Restoring force
Restoring force, in a physics context, is a variable force that gives rise to an equilibrium in a
physical system. If the system is perturbed away from the equilibrium, the restoring force will tend
to bring the system back toward equilibrium.
Stress
Stress
ess is a measure of the internal force an object is experiencing per unit cross sectional area.
Hence, the formula for calculating stress is the same as the formula for calculating pressure:
where σ is stress (in Newtons per square metre or, equivalently
equivalently,, Pascals). F is force (in Newtons,
commonly abbreviated N), and A is the cross sectional area of the sample.
The stress applied to a material is the force per unit area applied to the material. The maximum stress
a material can stand before it breaks is ccalled the breaking stress or ultimate tensile stress.
Tensile means the material is under tension. The forces acting on it are trying to stretch the material.
Compression is when the forces acting on an object are trying to squash it.
The equation below is used to calculate the stress.
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PROF., DEPTT. PHYSICS
LNCT, JABALPUR
stress = stress measured in Nm-2 or pascals (Pa)
F = force in newtons (N)
A = cross-sectional area in m2
There are three main types of stress. If we stretch or compress an object, we are subjecting it to
a tensile stress.. If an object is subjected to a force along an entire surface, changing its volume,
then it is said to be experiencing a bulk stress.. Finally, if the force is acting tangentially to the
surface, causing it to twist, then we are subjecting it to a shear stress.
Strain
The ratio of extension to original length is called strain it has no units as it is a ratio of two lengths
measured in metres.
strain = strain it has no units
L
L =extension measured in metres
L = original length measured in metres
.
Hooke's Law
Hooke's law of elasticity is an approximation that states that the Force (load) is in direct proportion
with the extension of a material as long as this load does not exceed the elastic limit. Materials for
which Hooke's law is a useful approxi
approximation are known as linear-elastic
The relation is often denoted
The work done to stretch a wire or the Elastic Potential Energy is equal to the area of the triangle on
a Tension/Extension graph, but can also be expressed as
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PROF., DEPTT. PHYSICS
LNCT, JABALPUR
Hooke’s Law:the law stating that the stress on a solid substance is directly proportional to the strain produced,
provided the stress is less than the elastic limit of the substance.
Hooke’s Law is a law that shows the relationship between the forces applied to a spring and its
elasticity. The relationship is best explained by the equation F=
F=-kx.
kx. F is force applied to the spring
this can be either the strain or stress that acts upon the spring
spring.. X is the displacement of the spring
with negative value demonstrating that the displacement of the spring when it is stretched. When the
spring is compressed the the x value is positive. K is the spring constant and details how stiff the
spring is. This law gets its name from the Robert Hooke the 17th century physicist who discovered it
in 1660 and published a work that included a description of it in 1678.
The principle that the stress applied to stretch or compress a body is proportional to the strain or to
the change in length thus produced, so long as the limit of elasticity of the body is not exceeded.
young modulus.
For the description of the elastic properties of linear objects like wires, rods, columns which are
either stretched or compressed, a convenient parameter is the ratio of the stress to the strain, a
parameterr called the Young's modulus of the material. Young's modulus can be used to predict the
elongation or compression of an object as long as the stress is less than the yield strength of the
material.
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PROF., DEPTT. PHYSICS
LNCT, JABALPUR
surface tension
Property of a liquid surface that causes it to act like a stretched elastic membrane Its strength
depends on the forces of attraction among the particles of the liquid itself and with the particles of
the gas, solid, or liquid with which it comes in contact. Surface tension allows certain insects to
stand on the surface of water and can support a razor blade placed horizontally on the liquid's
surface, even though the blade may be denser than the liquid and unable to float. Surface tension
results in spherical drops of liquid, as the liquid tends to minimize its surface area.
The property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of
its molecules.
The cohesive forces between liquid molecules are responsible for the phenomenon known as surface
tension. The molecules at the surface of a glass of water do not have other water molecules on all
sides of them and consequently they cohere more strongly to those directly associated with them (in
this case, next to and below them, but not above).).
