Science Introduction

P-N JUNCTION DIODE

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P-N junction is obtained by P-type semiconductor with an N semiconductor. The figure shows the P-N junction diode before the formation of the junction.

There are excess holes, shown as small circles, in the P-section which exist in the covalent bond between the host atoms and the impurity atoms. The figure shows two impurity atoms of Aluminum near the junction.

There are excess electrons in the N section obtained from the pentavalent impurity atoms. The figure shows two Arsenic impurity atoms near the junction. Both N and P sections are electrically neutral.

The electron defuse from N to P section as the N section has excess of electrons as compared to P section. These electrons occupy holes of P side near the junction. A small amount of holes also diffuse from P to N section.

The adjoining figure shows the situation after some diffusion has occurred. Two electrons of Arsenic are shown to occupy the two holes near the Aluminum atoms. This leaves Arsenic atoms as positive ions and Aluminum atoms as negative ions. As the diffusion progresses, more and more Arsenic and Aluminum atoms become positive and negative ions respectively.

This result in the steady electric field near the junction due to the charges on the ions direction of which is from N to P region. The electrons have to overcome this increasing electric field to diffuse from N to P side. The diffusion of electrons stops when the electric field is sufficiently established to oppose the diffusion. This situation is shown in the following figure.

Two points are noteworthy:

(1) Electrons are no longer the majority charge carriers in the small region of the N type material near the
junction and the holes are not the majority charge carriers in the small region of the P-type semiconductor near the junction. These regions are known as depletion region as they are deplete of their majority charge carriers. The width of the depletion region is approximately 0.5 μm.

(2) The varying electric potential at the region near the junction is called the depletion barrier. Its value is about 0.7 V for Si and 0.3 V for Ge.

It can be seen from the band diagram of the P-N junction shown that the charge carriers need about qVB energy to cross the junction and go into the other region of the diode.

Less the amount of impurity atom added to the P and N type semiconductors, wider is the depletion region and weaker the electric field intensity near the junction.

The depletion region contains immobile positive and negative charges which constitute a capacitor having depletion capacitance or transition capacitance, C d. The width of the depletion region increases with the increase in the reverse bias which decreases the value of the capacitance. Such diode in which value of the capacitance varies with voltage is known as varactor diode or variable diode.

N AND P TYPE SEMICONDUCTORS

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N-TYPE SEMICONDUCTORS: -

N-type semiconductors is prepared by adding pentavalent impurities like Antimony or Arsenic in pure semiconductor. P-type semiconductor is prepared by adding trivalent impurities like Aluminium, Gallium or Indium.
The figure shows N-type semiconductor in which two Arsenic atoms have replaced two Germanium atoms in the lattice structure of Ge crystal. Four of the five valence electrons of As atom are used up in forming covalent bonds and the fifth electron can act as a free electron with 0.01 eV energy. This energy is 0.05 eV in case of Silicon atom. This much energy is easily available at room temperature as thermal energy.

The pentavalent impurity is called donor impurity as it denotes the electric charge carrier electron, to the host atom. It is added in proportion of 1 in 106 pure atoms. Hence in one mole of crystal, about 1017 impurity atoms and 1017 free electrons are present. A good conductor like copper contains nearly 1023 free electrons per mole. Besides these, some more free electrons and equal number of holes result from breaking of covalent bonds. As their number is very small as compared to the free electrons from the impurity atoms, electrons are the majority charge carriers and holes minority charge carriers in the case of N-type semiconductors ( n e > n h ).

P-TYPE SEMICONDUCTORS: -

If trivalent impurities like Aluminum is
added to Ge or Si, then three free electrons of this impurity atom form covalent bonds with its neighbouring three Ge or Si atoms. Thus there is a deficiency of one electron in the formation of the fourth covalent bond. This deficiency of electron can
considered as a hole which is present in one of the bonds between the aluminium and Ge or Si atoms. This hole has a tendency to attract electron. Hence aluminium atom is known as acceptor impurity. Here, holes which behave as positively charged particles are majority charge carriers and electrons are minority charge carriers. Hence such a semiconductor is known as P-type semiconductors (n e > n h). The figure shows symbolic representation of aluminium impurity added to Ge crystal lattice.

CONDUCTORS, INSULATORS AND INTRINSIC SEMICONDUCTOR

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The elements in the first three groups of the periodic table like alkali metals, noble metals, Aluminum, etc. are good conductors due to the presence of free electrons. Non-metals are bad conductors of electricity due to lack of free electrons. The elements in the fourth group of the periodic table like Si and Ge have greater resistance than good conductors but less than bad conductors. They are known as semiconductors. They behave as bad conductors at absolute zero temperature in their pure form.

