Young's Modulus Setup NV6040 · Nvis Technologies Pvt. Ltd. 3 NV6040 Introduction NV6040 Young's Modulus Setup is a complete system used to determine Young’s modulus of elasticity

Young's Modulus SetupNV6040

Learning MaterialVer 1.1

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NV6040

Nvis Technologies Pvt. Ltd.

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Young's Modulus SetupNV6040

Table of Contents

1. Introduction 3

2. Features 4

3. Technical Specifications 5

4. Theory 6

5. Experiment 34

Determination of Young's Modulus of elasticity of the given sample material by bending.

6. Warranty 38

7. List of Accessories 38



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NV6040

IntroductionNV6040 Young's Modulus Setup is a complete system used to determine Young’s modulus of elasticity of materials. When a metal wire is stretched beyond its elastic limit then its cross section is reduced, its structure is changed internally, and for example when it has been drawn through a die. These changes increases with repeated drawings and the hardness and elasticity of the material are profoundly affected. Setup is used to investigate the change in length of a material's sample under a varying tension.

The setup provided with three different types of materials. The sample of different materials is fixed on stand. At the middle of the sample, weights are hanged with different amount. The change in length is measured with the help of Spherometer. A buzzer indication is provided for accurate measurement.

Young’s modulus is a constant of proportionality between the tensile stress and strain, also known as the elastic modulus. It 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. Young's modulus is an extremely important characteristic of a material. It is the numerical evaluation of Hooke's law, namely the ratio of stress to strain.

The Young's modulus allows to know the behavior of a bar made of an isotropic elastic material to be calculated under tensile or compressive loads. For instance, it can be used to predict the amount of material will bring under tension or buckle under compression.

Young's modulus is not always the same in all orientations of a material. Most metals and ceramics, along with many other materials, are isotropic: Their mechanical properties are the same in all orientations. However, metals and ceramics can be treated with certain impurities, and metals can be mechanically 'worked,' to make their grain structures direct ional. These materials then become anisotropic, and Young's modulus will change depending on which direction the force is applied from. Anisotropy can be seen in many composites as well. For example, carbon fiber has a much higher Young's modulus (is much stiffer) when force is loaded parallel to the fibers (along the grain), and is an example of a material with transverse isotropy. Other such materials include wood and reinforced concrete. Engineers can use this directional phenomenon to their advantage in creating various structures in our environment.

For many materials, Young's modulus is essentially constant over a range of strains. Such materials are called linear, and are said to obey Hooke's law. Examples of linear materials include steel, carbon fiber, and glass. Rubber and soils (except at very small strains) are non-linear materials.



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NV6040

· Buzzer indicatorFeatures

· Self-contained and easy to operate

· Precise Measurement by Spherometer

· Provided with different types of materials – Aluminum, Brass, and Iron

· A complete setup with stand, weights and different samples


Sample 1 :Technical Specifications

Material : Iron

Length : 100cm

Breadth : 2.5cm

Depth : 0.6cm

Sample 2 :

Material : Brass

Length : 100cm

Breadth : 2.6cm

Depth : 0.5cm

Sample 3 :Material : Aluminum

Length : 100cm

Breadth : 2.55cm

Depth : 0.5cm

Weight (4 nos.) : 0.5kg

Buzzer Indicator : 12V DC

Power Supply : 230 V +10%, 50 Hz/60 Hz

Adaptor Output : 12V, 500mA

Spherometer:

Main scale : 10-0-10mm

Circular scale : 100 divisions

Least Count : 0.01mm


States of Matter :

Theory

There are five main states of matter. Solids, liquids, gases, plasmas, and Bose-Einstein condensates are all different states of matter. Each of these states is also known as a phase. Elements and compounds can move from one phase to another phase when special physical forces are present. One example of those forces is temperature. The phase or state of matter can change when the temperature changes. Generally, as the temperature rises, matter moves to a more active state.

Figure 1

Phase describes a physical state of matter. The key word to notice is physical. Things only move from one phase to another by physical means. If energy is added (like increasing the temperature or increasing pressure) or if energy is taken away (like freezing something or decreasing pressure) you have created a physical change.

One compound or element can move from phase to phase, but still be the same substance. You can see water vapor over a boiling pot of water. That vapor (or gas) can condense and become a drop of water. If you put that drop in the freezer, it would become a solid. No matter what phase it was in, it was always water. It always had the same chemical properties. On the other hand, a chemical change would change the way the water acted, eventually making it not water, but something completely new.

Particles in a :

· Gas is well separated with no regular arrangement.

· Liquid are close together with no regular arrangement.

· Solid are tightly packed, usually in a regular pattern.

Particles in a :

· Gas vibrates and moves freely at high speeds.

· Liquid vibrate, move about, and slide past each other.

· Solid vibrate (jiggle) but generally do not move from place to place.


Liquids and solids are often referred to as condensed phases because the particles are very close together.


Molecular Structure of Material :

Metals behave differently than ceramics, and ceramics behave differently than polymers. The properties of matter depend on which atoms are used and how they are bonded together.

The structure of materials can be classified by the general magnitude of various features being considered. The three most common major classification of structural, listed generally in increasing size, are:

Atomic structure, which includes features that cannot be seen, such as the types of bonding between the atoms, and the way the atoms are arranged. Microstructure, which includes features that can be seen using a microscope, but seldom with the naked eye. Macrostructure, which includes features that can be seen with the naked eye.

The atomic structure primarily affects the chemical, physical, thermal, electrical, magnetic, and optical properties. The microstructure and macrostructure can also affect these properties but they generally have a larger effect on mechanical properties and on the rate of chemical reaction. The properties of a material offer clues as to the structure of the material. The strength of metals suggests that these atoms are held together by strong bonds. However, these bonds must also allow atoms to move since metals are also usually formable. To understand the structure of a material, the type of atoms present, and how the atoms are arranged and bonded must be known.

Interatomic Force :

The realization that matter is composed of tiny corpuscles called atoms is perhaps the greatest breakthrough in the history of science. The atomic hypothesis identifies the (usually) indivisible carriers of chemical identity and structure, which opens the possibility of predicting macroscopic materials phenomena from the microscopic level. Obviously, we could not understand chemical reactions like dissolution, catalysis and burning without talking about atoms because they are needed to identify the reacting substances, but the atomic hypothesis is also essential in cases not involving chemical changes. By thinking of matter as a collection of incompressible, indestructible atoms of finite size and mass that stick to each other, we can define physical concepts like heat (kinetic energy of atomic motion) and cohesion (potential energy of atomic arrangement). These ideas suffice for an intuitive picture of processes like sound propagation, evaporative cooling, melting, crystal growth, viscous fluid flow, solid deformation and fracture. Indeed, a central task of modern materials science is to understand macroscopic phenomena such as these in terms of the underlying atomic mechanisms.

