Waves and Sound

Definitions
1. Vibration
One complete round trip of a simple harmonic motion is called vibration.
or
If a body in periodic motion moves to and fro over the same path, this motion is called Oscillation.

2. Time Period (T)
The time required to complete vibration is known as time period.

3. Frequency
It is the number of vibrations executed by an oscillating body in one second.
4. Displacement
It is the distance of a vibrating body at any instant from the equilibrium position.

5. Amplitude
The maximum distance of the body on either side of its equilibrium position is known as amplitude.

6. Wave Length
The distance between two consecutive crests and troughs is called wavelength.

7. Natural Frequency
The frequency at which an object will vibrate freely (without any external periodic force or resistance) is known as natural frequency of that object.
8. Audible Sound
Our ear can hear only those sounds whose frequency is between 20Hz and 20000Hz. This range is known as audible sound.

9. Ultrasonic Sound
Sound with frequency greater than 20000 Hz is known as ultrasonic sound.

10. Octave
The interval between a waveform and another of twice the frequency is known as Octave.
Units
Frequency: Cycles per second (eps) or Hertz (hz)
Wavelength: Meter
Intensity of Sound: Watt/meter2 or W/m2
Noise: Decibel (DB)
Simple Harmonic Motion (S.H.M)
Definition
“To and fro motion of a body in which acceleration is directly proportional to displacement and always directed towards mean position is known as Simple Harmonic Motion.”
Condition for S.H.M
The conditions for simple Harmonic Motion are given below:

• Some resisting force must act upon the body.
• Acceleration must be directly proportional to the displacement.
• Acceleration should be directed towards mean position.
• System should be elastic.

Examples
Following are the examples of S.H.M:

• Body attached to a spring horizontally on an ideal smooth surface.
• Motion of a simple and compound pendulum.
• Motion of a swing.
• Motion of the projection of a body in a circle with uniform circular motion.

Resonance
Definition
“The large amplitude vibration of an object when given impulses at its natural frequency is known as Resonance.”
Experiment
Consider a long string stretched tightly between two pegs. Four pendulums A, B, C and D of different lengths are fastened to the string. Another pendulum E of same length as A is also fastened.
When pendulum E is set to vibrate, it will be observed that all the pendulums start to swing but pendulum A begins to vibrate with larger amplitude, as pendulum E is set into vibration. It imparts its motion to the string. This string in turn imparts the same periodic motion to the pendulums. The natural frequency of all other pendulums except A is different. Due to the same natural frequency only A vibrates as the same vibration of E. This phenomenon under which pendulum A begin to vibrate is called resonance.
Example
March of Soldiers while Crossing the Bridge
Each bridge has its own natural frequency and marching of soldiers is another vibrating system. So there may occur a force on vibration in bridge. This may damage the bridge. So, for safely precautions, it is written that soldiers must march out of stop while crossing the bridge.
Wave
Definition
” A method of energy transfer involving some form of vibration is known as a wave.”
Wave Motion
Wave motion is a form of disturbance, which travels through a medium due to periodic motion of particles of the medium about their mean position.
Experiment
We see that if we dip a pencil into a tap of water and take it out a pronounced circular ripple is set up on the water surface and travels towards the edges of the tub. However if we dip the pencil and take it out many times, a number of ripples will be formed one after the other.
Waves can also be produced on very long ropes. If one end of the rope is fixed and the other end is given sudden up and down jerk, a pulse-shaped wave is formed which travels along the rope.
Transverse Wave
Definition
“The wave in which amplitude is perpendicular to the direction of wave motion is known as Transverse Wave.”
Examples

• Radio Waves
• Light Waves
• Micro Waves
• Waves in Water
• Waves in String

Longitudinal Wave
Definition
“The wave in which amplitude is parallel to wave motion is called longitudinal wave.”
Example

• Sound Waves
• Seismic Waves

Sound
Definition
“A vibration transmitted by air or other medium in the form of alternate compressions and rarefactions of the medium is known as Sound.”
Production of Sound
Sound is produced by a vibrating body like a drum, bell, etc, when a body vibrates. due to the to and fro motion of the drum, compressions and rarefactions are produced and transmitted or propagated in air.
Propagation of Sound Waves
When a body vibrates in air, it produces longitudinal waves by compressions and rarefactions. These compressions and rarefactions are traveled by the particles of the medium and transferred into the next particles. Due to this transference, sound propagates in a medium.
Experiment
(Diagram)
Suspend an electric bell in a jar by its wires through a cork fixed in its mouth. Switch on the bell, we will hear the sound of the bell. Now start removing air from jar with the help of an exhaust (vacuum) pump. The sound will decrease, although the hammer is still seen striking the bell. This experiment shows that air or any other medium is necessary for the propagation of sound.
Velocity of Sound
It is a matter of common experience that the flash of lightning is seen earlier than hearing the thunder of cloud. Similarly when a gun is fired its sound is heard a little after seeing its flash. The reason is that light is faster than sound. Due to its slow velocity sound lags behind.
Experiment
Select two stations at a distance of 8 km (or any more distance) such that there is no obstacle between them. Fire a gun at station A and note the time of sound taken for such distance. Repeat the process and note the time taken by the sound to travel from B to A. If we substitute the mean of the two times recorded and distance S (8km) in the formula V = S/t, we will get the velocity of sound.
Factors Effecting Velocity of Sound
The factors are given below:

• Velocity of air or any other medium.
• Density of the medium.
• Temperature of the medium.
• Nature of the medium

Characteristics of Sound
The characteristic properties of sound by which we can distinguish between noise and music, shrill and grave sounds or sound of men and women are known as characteristics of sound. The properties of sound are given below:
1.Loudness
Definition
“Loudness is the magnitude of auditory sensation produce by sound.”
Intensity can be defined as the energy carried by the sound waves through a unit area placed perpendicular to the direction of waver per second.
Factors Effecting Loudness of Sound
Loudness depend on following factors:
Area of Vibration of Body: Greater will be the surface area more will be the loudness.
Amplitude of Motion of Vibrating Object: Greater will be the amplitude, more will be the loudness.
Density of Medium: Loudness is directly proportional to the density of medium.
Motion and Direction: If source of sound is moving towards the listener loudness will be greater or if wind supports the velocity of sound the loudness will be greater.
2. Pitch
Definition
“The sensation that a sound produces in a listener as a result of its frequency is known as Pitch.”
This is the property of sound by virtue of which we can distinguish between a shrill and grave sound.
Factors Effecting Pitch of Sound
Pitch depends on following factors:
Frequency of Vibrating Body: The greater the fundamental frequency, more shrill will be the sound.
Relative Motion of Sound: If source and listener both are coming closer pitch will increase.
3. Quality or Timbre or Tone
Definition
“The characteristic of a musical note that is determined by the frequency present is known as Quality or Timbre or Tone of that sound.”
This is the property of sound by virtue of which it is possible to identify a sound of the same loudness and pitch but originating from different instrument.
Factors Effecting Quality
Quality depends upon the following factors:

• Phase of the Sound Wave.
• Shape of Waves

Harmful Effects of Sound (Noise)
Nowadays noise is considered as a great pollution, which is very dangerous for us. Some of them are as follows:

• Continuous noise damages hearing and can result in complete deafness.
• Noise has become a great cause for depression and blood pressure.
• Mental system shows less efficiency due to noise.
• Consequently it is harmful in all respects for living body.