The resistivity of the good conductors increases with temperature, while the resistivity of the semiconductors decreases on increasing the temperature unto a certain limit. The conductivity of the semiconductors is changed by making radiation of suitable frequency incident on them.

Two very important semiconductors Ge and Si are discussed here. Both have diamond crystal structure. If an atom of Si is considered at the center of the tetrahedron, then its four nearest neighbours are at the vertices's of a tetrahedron as shown in the figure. Diamond crystalline structure is obtained on extending this arrangement in a three dimensional space.

The electronic arrangement of Si is 1s² 2s² 2p⁶ 3s² 3p². The electrons in 1s² 2s² 2p⁶ completely occupy the K and L shells. 3s² 3p² electrons are the valence electrons. These 2 s orbitals and 2 p orbitals combine to form 4 sp³ complex orbitals. These orbitals combine with similar such orbital’s of the neighbouring atoms and form covalent bonds. Thus, each of the four valence electrons of the silicon forms a covalent bond with its four neighbouring atoms as shown in the figure.

At absolute zero temperature, Si and Ge behave as insulators as the valence electrons are bound in covalent bonds. At room temperature, these bonds break due to thermal oscillations of atoms freeing the electrons which increase conductivity. Deficiency of electron in a bond produces a vacant space which is known as a hole. The hole has the ability of attracting electrons and the randomly moving free electron can get trapped in a hole. Thus hole behaves as a positive charge though it is neither a real particle nor has any positive charge.

On applying p.d. between two ends of a crystal as shown in the figure, electric current gets set up. Now, thermal oscillations and external electric field cause covalent bonds to break and the free electrons produced get trapped in the holes during their motion. Simultaneously, new holes are produced by electrons breaking free from the covalent bonds. The free electrons move towards the positive end and the holes to the negative end. The motion of holes towards the negative end is equivalent to the motion of bound electrons towards the positive end. Thus current in a semiconductor is due to ( i ) motion of free electrons and ( ii ) motion of bound electrons. Both these currents are in the same direction.

The number density of free electrons n_e and holes n_h in a pure semiconductor are equal. Pure semiconductor is called intrinsic semiconductor. Hence electrons and holes are called intrinsic charge carriers and their number density is indicated by n_i. n_e = n_h = n_i.

BEATS

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DEFINITION: -

"Beats can be defined as the periodic variation in the intensity of sound at a given point

due to super-position of two waves having slightly different frequencies."

EXPLANATION: -

When two waves having slight difference of frequency and same amplitude pass through the same region of space, interference takes place. This type of interference is known as 'Beats'. In this case when two waves are observed at a given point they are periodically in or not of step with one another. That is, there is an alternation in time b/w constructive and destructive interference. This alternation is called Beats

EXPLANATION WITH EXAMPLE: -

If two tuning forks of slightly different frequencies are set to vibrate simultaneously, we hear a sound of alternating high and low intensity. This is called a beat and phenomenon is called is Beats.

BEAT FREQUENCY: -

Beat frequency is the no. Of beats one hears in one second. It is defined as the difference infrequency b/w two sounds.

The maximum beat frequency that a human ear can detect is 7beats/seconds.

ULTRASONICS: -

Definition: -

The longitudinal waves with frequencies above the audible range are known as ULTRASONICS. Ultrasonic have frequency greater than 20,000Hz.

PRODUCTION OF ULTRASONICS: -

Ultrasonic are produced by vibrating quartz crystals electricity. With the help of this device very high frequency range ultrasonic waves can easily be produced.

USES OF ULTRASONICS IN MEDICINE: -

· Ultrasonic is now widely used as diagnostic therapeutic and surgical tool in medicine.

· Ultrasonic is preferred over x-rays due to safety.

· To kill microbes in liquids.

IN INDUSTRY: -

· To find cracks in metal structures.

IN TECHNOLOGY: -

· They are used in echo-depth sounding devices for determining depth of sea.

· In under water navigation ultrasonic is used instead of RADAR.

IN GENERAL: -

· In guidance devices for blind persons.

SECOND'S PENDULUM: -

A pendulum that completes its one vibration is two seconds is known as 2nd’s pendulum.

A pendulum whose time period is 2 sec is called second's pendulum.