Intermolecular Force :

Force of attraction between molecules. Intermolecular forces are relatively weak;hence simple molecular compounds are gases, liquids, or low-melting-point solids.


Such forces may be eit her attractive or repulsive in nature. They are conveniently divided into two classes: short-range forces, which operate when the centers of the molecules are separated by 3 angstroms or less, and long-range forces, which operate at greater distances. Generally, if molecules do not tend to interact chemically, the short-range forces between them are repulsive. These forces arise from interactions of the electrons associated with the molecules and are also known as exchange forces. Molecules that interact chemically have attractive exchange forces; these are also known as valence forces. Mechanical rigidity of molecules and effects such as limited compressibility of matter arise from repulsive exchange forces. Long-range forces, or van der Waals forces as they are also called, are attractive and account for a wide range of physical phenomena, such as friction, surface tension, adhesion and cohesion of liquids and solids, viscosity, and the discrepancies between the actual behavior of gases and that predicted by the ideal gas law. Van der Waals forces arise in a number of ways, one being the tendency of electrically polarized molecules to become aligned. Quantum theory indicates also that in some cases the electrostatic fields associated with electrons in neighboring molecules constrain the electrons to move more or less in phase.

These are fundamentally electrostatic interactions (ionic interact ions, hydrogen bond, dipole-dipole interactions) or electrodynamic interactions (van der Waals/London forces). Electrostatic interactions are classically described by Coulomb's law, the basic difference between them are the strength of their charge. Ionic interactions are the strongest with integer level charges, hydrogen bonds have partial charges that are about an order of magnitude weaker, and dipole-dipole interactions also come from partial charges another order of magnitude weaker.

These non-covalent forces, which give rise to bonding energies of less than a few kcal/mol, are generally much weaker than the forces. Nevertheless, intermolecular forces are responsible for a wide range of physical, chemical, and biological phenomena. Listed in order of decreasing strength, these forces are:

· Ionic interactions

· Hydrogen bonds

· Dipole-dipole interactions

· London Dispersion Forces

Ionic Interactions :These are interactions that occur between charged species (ions). Like charges repel, while opposite charges attract. These bonds form when the electronegativities between two atoms is large enough that one steals an electron from the other. Then oppositely charged ions are attracted. The opposite charges mean that the ions are strongly attracted to each other. The formation of the bond means that each atom becomes more stable, having a full quota of electrons in its outer shell.

Each ion has the electronic structure of a (rare gas; see ). The maximum number


of electrons that can be gained is usually two.


There are some physical properties which are often taken as being indicative of the presence of ions in a solid. For example, such solids are generally insulators but, on melting, the electrical conductivity rises sharply; this is at tribute to the ions being immobile in the solid but free to move in the liquid.

Hydrogen Bonding :

Hydrogen bonding is an intermolecular interaction with a Hydrogen atom being present in the intermolecular bond. This hydrogen is covalently (chemically) bound in one molecule, which acts as the proton donor. The other molecule acts as the proton acceptor. In the following important example of the water dimer, the molecule on the right is the proton donor, while the one on the left is the proton acceptor.

Figure 2The hydrogen atom participating in the hydrogen bond is often covalently bound in the donor to an electronegative atom. Examples of such atoms are nitrogen, oxygen, or fluorine. The electronegative atom is negatively charged (carries a charge δ-) and the hydrogen atom bound to it is positively charged. Consequently the proton donor is a polar molecule with a relatively large dipole moment. Often the positively charged hydrogen atom points towards an electron rich region in the acceptor molecule. The fact that an electron rich region exists in the acceptor molecule, implies already that the acceptor has a relatively large dipole moment as well. The result is a dimer that to a large extent is bound by the dipole-dipole force.

Hydrogen bonds are found throughout nature. They give water its unique properties that are so important to life on earth. Hydrogen bonds between hydrogen atoms and nitrogen atoms of adjacent base pairs provide the intermolecular force that help more precisely bind together the two strands in a molecule of DNA. Hydrophobic effects between the double-stranded DNA and the surrounding aqueous environment, however, are more important in maintaining the DNA in its double stranded form.

Dipole-Dipole Interactions :Dipole-dipole interactions, also called Keesom interactions after Willem Hendrik Keesom who produced the first mathematical description in 1921, are the forces that occur between two molecules with permanent dipoles. These work in a similar manner to ionic interactions, but are weaker because only partial charges are involved. An example of this can be seen in hydrochloric acid:

(+)(-) (+) (-)


H-Cl-----H-Cl



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London Dispersion Forces :Also called London forces or Van der Waals forces, these involve the attraction between temporarily induced dipoles in nonpolar molecules. This polarization can be induced either by a polar molecule or by the repulsion of negatively charged electron clouds in nonpolar molecules. An example of the former is chlorine dissolving in water.

Chemical Bonding :

Chemical compounds are formed by the joining of two or more atoms. A stable compound occurs when the total energy of the combination has lower energy than the separated atoms. The bound state implies a net attractive force between the atoms, a chemical bond. The two extreme cases of chemical bonds are:

Covalent Bond :The bond in which one or more pairs of electrons are shared by two atoms.

Covalent chemical involve the sharing of a pair of valence electrons by two atoms, in contrast to the transfer of electrons in bonds. Such bonds lead to stable molecules if they share electrons in such a way as to create a noble gas configuration for each atom.

Figure 3Hydrogen gas forms the simplest covalent bond in the diatomic hydrogen molecule. The halogens such as chlorine also exist as diatomic gases by forming covalent bonds. The nitrogen and oxygen which makes up the bulk of the atmosphere also exhibits covalent bonding in forming diatomic molecules.

Ionic Bond :

Bond in which one or more electrons from one atom are removed and attached to another atom, resulting in positive and negative ions which attract each other.

In chemical bonds, atoms can either transfer or share their valence electrons. In



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the



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extreme case where one or more atoms lose electrons and other atoms gain them in order to produce a noble gas electron configuration, the bond is called an ionic bond.

Typical of ionic bonds are those in the alkali halides such as sodium chloride, NaCl.

Figure 4Other types of bonds include metallic bond and hydrogen bonding. The attractive forces between molecules in a liquid can be characterized as van der Waals bonds.

Solid State :

The physical state of a substance tells us something about its properties. The most common states of matter that we are familiar with are solids, liquids and gases. From our experiences, we can easily tell the difference between solids, liquids and gases. To define the physical state at a more microscopic level, we must look further. For example, matter in the form of a solid consists of particles that are arranged in a relatively ordered fashion. These particles are in close contact with one another, resulting in strong interactions that hold the individual particles in place. For us, on the macroscopic level, this leads too many familiar properties that help us tell the difference between solids and liquids. For example, solids must move as a unit, rather than flowing like gases or liquids. Solids also have a definite shape, unlike liquids and gas, whose shapes are determined by their containers.