Musical Sound
The sound producing pleasing effect on our ears are called musical sounds.
Difference Between Longitudinal and Transverse Waves
Longitudinal Waves
1. In longitudinal waves, particles of the medium vibrate in the direction of the waves.
2. The portion of wave in which particles of medium are very close to each other is called compression.
3. Examples of longitudinal waves are sound wave and seismic waves.
4. Distance between the centre of two compressions and rarefactions is called wavelength.
Transverse Waves
1. In transverse waves, particles of the medium vibrate in the direction perpendicular to the direction of wave.
2. The portion in which particles of medium are higher than their normal position is called crest.
3. Examples of transverse wave are microwaves and radio waves.
4. Distance between two crests and troughs is called wavelength

Heat

Definitions 1. Internal Energy
Internal Energy of a body is the sum of all kinetic and potential energy of all molecules constituting the body.
2. Joules
It is the amount of heat required to rise the temperature of 1/4200 kg of pure water from 14.5 C to 15.5 C.
3. Calorie
It is the amount of heat required to rise the temperature of 1 g of pure water from 14.5C to 15.5C.
4. British Thermal Unit
It is the amount of heat tht is required to rise the temperature of 1 pound of pure water from 63F to 64F.
Difference Between Heat and Temperature
Heat

• Heat is the energy in transit from one body to another due to temperature difference.
• It is the total kinetic energy of the body.
• Heat is measured using Joule meter.
• Its unit is Joule.

Temperature

• Temperature is the degree of hotness or coldness of a body.
• It is the average kinetic energy of the body.
• Temperature is measured using thermometer.
• Its units are F, C and K.