· Frequency of second pendulum is 0.5Hz

· Length of second's pendulum is 100cm.

CHARACTERISTICS OF SOUNDS

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Musical sound has the following characteristics:

1. Loudness

2. Pitch

3. Quality or Timber

LOUDNESS OF SOUND: -

Definition: -

Loudness is that characteristics of musical sound which enables us to distinguish between a faint sound and a loud sound.

Loudness is defined as the auditory sensation produced by the sound in ear.

Loudness of sound depends upon the intensity of sound. Loudness is actually a sensation of human consciousness. It is denoted by 'L'.

Loudness of sound is directly proportional to the logarithm of the intensity of sound

i.e.

L ∞ Log I

L = K (Log I)

Where "I" is the intensity of sound.

FACTORS ON WHICH LOUDNESS DEPENDS: -

Area of vibrating body: -

The larger the area of vibrating body the louder the sound produced. For example a DHOOL produces a loud sound due to larger area. Similarly a small DHOLAC or CONGO produces a small loudness.

Amplitude of vibrating body:

The greater the amplitude of vibrating body, the louder the sound produced.

Distance b/w source and listener:

Smaller is the distance b/w source of sound and the listener greater is the loudness of sound as heard by the listener.

PITCH OF SOUND: -

"The characteristic of sound by which a shrill sound can be distinguished from a grave sound is known as PITCH."

Pitch of sound depends upon the frequency of sound. The greater the frequency, the higher is the pitch and vice versa. It is the pitch of sounds that enable us to distinguished b/w a sound of man and woman or man and dog. Etc. sound of a woman is shrill due to high pitch. Sound of a dog is grave due to low pitch and low frequency.

QUALITY OR TIMBER: -

"The property of sound by virtue of which we can distinguish between two sounds of the Same pitch and the loudness originating from two different musical instruments."

The sound produced by two different instruments is usually complex. It is a mixture of several tones. The tone of lowest frequency is called Fundamental frequency and other tones are known as OVERTONES OR HARMONICS. The loudness of sound depends upon the amplitude of vibration. And pitch determined by its fundamental frequency. Two or more sound may have the same loudness and the same pitch but that they may differ in number and relative intensities of overtones. The quality of sound depends upon the wave form of the resultants. Nature has such a great diversity that it is very rare to have some overtones of two persons exactly. So this difference is overtones make it possible to recognize each sound. This characteristic of sound is called QUALITY.

INTENSITY OF SOUND: -

"The intensity of sound is defined as the amount of energy transmitted per second through unit area held perpendicularly in the direction of sound waves."

Intensity of sound = E / t. A

I = E / t. A

Unit:

In international system the unit is Watt / m²

STANDING WAVES

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When two identical progressive waves with sane amplitude and frequency travel through a medium with equal velocity in opposite direction, they super impose over each other and produce a new type of wave which is known as Stationary Wave or Standing Wave.

In stationary waves there is no flow of energy along the waves.

When stationary waves are set up in a medium, the medium vibrates in several segments called Loops.

The point of destructive interference is called NODE, at nodes displacement is zero.

The point of constructive interference is called anti nodes; at anti node displacement is maximum.

INTERFERENCE

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When two waves pass through a medium at a point, then the resultant displacement at that point is the vector sum of the displacements due to two component waves. This modification in displacement as a result of superposition of two waves is called INTERFERENCE.

The phenomenon in which two waves traveling in same direction reinforce each other at some points and cancel the effect of each other at some different points is called Interference of waves.

CONSTRUCTIVE INTERFERNCE: -

Type of interference in which two waves overlap each other in such a way that they reinforce or increase the effect of each other is called Constructive Interference.

In constructive interference crest of one wave coincides that crests of other and trough coincides with trough.

In constructive interference path difference of two waves is 'm λ’

DESTRUCTIVE INTERFERENCE: -

Type of interference in which two waves overlap each other in such a way that they cancel the effect of each other is called Destructive Interference.

In destructive interference crest on wave coincides the trough the other wave.

In destructive interference path difference of two waves is (m + ½) λ.

WAVE MOTION

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The mechanism by which energy travels (transfers) from one point to the other point is called as Wave Motion. Wave motion is one of the most important ways of transferring energy.

A wave motion may be defined as a disturbance which travel in the material medium and carry energy.

LONGITUDINAL WAVES: -

The type of wave motion in which particles of medium vibrates to and fro and execute S.H.M. in the direction of propagation of waves is called Longitudinal Wave.