Solids are responsible for a great deal of modern technology including: steel construction, computer chips, ceramic engines and catalytic converters.

In addition to having a diverse array of properties for modern uses, solid state materials can be highly colored. Some compounds include ancient and modern pigments, metals and gemstones. The bright light given off by photodiodes also shows its origins to solid state materials.



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Types of Solids :

Solids can be categorized into groups based on their structural and bonding properties. A typical classification scheme is given here.

· Ionic Solid

· Covalent Solid

· Molecular Solid

· Metallic Solid

Molecular Solid :

Figure 5

A molecular solid is a solid composed of molecules held together by relatively weak intermolecular forces. Because these forces are weaker than chemical covalent bonds, molecular solids are soft, and generally have low melting and boiling temperatures. Most molecular solids are nonconducting when pure, because molecules are uncharged and can't carry electric current. Another common property of molecular substances is insolubility in water, but solubility in non-polar solvents; a few molecular substances such as ethanol dissolve in water, and a few polar ones such as HCl will ionize, but most such as oil, benzene or H2 won't. Examples of molecular solids include sulfur, ice, sucrose, solid carbon dioxide, crystals of coordination compounds, etc.

(a)



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(b) Figure 6


In figure 6(a): Water is represented by the vertical ovals and the polar molecular solid by the horizontal ovals. The dashed lines represent electrostatic attractions. The electrostatic attractions between water and the polar solid make the solution of the solid possible.

Same as above in figure 6(b): Except the solid is nonpolar. Note that there are no attractions between water and solid. Thus the solid will not dissolve.

Ionic Solid :

An ionic compound is a chemical compound in which ions are held together in a lattice structure by ionic bonds. Usually, the positively charged portion consists of metal cations and the negatively charged portion is a halogen or polyatomic ion. Ions in ionic compounds are held together by the electrostatic force between oppositely charged bodies. Ionic compounds have a high melt ing and boiling point, and they have a high hardness and are very brittle.

Ions can be single atoms, as in common table salt sodium chloride, or more complex groups such as calcium carbonate. But to be considered an ion, they must carry a positive or negative charge. Thus, in an ionic bond, one 'bonder' must have a positive charge and the other a negative one. By sticking to each other, they resolve, or partially resolve, their separate charge imbalances. Positive to positive and negative to negat ive ionic bonds do not occur (For an easily visible analogy, experiment with a pair of bar magnets).

Chemical compounds are rarely strictly ionic or strictly covalent. Except for the most electronegative/electropositive pairs such as caesium fluoride, ionic compounds usually exhibit a degree of covalency. Similarly, covalent compounds often exhibit charge separations.

Ionic compounds have strong electrostatic bonds between particles. As a result, they generally have high melting and boiling points. They also have good electrical conductivit y when molten or in aqueous solution. While ionic inorganic compounds are solids at room temperature and will usually form crystals, organic ionic liquids are of increasing interest.

Figure 7


The crystal structure of sodium chloride, NaCl, a typical ionic compound. The dark color spheres are sodium cations, Na+, and the light color spheres are chloride anions, Cl−.

Ionic compounds dissolve in polar solvents, especially those which ionize, such as water and ionic liquids. They are usually appreciably soluble in other polar solvents such as alcohols, acetone and dimethyl sulfoxide as well. Ionic compounds tend not to dissolve in nonpolar solvents such as diethyl ether or petrol (gasoline).When sodium and chlorine atoms are placed together, there is a transfer of electrons from the sodium to the chlorine atoms, resulting in a strong electrostatic attraction between the positive sodium ions and the negative chlorine ions. This explains the strong attraction between paired ions typical of the gas or liquid state.

Formation of Ionic Bond in NaCl

Na+ and Cl- ions formed by Ionic bond mechanism

Figure 8

Figure 9

Ionic solids are characterized by the following properties :

1. High melting and boiling points - for example, NaCl has a melting point of about800oC, and magnesium oxide, MgO, another ionic solid, has a melting point over 2800oC. Ionic bonds are quite strong, so high temperatures are needed tobreak their attractive forces.

2. Poor conduction of heat and electricity - at least in the solid state. When such compounds are melted or dissolved in water, and the ions can move freely, they do conduct electricity.


3. Hard and brittle.


4. Many are soluble in water (but not all).

5. Examples of ionic compounds around the house includes :

NaCl - sodium chloride - table salt

KCl - potassium chloride - present in "light" salt (mixed with

NaCl) CaCl2 - calcium chloride - driveway salt

NaOH - sodium hydroxide - found in some surface cleaners as well as oven anddrain cleaners

CaCO3 - calcium carbonate - found in calcium supplements

NH4NO3 - ammonium nitrate - found in some fertilizers

Strength of an Ionic Bond :The strength of an ionic bond depends on the size of the charge on each ion and on the radius of each ion.

The larger the charges on the ions the greater the force of attraction, or the stronger the bond. This factor places larger values for the variables q1 and q2 in the numerator of Coulomb's Law.

The larger the radii of the bonded ions, the weaker the force of attraction, or the weaker the ionic bond. This factor places a larger distance between the centers of the charged objects, and reduces the force of attraction according to Coulomb's Law.

Covalent Solid :

The interatomic linkage that results from the sharing of an electron pair between two atoms. The binding arises from the electrostatic attraction of their nuclei for the same electrons. A covalent bond forms when the bonded atoms have a lower total energy than that of widely separated atoms. Silicon, carbon, germanium, and a few other elements form covalently bonded solids. In these elements there are four electrons in the outer sp-shell, which is half filled. (The sp-shell is a hybrid formed from one s and one p sub shell.) In the covalent bond an atom shares one valence (outer-shell) electron with each of its four nearest neighbor atoms.

Figure 10


Covalent Bonding :

Figure 11In diamond, each carbon atom is covalently bonded to four other carbon atoms arranged in a tetrahedron around it. The strong covalent bonds and the perfectly tetrahedral arrangement lead to diamond's great strength and hardness. Graphite (right) is an example of a "low dimensional" covalent network solid. Notice the arrangement of the atoms occurs in layers. Within each layer, there is covalent bonding between the atoms and the atoms are fairly close together.

The properties do overlap. Obviously the strong covalent bonds are difficult to break in both structures, and both have extremely high melting points (and boiling points). The strength of the bonds also explains why diamond is one of the hardest substances there is. Moreover, it is difficult to distort the bonds at all, without breaking them: diamond is brittle as well as hard.

But graphite is soft. This is a little surprising at first sight. The covalent bonds are slightly harder to break than those in diamond, because they have multiple characters. However, the carbon atoms are arranged in covalently bonded layers and the bonds between one layer and another are weak Van Der Waals bonds. It is these weak bonds which are broken first.