Thermal Expansion
Change in length, breadth and height of a body due to heating is known as Thermal Expansion. It occurs in all the three states, i.e. solids, liquids and gases.
Thermal Expansion of Solids
Solids expand on heating. Their ability to expand depends on their molecular structure. As the temperature is increased, the average kinetic energy of the molecules increases and they vibrate with larger amplitudes. This results in increase in the distance between them. Hence, they expand on heating. Thermal Expansion of solids can be classified into three types.
1. Linear Thermal Expansion
Change in length or any one dimension of a solid on heating is known as LInear Thermal Expansion.
2. Real Expansion
The sum of the observed increase in the volume of a liquid and that of the containing vessel is called real Thermal expansion.
Real Expansion = Apparent Expansion + Expansion of the Vessel
3. Apparent Expansion
Apparent Expansion is the expansion in which only the expansion of liquid is considered and expansion of the vessel is not taken into account. Apparent expansion is less the real expansion.
Anomalous Expansion of Water
The increase in the volume of water as its temperature is lowered from 4 C to 0C is known as anomalous expansion of water.
Effects of Anomalous Expansion of Water
1. In winter, the temperature in the north and south poles of the earth falls. As the temperature fall below 4 C water on the surface expands and stays afloat. Ice continues building up at the surface while the temperature at the bottom remains at 4 C. This helps fish and other forms of marine life to live.
2. During the rainy season a lot of water seeps through the cracks in the rocks. In winter, when the water expands, the rock get broken due to this expansion.
3. In cold climate, water supply pipes burst when the water expands on cooling.
GAS LAWS
1. Boyle’s Law
The volume of a given mass of a gas is inversely proportional to the pressure, If the temperature is kept constant.
P < 1/V (Here < represents sign of proportionality. Do not write this in your examination paper)
P = C * 1/V
C = PV
The above equation is known as equation of Boyle’s Law.
2. Charle’s Law
The volume of a given mass of a gas is directly proportional to the temperature, if the pressure is kept constant.
V < T (Here < represents sign of proportionality. Do not write this in your examination paper)
V = C * T
C = V/T
The above equation is known as equation of Charle’s Law.
3. Pressure Law
The pressure of a given mass of a gas is directly proportional to the temperature, if the volume is kept constant.
P < T
P = C * T
C = P/T
The above is known as the equation of the Pressure Law.
THERMOMETER
The instrument that is used to measure temperature is called a thermometer.
Types of Thermometer
1. Ordinary Liquid-in-Glass Thermometer
Introduction
An ordinary liquid-in-glass thermometer is used in a laboratory to measure temperature within a range of -10C to 110C.
Construction
It consists of a glass stem with a capillary tube, having a small bulb at one end. This bulb is filled with a liquid, usually mercury or alcohol coloured with a red dye. The upper end of the capillary tube is sealed so that the liquid will neither spill not evaporate. The air from the capillary tube is also removed.
Working
When the bulb is heated, the liquid in it expands and rises in the tube. A temperature scale is marked on the glass stem to indicate temperatures according to the various levels of liquid in the tube.
2. Clinical Thermometer
Introduction
A clinical thermometer is a device that is used to find the temperature of the human body. It has a range from 35 C to 43 C (95F to 110F).
Construction
It consists of a glass stem with a capillary tube, having a small bulb at one end. This bulb is filled with a liquid usually mercury or alcohol colored with a red dye. The upper end of the capillary tube is sealed so that the liquid will neither spill nor evaporate. The air from the capillary tube is also removed. The glass stem of a clinical thermometer has a construction in its capillary tube near the bulb. This helps to stop the mercury thread from moving back when the thermometer is removed from the patient’s mouth.
Working
In order to find out the temperature, the thermometer is placed in the mouth or in the arm pit of the patient. The liquid in it expands and rises in the tube. A temperature scale is mrked on the glass stem to indicate temperatures according to the various levels of liquid in the tube.
3. Maximum and Minimum Thermometer
Introduction
This thermometer is used to read the maximum and minimum temperatures reached over a period of time.
Construction
This thermometer consists of a fairly large cylindrical bulb with alcohol in it. This bulb is connected through a U-shaped tube filled mercury. At the end of this U-shaped tube another bulb containing alcohol is provided.
Working
When the bulb is heated, alcohol in it expands and drives the mercury round towards the other end of the U-shaped tube. This mercury exerts pressure on the alcohol in the second bulb and its level rises. On each mercury surface, there is a small iron index provides with a light spring to hold it in position in the tube. When the mercury thread is moved, due to expansion or contraction of alcohol in the first bulb, the indices moves and are left in the extreme positions reached over a period of time. The lower end of the index on the left indicates the minimum and that on the right indicates the maximum temperature.
Heat Transfer
There are three methods of transferring heat from one place into another.
1. Conduction
Conduction is a mode of heat transfer by atomic or molecular collisions, without the movement of a bulk of a substance from one position to another, in a body. It mostly occurs in solids.
2. Convection
Convection is a mode of heat transfer by the actual movement of the bulk of the substance from one place to another through large distances. It mostly occurs in liquids and gases.
3. Radiation
Radiation is a mode of heat transfer which requires no material medium. Heat energy is carried by infra red electromagnetic waves from one place to another.
Bi-Metallic Strips
A bi-metallic strip is made of pieces of two different metals of different expansion rates, e.g. iron and brass. When it is heated, it bends with the brass on the outside of the curve because brass expands more quickly than iron.
1. Bi-metal Thermometer
Introduction
A bi-metal thermometer is made of a bi-metallic coil. No liquid is used in such type of thermometer.
Construction
It consists of a bi-metallic strip in the form of a long spiral. One end of the spiral is kept fixed, while a light pointer is attached to the other end.
Working
When the temperature rises, the bi-metal strip coil itself into an even tighter spiral due to different expansion rates of the two metals. the pointer moves across the temperature scale and in this way reading is noted.
2. Fire Alarm
Introduction
A fire alarm is used to warn people when there is a fire.
Construction
In a fire alarm, one end of a bi-metal strip is firmly fixed, while the other is free. One terminal of a 6 volt battery is connected to the fixed end of the strip through a 6 volt bulb or bell. The other terminal of the battery is connected with a metallic contact which is just above the free end of the bi-metallic strip.
Working
When a fire starts, heat energy is given off. It raises the temperature of the bi-metallic strip and its free end bends towards the contact. On touching the contact, electric circuit gets completed and the bulb starts to glow or in case of a bell, it rings warning about the fire.
Latent Heat of Fusion
The quantity of heat required to transform 1 kg of ice completely melts into water at 0C is known as Latent Heat of Fusion.
Latent Heat of Vaporization
the quantity of heat required to transform 1 kg of water completely into steam at 100 C is known as Latent Heat of Vaporization.
Effect of Pressure on Melting Point (Regelation)
The melting point of those substances, which expand on freezing, gets lowered when pressure oever one atmosphere is exerted on them.
Experiment
Take a bare copper wire with weights on its both ends. Place it across a block of ice. The copper wire sinks slowly through the block and weight falls to the floor. Pressure exerted by the copper wire lowers the freezing point of ice and the ice beneath the wire melts. The water flows round the wire and re-freezes on getting above the wire, releasing latent heat energy. This energy is conducted through the copper wire, which helps to melt the ice below the wire. In this way, ice below the wire melts while water above the wire freezes. This process continues until the wire cuts through the ice block.
Effect of Pressure on Boiling Point
If the pressure on the surface of a liquid is increased above the normal atmospheric pressure, its boiling point increases.
Experiment
Fill a round bottom flask to half its capacity. After boiling the water fro a few minutes, remove the burner and place a cork in the flask. Invert the flask and pour some cold water on the bottom of the flask. After some time, water starts to boil again although no more heat has been provided to it. The reason is that, when the water was boiled, it expelled all the air from the flask. When the flask was corked and allowed to cool the steam condensed into water. Since, no fresh air could enter the flask the pressure inside the flask lowered. This decreased the boiling point of water and water started to boil at normal temperature.
Evaporation
The process of change of a liquid into vapour without boiling is called evaporation.
Factors on which Evaporation Depends
Evaporation depends on the following factors:
1. Nature of Liquid: If the boiling point of a liquid is low, then they evaporate much quickly e.g. Alcohol and Ether.
2. Temperature of Liquid: If the surface temperature of a liquid is increased, then rate of evaporation also increases, e.g. ironing of clothes.
3. Surface Area of Liquid: If the surface area of a liquid is increased, then the rate of evaporation increases, e.g. liquids spread over large areas evaporate more quickly.
4. Dryness of Air: If there is more dryness in the air, then the rate of evaporation increases, e.g. in humid weather, clothes take a longer time to dry.
5. Wind speed: If the wind speed is greater, then evaporation rate increases.
6. Air Pressure on the Surface of The Liquid: If the pressure on the surface of the liquid is increased, the rate of evaporation decreases.
Law of Heat Exchange
For an isolated system comprising mixture of hot and cold substances, the heat lost by hot substances is equal to the heat gained by cold substances.
Heat lost by hot body = Heat gained by cold body
Refrigerator
Introduction
A refrigerator is a device that is used to keep fruits, vegetables and other eatables cool.
Construction
A refrigerator consists of a compressor, condenser and evaporator.
Refrigerant
Freon is used as the refrigerant in a referigerator. This gas liquifies at normal temperature if the pressure is increased.
Working
1. Compression: Freon gas is first compressed in the compressor of a refrigerator. It is then fed into the condenser.
2. Condensation: In the condenser, the gas is liquified under pressure. It converts into a liquid at normal temperature. This gas is then allowed to pass through a valve into the evaporator.
3. Evaporation: The pressure in the evaporator is comparatively less than in the condenser. Therefore, when liquid Freon enters the evaporator, it evaporates absorbing a large amount of heat. This results in cooling the area around the evaporator. This is where we keep our eatables.
(Diagram)
The gas is then again fed into the compressor and the process continues

Matter

Definition of Matter “Anything having mass and volume is called matter.”