A longitudinal wave is one in which the disturbance of medium particles in parallel to the direction of travel of the wave.

EXAMPLES: -

Sounds waves, waves, set-up in spring.

TRANSVERSE WAVES: -

The type of motion in which particles of medium vibrate to and fro or execute S.H.M. in the direction perpendicular to the direction of propagation of waves is called Transverse Waves.

EXAMPLES: -

Light waves, radio waves, microwaves

RIPPLE TANK

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INTRODUCTION: -

RIPPLE TANK is an apparatus which is used to study the features or characteristics of wave’s mechanics.

CONSTRUCTION: -

A ripple tank consists of a rectangular tray containing water. It is provided with a transparent glass sheet at the bottom. A screen is placed well below the tray to observe the characteristics of waves generated in water. A lamp is placed above the tray

WORKING: -

When an observer dips a rod or his finger into the water of ripple tank, waves are generated. There is also a mechanical way to generate pulses in water i.e. electric motor. The lamp enlightens the waves which are focused on the bottom screen. The wave crests act as converging lenses and tend to focus the light from the lamp. The wave troughs act as diverging lenses and tend to spread it. This results that crests appear as bright bends and troughs as dark bends on the screen.

PRODUCTION OF STRAIGHT RIPPLES: -

Straight pulses are produced by dipping a finger or a straight rod periodically in water.

PRODUCTION OF CIRCULAR RIPPLES: -

Circular pulses are produced by dipping the pointed end of a rod periodically in water.

ANALYSIS OF WAVES: -

If straight pulses are generated and a piece of paper is thrown on the surface of water, it is found that the paper simply moves up and down as each of the waves passes across it. By means of a stop watch time period of the rod and paper is measured. The two time periods are found to be equal. This shows that the particles of medium execute simple harmonic motion with the same time period as that of the body generating pulses.

SIMPLE PENDULUM

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Simple pendulum consists of a heavy mass particle suspended by a light, flexible and in-extensible string.

MOTION OF THE BOB OF SIMPLE PENDULUM: -

The motion of the bob of simple pendulum, simple harmonic motion if it is given small displacement. In order to prove this fact considers a simple pendulum having a bob of mass 'm' and the length of pendulum is 'l'. Assuming that the mass of the string as pendulum is negligible. When the pendulum is at rest at position 'A', the only force acting is its weight and tension in the string. When it is displaced from its mean position to another new position say 'B' and released, it vibrates to and fro around its mean position.

Suppose that at this instant the bob is at point 'B' as shown below:

FORCES ACTING ON THE BOB : -

· Weight of the bob (W) acting vertically downward.

· Tension in the string (T) acting along the string.

The weight of the bob can be resolved into two rectangular components:

1. W cos θ along the string.

2. W sin θ perpendicular to string.

Since there is no motion along the string, therefore, the component W cos θ must balance tension (T)

i.e. W cos θ = T

This shows that only W sin θ is the net force which is responsible for the acceleration in the bob of pendulum.

According to Newton's second law of motion W sin θ will be equal to m × a

i.e. W sin θ = m a

Since W sin θ is towards the mean position, therefore, it must have a negative sign.

i.e. m a = - W sin θ

But W = mg

m a = - m g sin θ

a = - g sin θ

In our assumption q is very small because displacement is small, in this condition we can take sinθ = θ

Hence a = - g θ ----------- (1)

If x be the linear displacement of the bob from its mean position, then from figure, the length of arc AB is nearly equal to x

From elementary geometry we know that:

Where s = x, r = l

Putting the value of q in equation (1)

As the acceleration of the bob of simple pendulum is directly proportional to displacement and is directed towards the mean position, therefore the motion of the bob is simple harmonic when it is given a small displacement.

Show that the motion of a mass attached to the end of a spring is SHM: -

Consider a mass "m" attached to the end of an elastic spring. The other end of the spring is fixed at the firm support as shown in figure "a". The whole system is placed on a smooth horizontal surface. If we displace the mass 'm' from its mean position 'O' to point "a" by applying an external force, it is displaced by '+x' to its right, there will be elastic restring force on the mass equal to F in the left side which is applied by the spring.

According to "Hook's Law

F = - K x ---- (1)

Negative sign indicates that the elastic restoring force is opposite to the displacement.

Where K= Spring Constant

If we release mass 'm' at point 'a', it moves forward to ' O'. At point ' O' it will not stop but moves forward towards point "b" due to inertia and covers the same displacement -x. At point 'b' once again elastic restoring force 'F' acts upon it but now in the right side. In this way it continues its motion from a to b and then b to a.