Cohesion and Surface Tension
The cohesive forces between molecules in a liquid are shared with all neighboring molecules. Those
on the surface have no neighboring molecules above and, thus, exhibit stronger attractive forces
upon their nearest neighbors on and below the surface. Surface tension could be defined as the
property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature
of the water molecules.
Due to the surface tension, small objects will "float" on the surface of a fluid, as long as the object
cannot break through and separate the top layer of water molecules. When an object is on the surface
of the fluid, the surface under tension will behave like an elastic membrane.
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LNCT, JABALPUR
Examples of surface tension
Walking on water: Small insects such as the water strider can walk on
water because their weight is not enough to penetrate the surface.
Floating a needle: A carefully placed small needle can be made to float on the surface of water even
though it is several times as dense as water. If the surface is agitated to break up the surface tension,
then needle will quickly sink.
Don't touch the tent!: Common tent materials are somewhat rainproof in that the surface tension of
water will bridge the pores in the finely woven material. But if you touch the tent material with your
finger, you break the surface tension and the rain will drip through.
Soaps and detergents: These help the cleaning of clothes by lowering the surface tension of the water
so that it more readily soaks into pores and soiled areas.
Washing with cold water: The major reason for using hot water for washing is that its surface
tension is lower and it is a better wetting agent. But if the detergent lowers the surface tension, the
heating may be unneccessary.
Why bubbles are round: The surface tension of water provides the necessary wall tension for the
formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into
spherical shapes.
Cohesive And Adhesive Forces
Cohesive Forces
Cohesive forces are the intermolecular forces (such as those from hydrogen bonding and Van der
Waals forces) which cause a tendency in liquids to resist separation. These attractive forces exist
between molecules of the same substance. For instance, rain falls in droplets, rather than a fine mist,
because water has strong cohesion which pulls its molecules tightly together, forming droplets. This
force tends to unite molecules of a liquid, gathering them into relatively large clusters due to the
molecules' dislike for its surrounding.
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LNCT, JABALPUR
Adhesive Forces
Adhesive forces are the attractive forces between unlike molecules. They are caused by forces acting
between two substances, such as mechanical forces (sticking together) and electrostatic forces
(attraction due to opposing charges). In the case of a liquid wetting agent, adhesion causes the liquid
to cling to the surface on which it rests. When water is poured on clean glass, it tends to spread,
forming a thin, uniform film over the glasses surface. This is because the adhesive forces between
water and glass are strong enough to pull the water molecules out of their spherical formation and
hold them against the surface of the glass, thus avoiding the repulsion between like molecules.
Effects of Cohesive and Adhesive Forces
When liquid is placed on a smooth surface, the relative strengths of the cohesive and adhesive forces
acting on that liquid determine the shape it will take (and whether or not it will wet the surface). If
the adhesive forces between a liquid and a surface are stronger, they will pull the liquid down,
causing it to wet the surface. However, if they cohesive forces among the liquid itself are stronger,
they will resist such adhesion and cause the liquid to retain a spherical shape and bead the surface.
Capillarity:Capillarity or capillary action is the ability of a narrow tube to draw a liquid upwards against
the force of gravity.
Examples
Wicking is the absorption of a liquid by a material in the manner of a candle wick. Paper towels
absorb liquid through capillary action, allowing a fluid to be transferred from a surface to the towel.
The small pores of a sponge act as small capillaries, causing it to absorb a comparatively large
amount of fluid. Some textile fabrics are said to use capillary action to "wick" sweat away from the
skin. These are often referred to as wicking fabrics, after the capillary properties of candle and lamp
wicks.
With some pairs of materials, such as mercury and glass, the intermolecular forces within the liquid
exceed those between the solid and the liquid, so a convex meniscus forms and capillary action
works in reverse.
viscosity
viscosity, resistance of a fluid (liquid or gas) to a change in shape, or movement of neighbouring
portions relative to one another. Viscosity denotes opposition to flow. The reciprocal of the viscosity
is called the fluidity, a measure of the ease of flow. Molasses, for example, has a greater viscosity
than water. Because part of a fluid that is forced to move carries along to some
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LNCT, JABALPUR
The viscosity of liquids decreases rapidly with an increase in temperature; the viscosity of gases
increases with an increase in temperature. Thus, upon heating, liquids flow more easily, whereas
gases flow more sluggishly.