Covalent solids are characterized by the following properties :

1. High melt ing points - both diamond and graphite melts at temperature over

3000oC, silica (quartz, SiO2) melts at around 1600oC. High temperatures are needed to break the strong covalent bonds found in these solids.

2. Often poor conduction of heat and electricity, though this varies from substance to substance.

3. Generally very hard, though low dimensional solids like graphite are extremely easy to cleave in one direction.


4. In covalent solid all the molecules are linked by covalent bonds, i.e., the bond formed by sharing of electrons. In Ionic solids the molecules are linked by ionic


bonds, i.e., the bond formed by the transfer of electrons. Ionic solid is stronger than covalent solid.

Strength of Covalent Bond :

The strength of a covalent bond depends on the size of the charge from the shared electrons, the nuclear charges of the bonded atoms and the radii of the bonded atoms.

1. The greater the number of electrons being shared, the greater the force of attraction, or the stronger the bond.

2. The greater the nuclear charge on each bonded atom, the greater the force of attraction or the stronger the bond.

3. The greater the radii of the bonded atoms, the greater the distance between the bonded nuclei and the shared electrons. According to Coulomb's Law, this increased distance will reduce the force of attraction, or decrease the strength of the covalent bond.

Metallic Solid :Metallic solids are composed of metal atoms which are held together by attractive forces called (not surprisingly) metallic bonds. In a metallic solid, we can imagine the solid to be composed of a regular array of positive nuclei, all sharing a "sea" of electrons. Metallic bonds are found in metals like Cu, Zn, and Na etc.

The metallic bond accounts for many physical characteristics of metals, such as strength, malleability, ductility, conduction of heat and electricity, and luster.

Metals tend to have high melting points and boiling points suggest ing strong bonds between the atoms. Even a metal like sodium (melting point 97.8°C) melts at a considerably higher temperature than the element (neon) which precedes it in the Periodic Table.

Sodium has the electronic structure 1s22s22p63s1. When sodium atoms come together, the electron in the 3s atomic orbital of one sodium atom shares space with the corresponding electron on a neighboring atom to form a molecular orbital - in much the same sort of way that a covalent bond is formed.

The difference, however, is that each sodium atom is being touched by eight other sodium atoms - and the sharing occurs between the central atom and the 3s orbital on all of the eight other atoms. And each of these eight is in turn being touched by eight sodium atoms, which in turn are touched by eight atoms - and so on , until you have taken in all the atoms in that lump of sodium.

All of the 3s orbital on all of the atoms overlap to give a vast number of molecular orbital which extend over the whole piece of metal. There have to be huge numbers of molecular orbital, of course, because any orbital can only hold two electrons.

The electrons can move freely within these molecular orbital, and so each electron becomes detached from its parent atom. The electrons are said to be delocalised. The


metal is held together by the strong forces of attraction between the positive nuclei


and the delocalised electrons.

Figure 12This is sometimes described as "an array of positive ions in a sea of electrons".

Metallic solids are characterized by the following properties :1. Low to high melting points - for example, mercury melts at -39oC (it is liquid

at room temperature), sodium melts at 97.5oC, Cr at 1890oC, and tungsten at3390oC.

2. Good conduction of heat and electricity.

3. Can be soft or hard. Usually malleable and ductile - can be hammered into sheets, for example.

4. Examples of metallic solids around the house include:

· 24 Karat gold ring - solid consisting of gold atoms, or lower Karat gold, alloys of gold and zinc

· Copper plumbing, copper cookware

· Aluminium soft drink cans

Amorphous Solid :

An amorphous solid is a solid in which there is no in which the atoms and molecules are not organized in a definite lattice pattern. (Solids in which there is long-range atomic order are called crystalline solids or amorphous). Most classes of solid materials can be found or prepared in an amorphous form. For instance, common window glass is an amorphous ceramic, many polymers (such as polystyrene) are amorphous, and even foods such as cotton candy are amorphous solids.

Amorphous solids are solids with random unoriented molecules. Examples of amorphous solids are glass and plastic. They are considered super cooled liquids in which the molecules are arranged in a random manner some what as in the liquid state. Amorphous solids do not have definite melt ing points.


Figure 13

In an amorphous solid such as glass or a lollipop, the atoms aren’t orderlyAmorphous materials are able to melt very rapidly, often prepared by rapidly cooling molten material, such as glass. The cooling reduces the mobility of the material's molecules before they can pack into a more thermodynamically favorable crystalline state. Amorphous materials can also be produced by additives which interfere with the ability of the primary constituent to crystallize. For example, addition of soda to silicon dioxide results in window glass, and the addition of glycols to water results in a vitrified solid.

Elasticity :An important property of many structural materials is their ability to regain their original shape after a load is removed. These materials are called elastic. Steel, glass and rubber are elastic; putty or modeling clay are not elastic. Each of these materials is elastic to varying degrees; steel and glass are both more elastic than rubber. The degree of elasticity or "stiffness" of a material is called its Modulus of Elasticity (E). The modulus of elasticity, possible deformations can be calculated for any material and loading.

Elastic body :A body which regains its original shape when the deformation force is removed is called an elastic body.

Inelastic or Plastic body :A body which cannot regain its original shape, when the deformation force is removed is called a plastic body. Elasticity is molecular property of the matter.

Elasticity is the property of an object or material which causes it to be restored to its original shape after distortion. It is said to be more elastic if it restores itself more precisely to its original configuration. A rubber band is easy to stretch, and snaps back to near its original length when released, but it is not as elastic as a piece of piano wire. The piano wire is harder to stretch, but would be said to be more elastic than the rubber band because of the precision of its return to its original length. A real piano string can be struck hundreds of times without stretching enough to go


noticeably out of tune. A spring is an example of an elastic object - when stretched; it exerts a



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restoring force which tends to bring it back to its original length. This restoring force is generally proportional to the amount of stretch. For wires or columns, the elasticit y is generally described in terms of the amount of deformation (strain) resulting from a given stress (Young's modulus). Bulk elastic properties of materials describe the response of the materials to changes in pressure.

Figure 14Some bodies break, others flow, but the observation is a useful one for most materials of construction under working loads. The amount of extension is measured by the change in a dimension divided by the dimension itself, called the strain e = Δl/l, and the force is measured by the force divided by the area on which it acts, called the stress p = F/A. When this is properly done, the ratio of stress to strain is a constant depending only on the material, not on its shape or size. This can only be managed in simple cases, but the result in more complicated cases, such as bending or torsion, can always be worked out from the simple ones. The constant is called the modulus, which has the same dimensions as the stress. It is the stress that would be required for unit strain, if unit strain could be produced elastically. However, practical strains are usually only a few percent at the most.