According to Newton's 2nd law of motion, force 'F' produces acceleration 'a' in the body which is given by

F = m a ---- (2)

Comparing equation (1) & (2)

m a = - k x

Here k / m is constant term, therefore,

a = - (Constant) x

a ∞ -x

This relation indicates that the acceleration of body attached to the end elastic spring is directly proportional to its displacement. Therefore its motion is Simple Harmonic Motion.

SIMPLE HARMONIC MOTION

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"Type of vibratory motion in which acceleration of body is directly proportional its displacement and the acceleration is always directed towards the equilibrium (mean) position is called Simple Harmonic Motion. "

Acceleration ∞- displacement

a ∞ - x

Negative sign indicates that acceleration and displacement are opposite in direction.

Examples of S.H.M:

BASIC CONDITIONS TO EXECUTE SHM: -

Basic conditions to execute simple harmonic motion are as under:

· There must be elastic restoring force acting on the system.

· The system must have inertia.

· The acceleration of the system should be directly proportional to its displacement and is always directed to mean position i.e. a ∞ - x

EXAMPLES OF SHM: -

· Motion of a body attached to the end of an elastic spring

· Motion of the bob as a simple pendulum if it is gives a small displacement.

Motion of an elastic strip.

· Motion of the prongs of a tuning fork.

· Motion of the wire of a guitar or violin.

CHARACTERISTICS OF SHM: -

· The motion must be vibratory.

· The motion should be a periodic motion.

· The restoring force should be directly proportional to the displacement of the body from its mean position.

RADIOACTIVITY, PROPERTIES OF RADIOACTIVE RAYS

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RADIOACTIVITY
All the elements having atomic number greater than 82 emit invisible radiation all the time. The phenomenon of emission of these powerful rays is called "Natural Radioactivity" and the element that emits such rays is called "Radio Active Element".
TYPES OF RADIO ACTIVE RAYS
There are three types of radioactive rays: · α-Rays · β-Rays · γ-Rays
· PROPERTIES OF α-RAYS: -

(a) NATURE: α ray consists of α particle. Each α particle consists of Helium (₂He⁴) nucleus.
(b) CHARGE: α particle carry positive charge.
(c) MASS: Mass of each α - particle is 4 times that of a proton or H-atom.
(d) IONIZATION: Ionization power of α ray is very high.
(e) PENETRATION POWER: Penetration power of α ray is very small.
(f) FLUORESCENCE: α ray’s produce fluorescence in different substances.
(g) EFFECT ON HUMAN BODY: α ray produce burn and sore on human body.
(h) ARTIFICIAL RADIO ACTIVITY: α rays can produce artificial radioactivity is certain nuclei.
· PROPERTIES OF β –RAYS: -
(a) NATURE: β rays consist of fast moving electrons.
(b) CHARGE: β rays have negative charge.
(c) VELOCITY: Velocity of β rays is from 9 x 10⁷ m/sec to 27 x 10⁷ m/sec.
(d) EFFECT ON PHOTO GRAPHIC PLATE: β rays affect photo graphic plate
(e) IONIZATION POWER: Ionization power of β rays is very small.
(f) KINETIC ENERGY: Kinetic energy of β rays is less than that of β - rays.
(g) FLUORESCENCE: β rays produce fluorescence in different substance.
· PROPERTIES OF γ – RAYS: -
(a) NATURE: γ rays are electromagnetic radiation.
(b) CHARGE: γ - rays are no charge.
(c) VELOCITY: γ - rays travel with the velocity of light that is 3 x 10⁸ m/sec.
(d) PENETRATION POWER: Penetration power of γ - rays is very large. It is about hundred times larger than that of γ rays.
(e) FLUORESCENCE: γ - rays produce feeble fluorescence When incident on screen coated with barium platino cyanide.

NUCLEAR FUSION-RADIOACTIVITY

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NUCLEAR FUSION: -

“The process of forming heavy nucleus from two or more light nuclei in which energy is released is called ‘NUCLEAR FUSSION’ ”

“The combining of two lighter nuclei to form a relatively heavier nucleus with the release of energy is called ‘NUCLEAR FUSSION’ ”

EXAMPLE: -

FUSSION OF DEUTERIUM AND TRITIUM: -

When ₁H² and ₁H³ nuclei are brought together they form ₂He⁴ nucleus with the re3lease of energy.