Kinetic Molecular Theory of Matter
The Kinetic Molecular Theory of Matter has the following postulates:

• Matter is made up of very small particles called molecules.
• These molecules are in the same state of motion, hence they possess kinetic energy. Their motion can be translatory, vibratory or rotational.
• The molecules attract each other with a force. This force depends upon the distance between them. Force is inversely proportional to the distance between the molecules.
• When a substance is heated its temperature as well as molecular motion increases. Due to this motion, kinetic energy also increases. we can say that when the kinetic energy of the molecules increases, then temperature of the substance rises.

Brownian Motion
In 1827, a scientist, Robert Brown observed the motion of molecules with the help of a microscope. He observed that the tiny particles in water are constantly moving in a zigzag path. He called the motion, Brownian Motion.
Explanation
The cause of this tiny particle motion is the rapid motion of the molecules, which collide with the particles and push them in one direction. If some molecules come from other direction and collide with the same particles, particles change their direction. This process continues and the motion becomes zigzag.
States of Matter
Matter has been classified into three states. These states are discussed below:
1.Solid

• According to the kinetic theory of matter, solid has the least kinetic energy. The properties of solids are given below:
• The particles are very close to each other.
• Their shape and volume is fixed.
• Particles in a solid vibrate to and fro from their mean position.
• On heating they melt and convert into liquid.
• Some solids also convert directly into gas on heating.

2. Liquid
According to the kinetic theory of matter, liquids have the following properties;

• They have greater kinetic energy than solids but less than that of gases.
• The volume of liquid is fixed.
• They move more freely than solids.
• The attraction between molecules is lower than solids.
• The distance between the molecules is greater than that of solids.
• On heating, they convert into vapours.
• On cooling, they convert into solid.

3. Gas
According to the kinetic molecular theory, gases possess the following properties.

• Gases possess more kinetic energy.
• Their shape and volume are not fixed.
• The distance between their molecules is large.
• Their temperature is proportional to their kinetic energy.
• Their temperature rises with increase in pressure.
• On cooling, they convert into liquid and gases.

Elasticity
Definition
” The tendency of a material to return to its original dimension after the deforming stress has been removed is known as elasticity.”

If we apply a force to a body, it is stretched. When the applied force is remove, the body returns to its original shape. The phenomenon of turning back to its original shape is called Elasticity.
Elastic Behaviour and Molecular Theory
The elastic behaviour of a material can be explained by the Kinetic Theory of Matter. Since the molecules in a solid are very close to each other, there exist strong attracting forces between them. Thus when force is removed, the attraction forces between the molecules pull them back again and the material is restored to its original shape. Different material have different elasticity depending on the nature of the material.
Elastic Limit
The maximum resisting force of a material is called the Elastic Limit of that material.
Stress
Definition
“When a body is made to change its length, volume or shape by the application of an external force, the opposing force per unit area is called Stress.”
Formula
Stress = Force / Area
o = F/A (Here o represents (Rho) do not write in your examination paper)
Units
S.I or MKS System – N/m2 or Pascal (Pa)
C.G.S system – Dyne/cm2
F.P.S or B.E System – lb/ft2 and lb/in2
(Here 2 in all above systems shows square)
Types of Stress
Following are some types of stress:
1. Tensile Stress: It is a stress tending to stretch a body.
2. Bulk Stress: It is an overall force per unit area, also known as pressure.
3. Shear Stress: It is a stress tending to produce an angular deformation.
Strain
Definition
Stress can produce a change in shape, volume or length in an object. This change in the shape of an object is called strain.
Formula
Mathematically,
Strain = Change in Length/Length or Strain = Change in volume / volume
Units
Since strain is a ratio between two similar quantities, it has no unit.
Types of Strain
Following are some types of strain.
1. Tensile Strain: It is a change in length divided by original length.
2. Bulk Strain: It is the change in volume divided by original volume.
3. Shear Strain: It is equal to the angular displacement produced.
Hook’s Law
Introduction
An English Physicist and Chemist Robert Hook discovered this law in 1678.
Statement
“Strain produced is proportional to the stress exerted within the elastic limit.”
Elastic Limit
The point at which a material becomes plastic is called elastic limit on yield point.
Yield Point
the yield point is the point at which the material begins to flow. It is also the point between elastic region and plastic region.
Elastic Region
When the material obey’s Hook’s Law, it is said to be in Elastic Region.
Plastic Region
When stress is applied beyond the elastic limit, the graph is no longer a straight line. In this case stress produces a permanent change in the material. The material is said to be in its Plastic Region.
Breaking Point
The material breaks at a certain point called the Breaking Point of the material.
Young’s Modulus
Definition
“The ratio of the stress on a on a body to the longitudinal strain produced is called Young’s Modulus.”
Mathematical Expression
According to the definition of YOung’s Modulus:
Young’s Modulus = Sress / Longitudinal Strain
Unit
In S.I system, Young’s Modulus is measured in N/m2.
Pressure
Definition
“The perpendicular force per unit area acting on a surface is called pressure.”
Mathematical Expression
Pressure = Force /Area
P = F/A
Unit
S.I or M.K.S System – N/m2 or Pascal.
C.G.S system – Dyne/cm2.
F.P.S or B.E System – lb/ft2 and lb/in2.
Pressure in Liquids
In water or other liquids, the weight exerted on a body or the bottom of the liquid is its pressure.
Pascal’s Principle
Statement
When a pressure is applied to a liquid contained in a vessel, it is transmitted undiminished equally in all directions and acts perpendicularly to the walls of the container.
Applications – Hydraulic Press
Pascal’s Principle has the application in Hydraulic press. In a hydraulic press a narrow cylinder A is connected with a wider cylinder B and they are fitted with airtight piston. It is filled with some incompressible liquid. Pressure can be applied by moving the piston cylinder A in the downward direction. Piston B is used to lift the object. The hydraulic press is provided with a rigid roof over it. When piston B moves upward, it compresses any material placed between the rigid roof and this piston. The hydraulic press is used for compressing soft materials like cotton into a cotton bale and powdered materials into compact solids.
(Diagram)
Pressure in Gases
The kinetic theory enables us to account for the pressure a gas exerts on the walls of its container. When a moving molecule strikes the walls of its container, a force is exerted on the walls during hte impact.
Atmospheric Pressure
The atmosphere, because of its weight exerts a pressure on the surface of the earth and on every object on the earth including human beings. The pressure is known as Atmospheric Pressure.
Applications of Atmospheric Pressure
The fact that the atmosphere exerts pressure has been put into use in several devices such as siphons, pumps and syringes.
Barometer
Definition
“A device for measuring the atmospheric pressure is called Barometer.”
Mercury Barometer
In the laboratory, the atmospheric pressure is measured by means of a mercury barometer. A mercury barometer consists of a thick walled glass tube of 1m length, which is opened at one end and closed from the other side. The tube is filled with mercury. The open end is firmly covered with a thumb and then carefully inverted in a vessel containing mercury. When the open end is completely immersed in the mercury, the thumb is removed. Some of the mercury from the columns drops in the vessel leaving a space. This space is called vacuum. If the mercury columns is measured, it is found to be 760 mm. This length always remains constant even if different diameter tubes are taken. The length of the mercury column is referred to as the atmospheric pressure.
Archimede’s Principle
Statement
“When an object is immersed in a liquid, an upward thrust acts upon it, which is equal to the weight of the liquid displaced by the object.”
Mathematical Expression
Mathematically, Archimede’s Principle may be represented by:
Apparent Weight = Actual Weight – Weight of the liquid displaced by the object
Buoyancy
It is the tendency of an object to float. It is equal to the up-thrust or weight of the water displaced by the object.
Conditions for Floating Bodies
A body will float in a liquid or a gas if it displaces liquid or gas whose weight is greater than the weight of the body.
A body will sink if it displaces liquid or gas whose weight is less than the weight of the body