Hooke's Law implies that the strain produced by several forces is the sum of the strains that would be produced by each force separately, and that the relation between stress and strain is the same for a force in either direction. These things are true only when the strains are less than the elastic limit for the material. A material may, indeed, have no elastic region at all. The typical relation between stress and strain for a steel rod subjected to tension is shown in the figure 14. It shows the stress and strain calculated on the basis of the original measurements. For steel, there is little change in the original measurements except near the breaking point, where the tension sample necks down. In the Figure, the elastic limit, the yield point, which is rather arbitrary, the ultimate or maximum strength, and the breaking strength are labeled. For steel, the elastic region is long, and the distance from the elastic limit to the yield point is short. For cast iron, it is exactly the reverse. There may be no permanent set when the load is removed, even between the elastic and yield points, as occurs in cast iron, but there is usually permanent set beyond the yield point.

Hooke's Law applies as long as the material stress does not pass a certain point known as its proportional limit. This is the point at which the physical properties of the



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material actually change. Any time an elastic material is loaded between zero and the proportional limit, the stress and strain are directly proportional and if the load is released the material will regain its initial dimensions. If the stress is doubled the strain is doubled; if the stress is tripled the deformation is three times as great, etc.

The English physician and physicist Thomas Young (1773 - 1829) noted that if stress is proportional to strain, then for any given material, stress divided by strain would be a constant. This constant is known today as Young's Modulus or the Modulus of Elasticity.

The Modulus of Elasticity is represented by E = Stress / Strain.

This relationship is found as the slope of the curve of the stress-strain curve from initial loading to the proportional limit. A higher value of the modulus indicates a more brittle material (i.e. glass, ceramics). A very low value represents a ductile material (i.e. rubber).

Elastic Properties of different Materials

MaterialRigidity *

1010N/m2

Young's 10Modulus * 10

N/m2Poison's ratio

Steel 7.9 – 8.9 19.5 – 20.6 0.28

Aluminium 2.67 7.50 0.34

Copper 4.55 12.4 – 12.9 0.34

Iron(Wrought) 7.7 – 8.3 19.9 – 20.0 0.27

Brass 3.5 0.7 – 10.2 0.34 – 0.38

Modulus of Elasticity :A measure of the rigidity of metal. Ratio of stress, within proportional limit, to corresponding strain. Force which would be required to stretch a substance to double its normal length, on the assumption that it would remain perfectly elastic, i.e., obeys Hooke's Law throughout the twist. The ratio of stress to strain within the perfectly elastic range.

Specifically, the modulus obtained in tension or compression is Young's modulus, stretch modulus or modulus of extensibility; the modulus obtained in torsion or shear is modulus of rigidity, shear modulus or modulus of torsion; the modulus covering the ratio of the mean normal stress to the change in volume per unit volume is the bulk modulus. The tangent modulus and secant modulus are not restricted within the proportional limit; the former is the slope of the stress-strain curve at a specified point; the latter is the slope of a line from the origin to a specified



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point on the stress-strain curve also called elastic modulus and coefficient of elasticity.



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Rate of change of strain as a function of stress. The slope of the straight line portion of a stress-strain diagram. Tangent modulus of elasticity is the slope of the stress-strain diagram at any point. Secant modulus of elasticity is stress divided by strain at any given value of stress or strain. It also is called stress-strain ratio.

Figure 15

Tangent and secant modulus of elasticity are equal, up to the proportional limit of a material. Depending on the type of loading represented by the stress-strain diagram, modulus of elasticity may be reported as: compressive modulus of elasticity (or modulus of elasticity in compression); flexural modulus of elasticity (or modulus of elasticity in flexure); shear modulus of elasticit y (or modulus of elasticity in shear); tensile modulus of elasticity (or modulus of elasticity in tension); or torsional modulus of elasticity (or modulus of elasticity in torsion). Modulus of elasticit y may be determined by dynamic testing, where it can be derived from complex modulus. Modulus used alone generally refers to tensile modulus of elasticity. Shear modulus is almost always equal to torsional modulus and both are called modulus of rigidity. Moduli of elasticity in tension and compression are approximately equal and are known as Modulus of rigidity is related to by the equation:

E = 2G (r + 1)

Where E is Young's Modulus (psi), G is modulus of rigidity (psi) and r is Poisson's ratio. Modulus of elasticity also is called elastic modulus and coefficient of elasticity.

Hooke's Law :

One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law. In other words, Hooke's Law gives the relationship between the force applied to an unstretched spring and the amount the spring is stretched when the force is applied.



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Figure 16

This law discovered by the English scientist Robert Hooke in 1660--states that the force f exerted by a coiled spring is directly proportional to its extension dx. The extension of the spring is the difference between its actual length and its natural length (i.e., its length when it is exerting no force). The force acts parallel to the axis of the spring. Obviously, Hooke's law only holds if the extension of the spring is sufficiently small. If the extension becomes too large then the spring deforms permanently, or even breaks. Such behavior lies beyond the scope of Hooke's law.

Hooke's Law states that the restoring force of a spring is directly proportional to a small displacement. In equation form, we write

F = -kxWhere x is the size of the displacement. The proportionality constant k is specific for each spring.The object of this virtual lab is to determine the spring constant k. This equilibrium can be expressed as

W = kxW is the weight of the added mass. Therefore, the spring constant k is the slope of the straight line W versus x plot.Weight is mass times the accelerat ion of gravity or W = mg where g is about 980 cm/sec2. Using this relationship weights are computed for the masses in the table above. The results are on the right.Data from this table are plotted on the graph below. Note that the points fall precisely on the line since this is a virtual experiment.

Weight(dynes)

Displacement(cm)

49000 298000 4

147000 6196000 8



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Deformation :

Deformation is a change in shape due to an applied force. This can be a result of tensile (pulling) forces, compressive (pushing) forces, shear, bending or torsion (twisting). Deformation is often described in terms of strain.

Figure 17

In the figure it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the cylinder so that the original shape (dashed lines) has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change, thus the material is forced out laterally. Deformation may be temporary, as a spring returns to its original length when tension is removed, or permanent as when an object is irreversibly bent or broken.

The concept of a rigid body can be applied if the deformation is negligible.

Figure 18

This Stress-strain curve, showing the relationship between stress (force applied) and strain (deformation) of a ductile metal.

Types of deformation :Depending on the type of material, size and geometry of the object, and the forces applied, various types of deformation may result.



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Elastic deformation :

This type of deformation is reversible. Once the forces are no longer applied, the object returns to its original shape. As the name implies, elastic (rubber) has a rather large elastic deformation range. Soft thermoplastics and metals have moderate elastic deformation ranges while ceramics, crystals, and hard thermosetting plastics undergo almost no elastic deformation.