CHARACTERISTICS OF FUSION: -

(1)

(1) Energy release during a fusion process in greater than that of fission.

(2) To produce a fusion process a very high temperature is required to overcome repulsion between positive nuclei.

FISSION

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DEFINITION: -

"The process in which a heavy nucleus is broken into two lighter nuclei with the release of energy is called Nuclear Fission."

The disintegration of a heavy nucleus after capturing neutron with
the release of energy is called "Nuclear Fission."

In one fission of ₉₂U²³⁵ nucleus, about three neutrons are obtained.

FISSION IN ₉₂U²³⁵

In 1939, Hann and Stressman discovered that fission can be produced by bombarding ₉₂U²³⁵ with slow neutrons. When ₉₂U²³⁵is bombarded with neutron, it is broken down into two lighter nuclei and about 200Mev energy is released in this process.

COLLISION GEOMETRY: -

Fission reaction in uranium can be explained by the following schematic diagram.

FISSION CHAIN REACTION

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In one fission of ₉₂U²³⁵ nucleus, about three neutrons are obtained. These fast moving neutrons undergo successive collision with the other ₉₂U²³⁵ nuclei. As more and more nuclei are broken by the neutrons, more and more neutrons are obtained and an uncontrolled fission process is started which is referred to as FISSION CHAIN REACTION. If it is not controlled, then all the ₉₂U²³⁵ atoms are broken and a large amount of energy is produced. An interesting fact which must be noted down is that no fission chain reaction will take place if the amount of uranium is less than a certain mass known as CRITICAL MASS.

EINSTEIN’S MASS ENERGY EQUATION

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According to Einstein theory of relativity "Mass and Energy are inter convert able". Einstein established a relation between mass and energy known as "Einstein’s Mass Energy Equation".
E = mc²
	where E = Energy m = Mass C = Velocity of light (3x10⁸ m/sec) DEFINITION OF FISSION: - "The process in which a heavy nucleus in broken into two lighter nuclei with the release of energy is called Nuclear Fission." OR The disintegration of a heavy nucleus after capturing neutron with the release of energy is called "Nuclear Fission." In one fission of ₉₂u²³⁵ nucleus, about three neutrons are obtained. FISSION IN ₉₂U²³⁵ In 1939, Hann and Stressman discovered that fission can be produced by bombarding ₉₂u²³⁵ with slow neutrons. When ₉₂u²³⁵is bombarded with neutron, it is broken down into two lighter nuclei and about 200Mev energy is released in this process.

NUCLEUS

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Define a nucleus.

Generally the nucleus of an atom has the following features:

NUCLEUS

The center part of an atom is called Nucleus.

SHAPE OF NUCLEUS

Nucleus has spherical shape.

SIZE OF NUCLEUS

Nucleus has very small size. Diameter of nucleus is about 1x10 -14m.

CHARGE OF NUCLEUS

It has positive charge due to presence of proton.

NUCLEON

Neutron and protons are collectively known as Nucleon.

ATOMIC NUMBER OR CHARGE NUMBER

Total number of proton in the nucleus of an atom is called its atomic number.
OR
Total number of electrons in an atom is also known as atomic number, because
in an atom number of an electron is always equal to proton.

SYMBOL

It is denoted by z

z = number of protons
OR
z = number of electron

MASS NUMBER

Total number of a proton and neutrons in an atom is called Mass number.

SYMBOL

It is denoted by (A).

FORMULA

A = no. of proton + no of neutron
A = p+ n
OR
A = Z + n.

ARCHIMEDES PRINCIPLE

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According to Archimedes principle:

"When a body is immersed in a liquid, it loses its weight or an upward thrust acts upon it which is equal to the weight of an equal volume of the liquid displaced."

PROOF OF ARCHIMEDES PRINCIPLE: -

Consider a cylinder of length 'L' and area of cross-section 'A' immersed in a liquid of density 'r.'
Let the depth at point a = h₁ the depth at point b = h₂ Now, Pressure at point a and b is Pa = rgh₁, Pb = rgh₂ We know that [Thrust = P. A] Thrust at point a = rgh₁A Thrust at point b = rgh₂A Net thrust = rgh₂A - rgh₁A Net thrust = rgA (h₂- h₁) [But from figure h₂- h₁= L] There fore, Net thrust = rgAL Net thrust =rgV Net thrust = (rV) g Net thrust = mg Net thrust = W

Net thrust = weight of liquid displaced.

This shows that upward thrust on the cylinder is equal to the weight of liquid displaced.