Machines

Definitions 1. Machine
A machine is a device by means of which useful work can be performed conveniently and it can also transfer one form of energy into another form of energy.
2. Mechanical Advantage
The ratio between the resistance or weight to the power applied in a machine is called the mechanical advantage of that machine. It is denoted by M.A.
M.A. = Weight over-comed by Machine/ Force Applied on the Machine
3. Efficiency
The ratio between the useful work done and the work done on the machine is called efficiency.
M.A = (output/Input) * 100
4. Input
Input is the work done on the machine.
5. Output
Output is useful work done by the machine.
Lever
Definition
Lever is the simplest machine in the world. It is a rigid bar, which can be rotated about a fixed point.
Principle of Lever
In the lever the moment P acts opposite to that of work W. It means that force F tends to rotate the lever in one direction which the wight W rotates in opposite direction. If the magnitude of these moments acting in opposite direction is equal, then the lever will be in equilibrium. It means that:
Moment of P = Moment of W
Mechanical Advantage
We know that according to Principle of Lever:
Moment of P = Moment of W
=> Force * Force Arm = Weight * Weight Arm
P * AB = W X BC
AB/BC = W/P
Hence,
M.A = W/P = AB/BC = Weight Arm/ Force Arm
Kinds of Lever
1. First Kind of Lever
In the first kind of lever, the fulcrum F is in the between the effort P and Weight W.
Examples
Physical Balance
Handle of Pump
Pair of Scissors
See Saw
2. Second Kind of Lever
In the second kind of lever, the weight W is in between the fulcrum F and effort P.
Examples
Door
Nut Cracker
Punching Machine
3. Third Kind of Lever
In the third kind of lever, the effortP is in between the fulcrum F and weight W.
Examples
Human forearm
Upper and Lower Jaws in the Mouth.
A Pair of Forecepes
Inclined Plane
Definition
A heavy load can be lifted more easily by pulling it along a slope rather than by lifting in vertically. Such a slope is called an Inclined Plane.
Mechanical Advantage
M.A = W/P = l/h = Length of Inclined Plane/Perpendicular Height
Pulley
A pulley consists of a wheel mounted on an axle that is fixed to the framework called the block. The wheel can rotate freely in the block. The groove in the circumference prevents the string from slipping.
Fixed Pulley
If the block of the pulley is fixed then it is called a fixed pulley.
Mechanical Advantage of Fixed Pulley
In a fixed pulley, the force P is the applied force and weight W is lifted. If we neclect the force of friction then:
Load = Effort
In the given case:
Load = W * Load Arm
Load = W * OB
Also,
Effort = P * Effort Arm
Effort = P * OA
So,
W*OB = P*OA
=> W/P = OA/OB
But, OA = OB, then
M.A = W/P = OB/OB
M.A = 1
Moveable Pulley
In this pulley, one end of the rope that is passing around the pulley is tied to a firm support and effort P is applied from its other end. The load and weight to be lifted is hung from the hook of block. In this system, the pulley can move. Such a pulley is called moveable pulley.
Mechanical Advantage of Moveable Pulley
In an ideal system of a moveable pulley, the tension in each segment of the rope is equal to the applied effort. As two segments support the weight, the ffort acting on the weight W is 2P. Therefore, according to the principle of lever:
W * Radius of the Wheel = 2P * Radius of the Wheel
=> 2P = W
The Mechanical Advantage is given by:
M.A = W/P
M.A = 2P/P
=> M.A = 2
Hence, the mechanical advantage of a moveable pulley is 2

Work, Energy and Power

Definitions 1. Joule
It is the work done by a force of one Newton when the body is displaced one meter.
2. Erg
It is the work done by a force of one Dyne when the body is displaced one centimeter.
3. Foot Pound (ft-lb)
It is the work done by a force of one pound when the body is displaced one foot.
4. Force
It is an agent that moves or tends to move or stops or tends to stop a body.
5. Watt
Watt is the unit of power that is equal to the quantity of 1 Joule work done in 1 second.
Work
When a force produces displacement in a body, it is said to do work.
Units of Work

• S.I System – Joule
• C.G.S System – Erg

Explanation
When force is applied in the direction of the displacement we can find the work by using definition
Work = Force * Displacement
W = F*s
W = Fs
Suppose a man is pulling the grass cutting machine then the direction of the foce and displacement is not same. The applied force makes an angle @ with the ground while the motion takes place along the ground.
In this case force is resolved into its components.
Fx = Fcos@
Fy = Fsin@
As the machine moves along the ground, so Fx is doing the work, Hence:
W = Force * Displacement
W = Fcos@*s
W=Fscos@
Energy
Energy is define as the capability to do work. Energy is also measured in Joules.
Some Types of Energy

• Potential Energy
• Kinetic Energy
• Chemical Energy
• Heat Energy
• Light Energy
• Nuclear Energy