Metal Fatigue :

A phenomenon only discovered in modern times is metal fatigue, which occurs primarily in ductile metals. It was originally thought that a material deformed only within the elastic range returned completely to its original state once the forces were removed. However, faults are introduced at the molecular level with each deformation. After many deformations, cracks will begin to appear, followed soon after by a fracture, with no apparent plastic deformation in between. Depending on the material, shape, and how close to the elastic limit it is deformed; failure may require thousands, millions, billions, or trillions of deformations.

Metal fatigue has been a major cause of aircraft failure, such as the De Havilland Comet, especially before the process was well understood. There are two ways to determine when a part is in danger of metal fatigue; either predict when failure will occur due to the material/force/shape/iteration combination, and replace the vulnerable materials before this occurs, or perform inspections to detect the microscopic cracks and perform replacement once they occur. Selection of materials which are not likely to suffer from metal fatigue during the life of the product is the best solution, but not always possible. Avoiding shapes with sharp corners limits metal fatigue by reducing force concentrations, but does not eliminate it.

Plastic Deformation :

This type of deformat ion is not reversible. However, an object in the plastic deformation range will first have undergone elastic deformation, which is reversible, so the object will return part way to its original shape. Soft thermoplastics have a rather large plast ic deformation range as do ductile metals such as copper, silver, and gold. Steel does, too, but not iron. Hard thermosetting plastics, rubber, crystals, and ceramics have minimal plastic deformation ranges. Perhaps the material with the largest plastic deformat ion range is wet chewing gum, which can be stretched dozens of times its original length.

Fracture :This type of deformation is also not reversible. A break occurs after the material has reached the end of the elastic, and then plastic, deformation ranges. At this point forces accumulate until they are sufficient to cause a fracture. All materials will eventually fracture, if sufficient forces are applied.



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Moduli of Elasticity :

1. Young's modulus (Y) :Within the elastic limit of a body, the ratio between the longitudinal stress and the longitudinal strain is called the Young's modulus of elasticity.

Y = longitudinal stress / longitudinal strain = Fl / A 1

Where F is the force acting on the surface of area A l is the increase in length in a length l of the wire. (Or)

Y = Mg / pr 2 * l / l

Where M is the mass r is the cross sectional radius of the material.

Units of Y: dyne / cm2 or N / m2 (Pascal (Pa)) 1 Pascal = 10 dynes cm-2

109 Pascal = 1 Giga Pascal

1 atmosphere = 1.02 * 105 Pa

2. Rigidity modulus :Within the elastic limit of a body, the ratio of tangential stress to the shearing strain is called rigidity modulus of elasticity.The rigidity modulus, n = tangential stress / shearing strain

= (F / A) / q = (F / A) / ( l / l) = Fl / A l

Where F / A is the tangential stress, l the displacement in a length l in the perpendicular direction

Units of n: N / m2

3. Bulk modulus (K) :It is defined as the ratio of stress to volumetric strain.

K = stress / bulk strain = -PV / V

Where P is the pressure, V is the original volume and v is the change in volume of the material

Unit of K: N / m 2

4. Compressibility :

The reciprocal of the bulk modulus is called compressibility. Or

Compressibility = 1 / K



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Bulk Elastic Properties :

The bulk elastic properties of a material determine how much it will compress under a given amount of external pressure. The ratio of the change in pressure to the fractional volume compression is called the bulk modulus of the material.



29

Figure 19The reciprocal of the bulk modulus is called the compressibility of the substance. The amount of compression of solids and liquids is seen to be very small.

The bulk modulus of a solid influences the speed of sound and other mechanical waves in the material. It also is a factor in the amount of energy stored in solid material in the Earth's crust. This buildup of elastic energy can be released violently in an earthquake, so knowing bulk moduli for the Earth's crust materials is an important part of the study of earthquakes.

A common statement is that water is an incompressible fluid. This is not strictly true, as indicated by its finite bulk modulus, but the amount of compression is very small. At the bottom of the Pacific Ocean at a depth of about 4000 meters, the pressure isabout 4 x 107 N/m2. Even under this enormous pressure, the fractional volumecompression is only about 1.8% and that for steel would be only about 0.025%. So it is fair to say that water is nearly incompressible.

Young's 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 parameter called the Young's modulus of the material. More correctly, Young's modulus (E) is a measure of stiffness, having the same units as stress: pounds per square inch or Pascal. When stress and strain are not directly proportional, E may be represented as the slope of the tangent or the slope of the secant connecting two points on the stress-strain curve. The modulus is then designated as tangent modulus or secant modulus at stated values of stress. The modulus of elasticity applying specifically to tension is called Young’s modulus.

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.

The elastic modulus applied to tensional stress when the object concerned is not constrained.

Young's modulus (E) = Applied load per unit area of cross section/increase in length per unit length.

According to Hooke's law the strain is proportional to stress, and therefore the ratio of the two is a constant that is commonly used to indicate the elasticity of the



30

substance. Young's modulus is the elastic modulus for tension, or tensile stress, and is the force



31

per unit cross section of the material divided by the fractional increase in length resulting from the stretching of a standard rod or wire of the material.

Figure 20

Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain:

Where,

E is the Young's modulus (modulus of elasticity) measured in

Pascal; F is the force applied to the object;

A0 is the original cross-sectional area through which the force is applied;

ΔL is the amount by which the length of the object changes;

L0 is the original length of the object.

The SI unit of modulus of elasticity (E, or less commonly Y) is the Pascal. Given the large values typical of many common materials, figures are usually quoted in mega Pascal or giga Pascal. Some use an alternative unit form, kN/mm², which gives the same numeric value as gigapascals.

The modulus of elast icity can also be measured in other units of pressure, for example pounds per square inch.

Cantilever :Beam supported at one end and carrying a load at the other end or distributed along the unsupported portion. The upper half of the thickness of such a beam is subjected to tensile stress, tending to elongate the fibers, the lower half to compressive stress, tending to crush them. Cantilevers are employed extensively in building construction and in machines. In building, any beam built into a wall and with the free end projecting forms a cantilever. Longer cantilevers are incorporated in a building when clear space is required below, with the cantilevers carrying a gallery, roof, canopy, runway for an overhead traveling crane, or part of a building above.

Depression for this is

d = Wl3/YI


Where W is weight, I is moment of inertia, l is length and Y is young's modulus.

Geometrical Moment of Inertia :The geometrical moment of inertia of a beam is defined as its moment of inertia if it has a unit mass per unit area.

For a beam of rectangular cross section

For a beam of circular cross section

Where r is the radius of the beam.

Double Cantilever :

I = bd3/12

I = r4/4

If a bar is supported at two knife edges A and B, l meter apart in a horizontal plane so that equal lengths of the bar project beyond the knife edges and a weight W is suspended at the middle point C, then it acts as a double cantilever.