RESULTS OF ARCHIMEDES PRINCIPLE: -

With the help of Archimedes principle we conclude that:

(1) A body will float over a liquid if displaces liquid whose weight is greater than the weight of body.

(2) A body will sink in a liquid if it displaces liquid whose weight is less than the weight of body.

Scientific Reason: -

Question: -

A huge ship floats over water but a small nail sinks into water. Explain why?

Answer: -

Floating of a huge ship or sinking of a nail is according to Archimedes principle.

A huge ship displaces water whose weight is greater than the weight of ship & the upward thrust on the ship balances its weight. That's why ship floats over water surface. On the other hand nail displaces water whose weight is less than the weight of the nail. Due to this reason nail sinks into water.

PRESSURE

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Pressure is defined as

“The perpendicular force acting per unit area of a surface."

Mathematically:

Pressure = Force / Area

P = F / A

Units of pressure: -

(i) N/m2 or Pascal (IN S.I. system)

(ii) Atmosphere

(iii) cm of Hg

(iv) mm of Hg or Torr

PRESSURE IN LIQUIDS: -

The pressure at any point in a liquid depends on the density and the depth in the liquid.

EXPLANATION: -

Consider a liquid of density “r “.

We know that:

Density = mass / volume

ρ = m / V

But area x height = volume i.e. A x h = V

ρ = m / Ah

m = ρ A h

Since W = mg, therefore

W = ρ A h g

Also

P = F / A ---------------- (i)

Force applied is equal to the weight of the liquid i.e.

F = W = ρ A h g

Putting the value of F in equation (i), we get

P = ρ A h g / A

P = ρ h g

This is the required expression for pressure in liquids.

PASCAL'S LAW: -

STATEMENT: -

Pascal's law states that:

“Liquids transmit pressure equally in all directions."

In other words

"When pressure on any portion of a confined liquid is changed, the pressure on every other part of the liquid is also changed by the same amount."

It has been observed that if we apply pressure to a liquid in a container, then it is transmitted equally in all direction & acts perpendicularly to the walls of the container.

USES OF PASCAL'S LAW: -

Pascal's Law has a number of applications in our daily such as:

· Hydraulic Brakes

· Hydraulic Press

· Hydraulic Lift

YOUNG'S MODULUS

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"The ratio of stress to the longitudinal strain is called Young's modulus."

Mathematically: -

Young's Modulus = Stress / Longitudinal Strain

Y = s / e .......... (i)

But s = F / A and e = DL / L

Putting these values in equation (i)

Y =( F / A) / (DL / L)

OR
Y = F L / A DL

In S.I. system unit of ‘Young's Modulus is N / m²

HOOK'S LAW

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Hook’s law is a quantitative relation between stress and strain.

STATEMENT: -

Hook's law states:

"Within elastic limit, strain produced in a body is directly proportional to stress"

i.e.

Strain ∞ Stress

Strain = (Constant) (Stress)

Where 1/K = constant of proportionality

Strain = (1/K)(Stress)

Stress / Strain = K

With the help of above equation Hook’s law can also be stated as:

"The ratio of stress to strain is constant."

ELASTICITY

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The property of solid by virtue of which a solid body recovers its original shape after the removal of an applied force is called "ELASTICITY".

ELASTIC LIMIT: -

If applied force on a solid is gradually increased, a state is reached after which the material will not return to it original shape even after the removal of applied force. This limit is called "ELASTIC LIMIT".

After elastic limit, material is permanently deformed. Different substances have different elastic limit.

STRESS: -

When a body is deformed, the internal force came into play per unit area to restore it to its original state is called "STRESS"

"Stress is an opposing force expressed per unit area which resists any change in shape."

Stress is equal to the force per unit area.

Mathematically: -

Stress produces when a body is made to change in length, volume or Shape by the application of an external force.

UNIT OF STRESS: -

(i) N/m2 in S.I. System

(ii) Dyne/cm2 in C.G.S. System.

STRAIN: -

"Strain is the fractional deformation produced in a body when it is subjected to a set of deforming forces."

The change in length, volume or shape due to the application of a deforming force is called "Strain".

"The fractional Deformation due to stress is called STRAIN."

Strain has no unit because it is a ratio of two similar physical quantities.

LONGITUDINAL STRAIN: -

"The change in length per unit length of a body due to a deforming force is called LONGITUDINAL STRAIN"

Mathematically: -

MATTER

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KINETIC MOLECULAR THEORY OF MATTER: -

According to kinetic theory of matter:

· Matter is made of very small particles called MOLECULES.