Potential Energy
Definition
The energy possessed by a body due to its position is known as the Potential Energy of the body. It is represented by P.E. and is measured in Joules in System International.
Examples
The energy of the following is potential energy:
A brick lying on the roof of a house.
The spring of a watch when wound up.
The compressed spring.
Water stored up in elevated reservoir in water-supply system.
Mathematical Expression
If we lift a body of mass m to a height h, then the force applied on it is the its weight and it will act through a distance h.
So,
Work = Force * Distance
W = W * h
Since W = mg, therefore:
W = mg * h
Since work is equal to energy possessed by a body:
P.E. = mgh
Kinetic Energy
Definition
The energy possessed by a body due to its motion is known as the Kinetic Energy of the body. It is represented by K.E.
Examples
The energy of the following is kinetic energy:
A bullet fired from a gun.
A railway engine moving at high speed.
Motion of a simple pendulum.
Mathematical Expression
Consider a body of mass m at rest (Vi = 0) on a frictionless surface. When a force F is applied, the body covers a distance S and its final velocity becomes Vf.
To calculate the amount of work done, we apply the formula.
W = F * S
According to Newton’s Second Law of Motion, the value of force is:
F = ma
The distance that the body traveled is calculated by using third equation of motion:
2as = vf2 – vi2 (Here 2 with Vf and Vi represents square)
We know that Vi = 0, therefore:
2as = v2
s = v2/2a
By substituting the values of F and s, we get:
W = (ma) * (v2/2a)
W = mv2/2
W = 1/2(mv2)
We know that work can be converted into Kinetic Energy, therefore:
K.E = 1/2(mv2)
So, Kinetic Energy of a body is directly proportional to the mass and square of velocity.
Factors on which Kinetic Energy Depends:
It is directly proportional to the mass of the body.
It is directly proportional to the square of the velocity.
Difference Between Kinetic Energy and Potential Energy
Kinetic Energy
1. Energy possessed by a body by virtue of its motion is known as Kinetic Energy.
2. Bodies in motion have Kinetic Energy.
3. It is calculated by K.E = 1/2 (mv2)
Potential Energy
1. Energy possessed by a body by virtue of its position is known as Potential Energy.
2. Bodies at rest have Potential Energy.
3. It is calculated by P.E. = mgh
Law of Conservation of Energy
Statement
Energy can neither be created, nor destroyed, but it can be converted from one form into the other.
Explanation
consider a body of mass mat height h above the ground. Its kinetic energy at that point A is:
K.E = 1/2(mv2)
K.E = 1/2 m * (0)
K.E = 0 …….. (i)
The potential Energy at point A is :
P.E = mgh …………(ii)
So the total energy at point A will be :
T.E = K.E + P.E
E(A) = 0 + mgh
E(A) = mgh
Suppose the body is released from this height and falls through a distance x. Its new height will be (h-x). The velocity with which it reaches point B is calculated by using the third equation of motion:
2gs = Vf2 – Vi2
As we know:
Vi = 0
S = x
Therefore,
2gx = Vf2 – 0
2gx = v2
The kinetic energy at point B is:
K.E. = 1/2 mv2
Substituting the value of v2:
K.E. = 1/2 * m * 2gx
K.E = mgx
The Potential Energy at point B is:
P.E = mgh
The height of the body is (h-x):
P.E. = mg(h-x)
The total energy at point B is :
E(B) = P.E + K.E.
E(B) = mgx + mg(h-x)
E(B) = mgx + mgh – mgx
E(B) = mgh
Hence, the total energy at point A and B are same. It means that the total value of energy remains constant.
Power
Definition
The rate of doing work is called power.
Mathematical Expression
Power = Rate of doing Work
Power = Work/Time
P = W/T
Unit of Power
The unit of Power is Joules per second (J/s) or Watt (W).
Need to Conserve Energy
The fuel that burns in running factories, transport and other activities is mainly obtained from underground deposits in the form of coal, oil, gas and other similar raw forms. These deposits are rapidly decreasing and one day all these resources of energy will be consumed. It is therefore highly important for us to avoid wastage of energy.
the consumption of two much energy is also having adverse effect on our environment. The air in big cities is heavy because of pollution caused by industrial wastes and smoke produced by automobiles. To ensure comfortable living with a neat environment, it is the responsibility of all of us as individuals to conserve energy.

Circular Motion and Gravitation

Centripetal Force Definition
“The force that causes an object to move along a curve (or a curved path) is called centripetal force.”

Mathematical Expression
We know that the magnitude of centripetal acceleration of a body in a uniform circular motions is directly proportional to the square of velocity and inversely proportional to the radius of the path Therefore,
a(c) < v2 (Here < represents the sign of proportionality do not write this in your examination and 2 represents square of v)
a(c) < 1/r
Combining both the equations:
a(c) < v2/r From Newton’s Second Law of Motion: F = ma => F(c) = mv2/r
Where,
Fc = Centripetal Force
m = Mass of object
v = Velocity of object
r = Radius of the curved path
Factors on which Fc Depends:
Fc depends upon the following factors:
Increase in the mass increases Fc.
It increases with the square of velocity.
It decreases with the increase in radius of the curved path.
Examples
The centripetal force required by natural planets to move constantly round a circle is provided by the gravitational force of the sun.
If a stone tied to a string is whirled in a circle, the required centripetal force is supplied to it by our hand. As a reaction the stone exerts an equal force which is felt by our hand.
The pilot while turning his aeroplane tilts one wing in the upward direction so that the air pressure may provide the required suitable Fc.
Centrifugal Force
Definition
“A force supposed to act radially outward on a body moving in a curve is known as centrifugal force.”

Explanation
Centrifugal force is actually a reaction to the centripetal force. It is a well-known fact that Fc is directed towards the centre of the circle, so the centrifugal force, which is a force of reaction, is directed away from the centre of the circle or the curved path.
According to Newton’s third law of motion action and reaction do not act on the same body, so the centrifugal force does not act on the body moving round a circle, but it acts on the body that provides Fc.
Examples
If a stone is tied to one end of a string and it is moved round a circle, then the force exerted on the string on outward direction is called centrifugal force.
The aeroplane moving in a circle exerts force in a direction opposite to the pressure of air.
When a train rounds a curve, the centrifugal force is also exerted on the track.
Law of Gravitation
Introduction
Newton proposed the theory that all objects in the universe attract each other with a force known as gravitation. the gravitational attraction exists between all bodies. Hence, two stones are not only attracted towards the earth, but also towards each other.
Statement
Every body in the universe attracts every other body with a force, which is directly proportional to the product of masses and inversely proportional to the square of the distance between their centres.
Mathematical Expression
Two objects having mass m1 and m2 are placed at a distance r. According to Newton’s Law of Universal Gravitation.
F < m1m2 ((Here < represents the sign of proportionality do not write this in your examination)
Also F < 1/r2 (Here 2 represents square of r)
Combining both the equations :
F < m1m2/r2
Removing the sign of proportionality and introducing a constant:
F = G (m1m2/r2)