The middle part of the bar is practically horizontal. It is, therefore, equivalent to two inverted cantilever fixed at the middle point C and loaded at A and B with load W/2 acting upward. The depression at C is given by

= W/2(1/2)3/3YI

= Wl3/48YI For a rectangular bar of breadth b and thickness d,

I = bd3/12

Depression Wl3/4Ybd3

Young's modulus of elasticity can be determined by using this formula

Y = mgl3 / 4bd3

W = mg, where m is mass in kg, g is gravity, l is length, b is breadth and d is depth of sample, and is depression of bar.

Stress and Strain :

Stress :The restoring force per unit area developed inside the body is called stress

Stress = force / area

Units : C G S system : dyne cm-2


S I system : Newton m-2 or Pascal

Pascal is also unit of pressure. Its Dimensional formula is ML-1T-2

The intensity of internal reactive forces in a deformed body and associated unit



changes of dimension, shape, or volume caused by externally applied forces.

Stress is a measure of the internal reaction between elementary particles of a material in resisting separation, compaction, or sliding that tend to be induced by external forces. Total internal resisting forces are resultants of continuously distributed normal and parallel forces that are of varying magnitude and direction and are acting on elementary areas throughout the material. These forces may be distributed uniformly or no uniformly. Stresses are identified as tensile, compressive, or shearing, according to the straining action.

Deformation occurs as a result of stress, whether that stress be in the form of tension, compression, or shear. Tension occurs when equal and opposite forces are exerted along the ends of an object. These operate on the same line of action, but away from each other, thus stretching the object. A perfect example of an object under tension is a rope in the middle of a tug-of-war competition. The adjectival form of "tension" is "tensile".

Earlier, stress was defined as the application of force over a given unit area, and in fact, the formula for stress can be written as F/A, where F is force and A area. This is also the formula for pressure, though in order for an object to be under pressure, the force must be applied in a direction perpendicular to—and in the same direction as— its surface. The one form of stress that clearly matches these parameters is compression, produced by the action of equal and opposite forces, whose effect is to reduce the length of a material. Thus compression (for example, crushing an aluminum can in one's hand) is both a form of stress and a form of pressure.

Note that compression was defined as reducing length, yet the example given involved a reduction in what most people would call the "width" or diameter of the aluminum can. In fact, width and height are the same as length, for the purposes of most discussions in physics. Length is, along with time, mass, and electric current, one of the fundamental units of measure used to express virtually all other physical quantities. Width and height are simply length expressed in terms of other planes, and within the subject of elasticity, it is not important to distinguish between these varieties of length. (By contrast, when discussing gravitational attraction—which is always vertical—it is obviously necessary to distinguish between "vertical length," or height, and horizontal length.)

The third variety of stress is shear, which occurs when a solid is subjected to equal and opposite forces that do not act along the same line, and which are parallel to the surface area of the object. If a thick hardbound book is lying flat, and a person places a finger on the spine and pushes the front cover away from the spine so that the covers and pages no longer constitute parallel planes, this is an example of shear. Stress resulting from shear is called shearing stress.

To sum up the three varieties of stress, tension stretches an object, compression shrinks it, and shear twists it. In each case, the object is deformed to some degree. This deformation is expressed in terms of strain, or the ratio between change in dimension and the original dimensions of the object. The



formula for strain is δL/Lo,



where δL is the change in length (δ, the Greek letter delta, means "change" in scientific notation) and Lo the original length.

Strain :

The change produced per unit magnitude of a body is called strain.

Three kinds of strain :

1. Longitudinal or linear strain or tensile strain.

2. Shearing strain or tangential strain.

3. Bulk strain or volume strain.

1. Longitudinal or linear strain or tensile strain :When an external force is applied to a rod along its length the fractional change in its length is called longitudinal strain. If l is the original length and l the longitudinal extension.

2. Shearing strain :

Longitudinal strain, e = l / l

When simultaneous compression and extension in mutually perpendicular directions take place in a body, the change of shape it undergoes is called shearing strain .

Where l is the displacement of the upper surface and l the length of the vertical edge, when q is small,

Shearing strain ( q ) = l / l

3. Volume or Bulk strain :

If V is the original volume V the change in volume, the bulk strain

v = - V / V The negative sign indicates the decrease in volume.

Units : Strain being a ratio, has no units or dimensions.

The strains associated with stress are characteristic of the material. Strains completely recoverable on removal of stress are called elastic strains. Above a critical stress, both elastic and plastic strains exist, and that part remaining after unloading represents plastic deformation called inelastic strain. Inelastic strain reflects internal changes in the crystalline structure of the metal. Increase of resistance to continued plastic deformation due to more favorable rearrangement of the atomic structure is strain hardening.

Poisson's ratio :When a sample of material is stretched in one direction, it tends to get thinner in



the other two directions. Poisson's ratio (ν, μ), named after Simeon Poisson, is a measure of this tendency. Poisson's ratio is the ratio of the relative contraction strain, or


transverse strain (normal to the applied load), divided by the relative extension strain, or axial strain (in the direction of the applied load). For a perfectly incompressible material deformed elastically at small strains, the Poisson's ratio would be exactly 0.5. Most practical engineering materials have ν between 0.0 and 0.5. Cork is close to 0.0, most steels are around 0.3, and rubber is almost 0.5. Some materials, mostly polymer foams, have a negative Poisson's ratio; if these exotic materials are stretched in one direction, they become thicker in perpendicular directions.

Assuming that the material is compressed along the axial

direction. Where,

ν is the resulting Poisson's ratio,

trans is transverse strain,

axial is axial strain.

At first glance, a Poisson's ratio greater than 0.5 does not make sense because at a specific strain the material would reach zero volume, and any further strain would give the material "negative volume". Unusual Poisson ratios are usually a result of a material with complex architecture.


Object :

Experiment

Determination of Young's Modulus of elasticity of the given sample material by bending.

Equipments Needed :1. Sample Stand

2. Weights of 500 gm

3. Samples (Iron, Aluminium, Brass)

4. DC Adaptor

5. Weight Holder

6. Spherometer Stand with Buzzer

Procedure:1. Mount the setup by fixing two long round rods with U-type brackets.

2. Tight the sample (Iron) on Sample stands.

3. Place it horizontally on the smooth surface.

4. Tight the Weight holder at the center of sample with the help of screw.

5. Place the spherometer stand, beyond the center of sample (Iron).

6. Adjust the spherometer height with the help of screw according to the sample.

Note : Spherometer leg must be in contact by rotating the Circular Scale with the center of the sample.

7. Connect buzzer with adaptor and connect patch cord with banana terminal, provided on the sample for buzzer connection.

8. Switch ‘On’ the supply for adaptor.9. Buzzer blows because at this stage spherometer leg is in contact with the sample.

10. Consider spherometer Main Scale divisions 0 to 20 mm from top to bottom.

11. Note Main Scale (M.S) reading and Circular Scale reading (C.S) i.e., no. of divisions * 0.01mm (least count) reading in Observation Table 1 and find total reading M.S + C.S i.e., T1.