· These molecules are in a state of motion.

· They possess Kinetic Energy.

· Molecular motion may be translational, rotational or vibrational.

· These molecules attract each other.

· As the temperature of a substance is increased, its molecular speed is also increased and vice versa.

· If a substance is compressed, The K.E of its molecules increases and its temperature rises

BROWNIAN MOTION: -

A famous scientist ROBERT BROWN observed that molecules of a substance are moved in ZIG ZAG path. Their motion is random. They collide with each other and move in a new direction after collision in ZIG ZAG fashion. This type of motion present in the molecules of matter is called "Brownian motion".

SCREW AND SCREW JACK

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SCREW: -

Screw is one of the most important machines. It is used to hold different parts of machines together. It has waste applications in our daily life plus in industries. It is used in every type of device.

CONSTRUCTION AND WORKING: -

It simply consists of a threaded rod with a head known as “Screw head”. It has a number of threads. The perpendicular distance between two adjacent threads is known as pitch of screw. The thread of screw can be regarded as a continuous inclined plane wrapped round a cylinder of radius d .

MECHANICAL ADVANTAGE: -

If we apply an effort ‘P’ on the head of screw then it turns one revolution and at the same time the screw moves forward in to the wood or wall through a distance equal to its pitch “h”. The effort ‘P’ moves through a distance 2pd. The screw remains in the wood due to frictional forces between the screw and the wood. A large amount of energy changes in to heat energy during the process of screwing.

Let us assume an ideal case when there is no loss of energy then; in this condition

Output = input

P x 2pd = W x h

W/P = 2 p d/h

Hence, the mechanical advantage of the screw will be.

M.A. = 2pd/h

The mechanical advantage of the screw depends upon the following factors.

· PITCH: -

In order to increase mechanical advantage of screw we must use a screw of small pitch.

· RADIUS OF SCREW: -

Larger is the radius of screw head, greater is the mechanical advantage.

SCREW JACK: -

A screw jack is a simple machine. It is used to lift cars or heavy automobiles. It consists of a long screw rod which passes through a threaded block B and a handle. The distance between two consecutive threads is known as pitch of screw.

MECHANICAL ADVANTAGE: -

When an effort is applied to the handle, the effort moves in a circle of radius “d” while “d” is the length of the rod and the block “B” moves up equal to the pitch of the screw jack. If the handle is turned through one complete revolution in a circle of radius “d” the effort moves through a distance 2pd and consequently the load is raised through a height h. Hence, the mechanical advantage is given by:

M.A. = 2pd/h

M.A. = Distance through which the effort is moved/height through which the load is raised

We know that the pitch of the screw is very small as compared to the length of the rod, so the mechanical advantage should be very large. Due to frictional force between the different parts of screw jack, the efficiency is less than one. It is due to the reason that lot heat energy is used for overcoming the frictional forces.

It should be remembered that in case of screw jack friction is a necessary part of operation, because in the absence of friction, it would unwind at once when applied force is removed.

WEDGE

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Wedge is also a type of simple machines. It is used in levers as a fulcrum. It is also used for splitting the wood in to small pieces. It is used as an Ax.

CONSTRUCTION OF WEDGE: -

A wedge is made of two inclined planes joined together. The effort ‘P’ is applied on the top of the wedge placed over a wood log. The wedge enters the wood and splits it. The reaction forces R1 & R2 are acting perpendicular on the inclined planes of the wedge. These forces and resultant frictional forces are responsible for keeping the wedge inside the wood firmly.

MECHANICAL ADVANTAGE OF WEDGE: -

Let us consider that the wedge is in equilibrium under the action of forces three forces R₁, P and R₂ and neglecting frictional forces. According to figure below the forces P, R₁ and R₂ are represented by the sides of D XYZ such that effort P the reaction R₁ and R₂ are represented by XY, YZ, and ZX which are the sides of, D XYZ respectively.

Mechanical Advantage (M.A). = load/effort

For equal sides of wedge i.e. = R₁ = R₂ = R

M.A. = R/P

M.A = ZX/XY

Triangle ABC and triangle XYZ are similar, therefore,

ZX=AC and XY=BC

M.A. = AC/BC

Mechanical advantage = length of inclined surface of wedge/thickness of wedge

From above expression it is clear that if the thickness of the wedge is decreased the mechanical advantage of the wedge will increase & if the wedge is more sharper, then the mechanical advantage will increase.