Statics

DEFINITIONS 1. Static
Statics deals with the bodies at rest under number of forces, the equilibrium and the conditions of equilibrium.
2. Resultant Force
The net effect of two or more forces is a single force, that is called the resultant force.
3. Moment Arm
The perpendicular distance between the axis of rotation and the line of the action of force is called the moment arm of the force.
TORQUE
It is the turning effects of a force about an axis of rotation is called moment of force or torque.
FACTORS ON WHICH TORQUE DEPENDS
1. The magnitude of the applied force.
2. The perpendicular distance between axis of rotation and point of application of force.
REPRESENTATION
Torque may be represented as,
Torque = Force * moment arm
T = F * d
CENTRE OF GRAVITY
The centre of gravity is a point at which the whole weight of the body appears to act.
Centre of Gravity of Regular Shaped Objects
We can find the centre of gravity of any regular shaped body having the following shapes:
1. Triangle: The point of intersection of all the medians.
2. Circle: Centre of gravity of circle is also the centre of gravity.
3. Square: Point of intersection of the diagnonals.
4. Parallelogram: Point of intersection of the diagonals.
5. Sphere: Centre of the sphere.
Centre of Gravity of Irregular Shaped Objects
We can find the center of gravity of any irregular shaped object by using following method. Drill a few small holes near the edge of the irregular plate. Using the hole A, suspend the plate from a nail fixed horizontally in a wall. The plate will come to rest after a few moments. It will be in a position so that its centre of gravity is vertically below the point of suspension.
Now, suspend a plumb line from the supporting nail. Draw a line AA’ in the plate along the plumb line. The centre of gravity is located somewhere on this line.
Repeat the same process using the second hole B. This gives the line BB’ on the plate. Also repeat this process and use hole C and get line CC’.
The lines AA’, BB’ and CC’ intersect each other at a point. It is our required point, i.e.e the centre of gravity. We can use this procedure with any irregular shaped body and find out its centre of gravity.
EQUILIBRIUM
A body will be in equilibrium if the forces acting on it must be cancel the effect of each other.
In the other word we can also write that:
A body is said to be in equilibrium condition if there is no unbalance or net force acting on it.
Static Equilibrium
When a body is at rest and all forces applied on the body cancel each other then it is said to be in static equilibrium.
Dynamic Equilibrium
When a body is moving with uniform velocity and forces applied on the body
cancel each other then it is said to be in the dynamic equilibrium.
CONDITIONS OF EQUILIBRIUM
FIRST CONDITION OF EQUILIBRIUM
“A body will be in first condition of equilibrium if sum of all forces along X-axis and sum of all forces along Y-axis are are equal to zero, then the body is said to be in first condition of equilibrium.”
( Fx = 0 Fy = 0 )
SECOND CONDITIONS OF EQUILIBRIUM
“A body will be in second condition of equilibrium if sum of clockwise(Moment) torque must be equal to the sum of anticlockwise torque(Moment), then the body is said to be in second condition of equilibrium.”
Sum of torque = 0
STATES OF EQUILIBRIUM
There are following three states of Equilibrium:
1. First State (Stable Equilibrium)
A body at rest is in stable equilibrium if on being displaced, it has the tendency to come back to its initial position.
When the centre of gravity of a body i.e. below the point of suspension or support, then body is said to be in stable equilibrium.
2. Second State (Unstable Equilibrium)
If a body on displacement topples over and occupies a new position then it is said to be in the state of unstable equilibrium.
When the centre of gravity lies above the point of suspension or support, the body is said to be in the state of unstable equilibrium.
3. Third State
If a body is placed in such state that if it is displaced then neither it topples over nor does it come back to its original position, then such state is called neutral equilibrium.
When the centre of gravity of a body lies at the point of suspension, then the body is said to be in neutral equilibrium.

Force and Motion

DYNAMICS “It is the branch of Physics which deals with causes of motion and their effects”
LAW OF MOTIONS
Newton formulated three laws of motion in his book.
NEWTON FIRST LAW OF MOTIONS
Newton’s first law of motion is also known as the Law of Inertia.
STATEMENT
“Every body continues its state of rest or uniform motion in a straight path until it is acted upon by an external, or unbalance force to change its state of rest or uniform motion”.
EXPLANATION
This law consists of a two parts
(a) When body is at rest
(b) When body is moving with uniform velocity
(a). When Body is At Rest
Newton’s Law states that when a body is at rest, it continues its rest unless we apply a force on it. When we apply a force, it changes its state of rest and starts moving along a straight line.
(b) When body is moving with uniform velocity
Newton’s Law states that when a body is moving, it moves in a straight line with uniform velocity, but when we apply an opposite force, it changes its state of motion and come to rest.
Examples
A body riding a push-bike along a leveled road does not come to rest immediately when we apply a force, it changes its state of rest and starts moving along a straight line.
If a bus suddenly starts moving, the passengers standing in the bus will fall in the backward direction. It is due to the reason that the lower part of the passengers which is in contract with the floor of the bus is carried forward by the motion of the bus, but the upper part of the body remains at rest due to inertia and so the passengers fall in backward direction.
SECOND LAW OF MOTIONS
STATEMENT
“When a force acts on an object it produces an acceleration which is directly proportion to the amount of the force and inversely proportional to the product of mass”
EXPLANATION
It is well known fact that if we push a body with greater force then its velocity increases and change of velocity takes place in the direction of the force. If we apply a certain force F on a mass m, then it moves with certain velocity in the direction of the force. If the force becomes twice then its velocity will also increase two times. In this way if we go on increasing the fore there will be increase in velocity, which will increase the acceleration.
DERIVATION
According to the Newton`s Second law of motion when a force acts on an object it produces an acceleration which is directly proportion to the amount of the force.
a < F { here < is the sign of directly proportional : Do not write this sentence in examination }
and inversely proportional to the product of mass
a < 1/m
Combining all:.
a < F/m
a = K F/m
If the Value of K is 1
so,
a = F/m
or
F = ma
1. FORCE
Force is an agent which produces motion in a body but some time force may not be succeeded to produce motion in a body so we can say that the force is an agent which produces or tends to produce motion in a body.
We can further say that:
Force is an agent which stops or tends to stop the motion of a body. In simple word we can also say that force is an agent which changes or tends to change the sate of an object.
2. MASS
The quantity of matter contained in a body is called mass.
FORMULA
F = ma
m = F/a
UNIT
The unit of mass in M.K.S system is Kilograme (kg)
3. WEIGHT
It is a force with which earth attracts towards its centre is called weight.
FORMULA
W = mg
UNIT
The unit of weight in M.K.S system is Newton (N).
THIRD LAW OF MOTION
” To every action there is always an equal and opposite reaction ”
EXPLANATION
According to Newton’s Law of Motion, we have:
F(action) = – F(reaction
The negative (-) sign indicates that the two forces are parallel but in the opposite direction. If we consider one of the interacting objects as A and the other as B, then according to the third law of motion:
F(AB) = – F(BA)
F(AB) represents the force exerted on A and F(BA) is the force exerted on B.
Examples
We we walk on the ground, we push the ground backward and as a reaction the ground pushes us forward. Due to this reason we are able to move on the ground.
If a book is placed on the table, it exerts some force on the table, which is equal to the weight of the book. The table as a reaction pushes the book upward. This is the reason thta the book is stationary on the table and it does not fall down.
INERTIA
Definition
“Inertia is the tendency of a body to resist a change in its state.”