Note: This time there is no load on the sample it is said to be initial reading.


Increment of the Loads :12. Now place the 500 gm weight on the Weight holder with the help of T – Pin,

at this stage buzzer stops blowing because spherometer leg is not in contact with sample owing to bending of rod.

13. Rotate the Circular Scale of spherometer (clock wise direction) till the buzzer blows (because when it touches the sample, circuit becomes complete and buzzer starts blowing).

14. Again note the readings of M.S. and C.S. * 0.01mm (least count) in Table 1, and then evaluate the total reading i.e., T2.

15. Displacement of sample determined by T2–T1. Tabulate the reading inObservation Table 1.

16. Place one more 500 gm weight on the Weight holder, total 1 kg weight is hanging, at this time again buzzer stop blowing because spherometer leg is not in contact with sample.

17. Rotate the Circular Scale of spherometer till the buzzer blows (because when it touches the sample, circuit becomes complete and buzzer starts blowing).

18. Again note the readings of M.S. and C.S. * 0.01 (least count) in Table 1, and then evaluate the total reading i.e., T3.

19. Displacement of sample is determined by T3–T1. Tabulate the reading inObservation Table 1.

20. Place 500 gm weights one by one on the Weight holder i.e., total weight will be1.5kg, 2kg, 2.5kg and 3.0kg. For these different weights position, repeat the steps 16 to 19 and tabulate the readings for T4, T5, T6 and T7.

21. Tabulate all the readings in the given Observation Table 1.

Decrement of the Loads :

22. At 0kg load decreasing, spherometer reading is same as 3kg increasing load. It means T7 for increasing load and T1 for decreasing load is same.

23. Now remove 500 gm weight from the Weight holder (i.e., decreasing of 0.5kg load from sample) and again note Main Scale reading (M.S), Circular Scale reading (C.S) i.e., no of divisions * 0.01mm (least count) and find total reading. This spherometer reading is T2.

Note : Before removing the weights rotate the spherometer fully anticlockwise.

24. Displacement of sample is T1– T2. Tabulate the reading in Observation Table 1.

25. Now again remove 500 gm. weight from the Weight holder (i.e., decreasing of1kg load from sample) and again note Main Scale reading (M.S), Circular Scale reading (C.S) i.e., no of divisions * 0.01mm (least count) and find total reading


i.e., T3.

26. Displacement of sample is T1 – T3. Tabulate the reading in Observation Table 1.

27. Remove 500 gm weights one by one from the Weight holder i.e., decrement of load will be 1.5kg, 2kg, 2.5kg and 3kg respectively. For these different weights position, repeat the steps 25 and 26 and tabulate the readings for T4, T5, T6 and T7.

28. Tabulate all the readings in the given Observation Table 1 in the load decreasing column.

Observation Table 1 :

S.No

Load(in kg)

Load increasing (in mm)

Displacement (x)(in mm)

xn=Tn+1-T1

Load decreasing (in mm)

Displacement (y)(in mm)yn=Tn+1-T1

Mean ofdisplace ments (in mm)d=(x+y)/2

M.S C.S*0.01

T =M.S+C. S

M.S C.S*0.01

T=M.S+C. S

1. 0 T1=…..

T1=…..

2. 0.5 T2=…..

x1=…. T2=…..

y1=….. d1 =….

3. 1.0 T3=…..

x2=…. T3=…..

y2=….. d2 =….

4. 1.5 T4=…..

x3=…. T4=…..

y3=….. d3 =….

5. 2.0 T5=…..

x4=…. T5=…..

y4=….. d4 =….

29. Take the mean of displacements individually d1 = (x1+y1)/2, d2 = (x2+y2)/2,..............and so on.

30. In Observation Table 2, insert all the values of individual Mean of displacements d1, d2, d3........

31. Find the depression of sample for particular amount of weight difference (for eg.0.5 kg).

32. Tabulate the depression (readings for 0.5 kg. in given Observation Table 2.

33. Take the mean of depression.www.hik-consulting.pl

Observation Table 2 :

S No. Load (in kg) Mean of displacements( in mm)

Depression for 0.5 kg (in mm) (for any particular amount)

1. 0

2. 0.5 d1=......... d1

3. 1 d2=......... d2 - d1 =.............4. 1.5 d3=......... d3 - d2 =.............

5. 2.0 d4=......... d4 - d3 =.............

.................... (in mm)

34. Take the length, breadth, depth of a given material of sample from the technical specification on page no.5.

35. Length, Breadth, Depth all are in cm. Change it into

meter. l =................... (in meter) 1 m = 100cm

b =.................. (in meter) 1 m = 1000mm

d =...................(in meter)

36. Put all the readings in given formula, where Y is elastic constant or Young'sModulus of elasticity.

mgl3

Y=4bd3d

Where 'm' is mass (in kg) for which at particular load, depression had determined (here it is 0.5 kg.), g = 9.8 m/sec2, length (l), breadth (b), depth (d), and depression in meters, and then Elastic Constant (Y) is in N/m2.

Precaution : After performing the experiment remove all the weights from theWeight holder.

37. Now take Aluminium and Brass samples one by one to determine their Young’s modulus of Elasticity, follow the same procedure as for Iron sample.

Precaution : The elasticity of Aluminium and Brass samples is less so doesn’t exceed weight more than 1.5kg on Weight holder.


Warranty

1) We guarantee the product against all manufacturing defects for 24 months from the date of sale by us or through our dealers. Consumables like dry cell etc. are not covered under warranty.

2) The guarantee will become void, if

a) The product is not operated as per the instruction given in the operating manual.

b) The agreed payment terms and other conditions of sale are not followed.

c) The customer resells the instrument to another party.

d) Any attempt is made to service and modify the instrument.

3) The non-working of the product is to be communicated to us immediately giving full details of the complaints and defects noticed specifically mentioning the type, serial number of the product and date of purchase etc.

4) The repair work will be carried out, provided the product is dispatched securely packed and insured. The transportation charges shall be borne by the customer.

List of Accessories1. Sample Stand……………………………………………….…….………....1 No.

2. Weight Holder………………………………………………………..…......1 No.

3. Samples of different material (Al., Brass, Iron)………………………..…...3 Nos.

4. Weights (500gms)…………………………………………………….…….4 Nos.

5. Stand with buzzer and spherometer………………………………………...1 No.

6. 12 Volt DC Adaptor…………………………………………………………1 No.

7. Learning Material…………………………………………………..…..…..1 No.

8. Patch Cords 12”………………………………………………………….…2 Nos.www.hik-consulting.pl

Young's Modulus Setup NV6040 · Nvis Technologies Pvt. Ltd. 3 NV6040 Introduction NV6040 Young's Modulus Setup is a complete system used to determine Young’s modulus of elasticity

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