Coefficient of Viscosity
Consider a liquid flowing over a horizontal solid surface in the form of parallel layers. The layer in
contact with the solid surface in the form of parallel layers. The layers in contact with the solid
surface is found to be at rest and as we move up, the velocity of the layers goes on increasing and the
layer at the top possesses maximum velocity.
Now consider two parallel layers P and Q at distances x,x+dx from the solid surface moving with the
velocities v and v+dv respectively.Then, dv/dx denotes the rate of change of velocity with the
distance in the direction of increasing distance and it is called the velocity gradient.The relation
motion between the two layers can take place only,if some external force acts between them.Due to
viscosity, a force F acts in opposite direction to destroy the relative motion.According to newton,the
viscous force F depends upon the following factors
1. It is directly proportional to the area of the layers in contact ie F is directly proportional to A
2. It is directly proportional to the velocity gradient between the layers ie F is directly proportional to
dv/dx
Combining these two factors we have
F is directly proportional to A x dv/dx
or F = [eta] x A x dv/dx
where [eta] is a constant depending upon the nature of the liquid and is called the coefficient of
viscosity.
Hence, The ratio of the shearing stress to the velocity gradient is a measure of the viscosity of the
fluid and is called the coefficient of viscosity [eta]
Streamline flow:
The flow of a fluid is said to be streamline (also known as steady flow or laminar flow), if every
particle of the fluid follows exactly the path of its preceding particle and has the same velocity as
that of its preceding particle when crossing a fixed point of reference.
Turbulent flow:
The flow of a fluid is said to be turbulent or disorderly, if its velocity is greater than its critical
velocity. Critical velocity of a fluid is that velocity up to which the fluid flow is streamlined and
above which its flow becomes turbulent. When the velocity of a fluid exceeds the critical velocity,
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LNCT, JABALPUR
the paths and velocities of the fluid particles begin to change continuously and haphazardly. The
flow loses all its orderliness and is called turbulent flow.
Stokes' law
the law that the force that retards a sphere moving through a viscous fluid is directly proportional to the
velocity of the sphere, the radius of the sphere, and the viscosity of the fluid.
When any object rises or falls through a fluid it will experience a
viscous drag, whether it is a parachutist or spacecraft falling through
air, a stone falling through water or a bubble rising through fizzy
lemonade. The mathematics of the viscous drag on irregular shapes
is difficult; we will consider here only the case of a falling sphere.
The formula was first suggested by Stokes and is therefore known as
Stokes' law.
Consider a sphere falling through a viscous fluid. As the sphere falls
so its velocity increases until it reaches a velocity known as the
terminal velocity. At this velocity the frictional drag due to viscous
forces is just balanced by the gravitational force and the velocity is
constant (shown by Figure 2).
At this speed:
Viscous drag = 6πηrv = Weight = mg
The following formula can be proved (see dimensional proof)
Frictional force (F) = 6πηrv (Stokes' law)
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LNCT, JABALPUR
Critical Velocity
Critical velocity is the velocity of a liquid flow upto which its flow is streamlined and after which its
flow becomes turbulent. The critical velocity depends on coefficient of viscosity 'h', density of the
liquid 'r', and radius of the tube (r). Using the methods of dimensions, one can show that
where k is constant of proportionality
Reynolds Number (NR)
The Reynolds number is a pure number that determines the nature of flow through a pipe. The
critical velocity 'VC' is given by
If the value of Reynolds Number NR lies between 0 to 2000, the flow of liquid is streamline or
laminar (the layers of liquid glide or slip over one another like sheets or laminar). If the value of NR
is greater than 3000, the flow is turbulent. For values inbetween, the flow is not steady and changes
from one to another.
Mr. INDRAPAL PATEL, ASST. PROF., DEPTT. PHYSICS
LNCT, JABALPUR