Examples
Cover a glass with a post card and place a coin on it. Now strike the post card swiftly with the nail of your finger. If the stroke has been made correctly, the postcard will be thrown away and the coin will drop in the glass.
If a moving bus stops suddenly, the passenger standing in it feels a jerk in the forward direction. As a result he may fall. It is due to the fact that the lower part of the standing passengers comes to rest as the bus stops. But the upper portion remains in motion due to inertia.
DIFFERENCE BETWEEN MASS AND WEIGHT
Mass
1. The quantity of matter present in a body is called mass.
2. The mass of a body remains constant everywhere and does not change by change in altitude.
3. Mass of a body possesses no direction. So it is a scalar quantity.
4. Mass can be determined by a physical balance.
Weight
1. The force with which the earth attracts a body towards its centre is called the weight of the body.
2. The weight of a body is not constant. It is changed by altitude.
3. Weight of a body has a direction towards the centre of the earth. So it is a vector quantity.
4. Weight can be determined by only a spring balance.
MOMENTUM
“The quantity or quality of motion is called momentum and it is denoted by P”
MATHEMATICAL DEFINITION
“It is the product of mass and velocity.”
MATHEMATICAL REPRESENTATION
P = mV
where:
p is the momentum
m is the mass
v the velocity
LAW OF CONSERVATION OF MOMENTUM
The law of conservation of momentum is a fundamental law of nature, and it states that the total momentum of a isolated system of objects (which has no interactions with external agents) is constant. One of the consequences of this is that the centre of mass of any system of objects will always continue with the same velocity unless acted on by a force outside the system
EXAMPLE
Consider two bodies A and B of mass m1 and m2 moving in the same direction with velocity U1 and U2 respectively such that U1 is greater than U2. Suppose the ball acquire velocity V1 and V2 respectively after collision
Momentum of the system before collision = m1U1 + m2U2
Momentum of the system after collision = m1V1 + m2V2
According to the law of conservation of momentum:
Total momentum of the system before collision = Total momentum of the system after collision =
m1U1 + m2U2 = m1V1 + m2V2
FRICTION
Definition
“When a body moves over the surface of another body then the opposing force is prodece and this opposing force is called force of friction”
Explanation
Suppose a wooden block is placed on a table and a spring balance is attached on it. If we apply a very small force of magnitude F by pulling the spring gradually and increase it, we observe that the block does not move until the applied force has reached a critical value. If F is less then critical value, the block does not move. According to Newton’s Third Law of motion an opposite force balance the force. This opposing force is known as the force of friction or friction.
Causes of Friction
If we see the surface of material bodies through microscope, we observe that they are not smooth. Even the most polished surfaces are uneven. When one surface is placed over another, the elevations of one get interlocked with the depression of the other. Thus they oppose relative motion. The opposition is known as friction.
Factors on which Friction Depends
The force of friction depends upon the following factors:
1. Normal Reaction (R)
Force of friction is directly proportional to normal reaction (R), which act upon the body in upward direction against the weight of the body sliding on the surface.
2. Nature of Surfaces
Force of friction also depends upon the nature of the two surfaces. It is denoted as u and has constant values for every surface. It is different for the two surfaces in contact.
COEFFICIENT OF FRICTION
The coefficient of friction is a number which represents the friction between two surfaces. Between two equal surfaces, the coefficient of friction will be the same. The symbol usually used for the coefficient of friction is U, where 0 ≤ U ≤ 1 .
The maximum frictional force (when a body is sliding or is in limiting equilibrium) is equal to the coefficient of friction × the normal reaction force.
F = UR
Where m is the coefficient of friction and R is the normal reaction force.
This frictional force, F, will act parallel to the surfaces in contact and in a direction to oppose the motion that is taking/ trying to take place.
ADVANTAGES OF FRICTION
1, We could not walk without the friction between our shoes and the ground. As we try to step forward, we push your foot backward. Friction holds our shoe to the ground, allowing you to walk.
2, Writing with a pencil requires friction. we could not hold a pencil in our hand without friction.
3, A nail stays in wood due to frction
4, Nut and bold cal hold due to friction
DISADVANTAGES OF FRICTION
1, In any type of vehicle–such as a car, boat or airplane–excess friction means that extra fuel must be used to power the vehicle. In other words, fuel or energy is being wasted because of the friction.
2, The Law of Conservation of Energy states that the amount of energy remains constant. Thus, the energy that is “lost” to friction in trying to move an object is really turned to heat energy. The friction of parts rubbing together creates heat.
3, Due to the friction a machine has less frequency 100%
4, Due to friction machine catch fire.
Methods of Reducing Friction
Friction can be reduced by the following methods:
1. The various parts of the machines that are moving over one another are properly lubricated.
2. In machines, the sliding of various parts is usually replaced by rolling. This id done by using ball bearings.
3. Where sliding is unavoidable, a thick layer of greasing material is used between the sliding surfaces.
4. The front of the fast moving objects, e.g. cars, aeroplanes are made oblong to decrease air friction.
Law of Friction
Statement
The value of limiting friction increases proportionally with the increase in normal reaction. Hence, liming friction F(s) is directly proportional to the normal reaction.
F(s) < R (Here < represents the sign of proportionality dont’ write it in the examination paper.)
=> Fs = uR ……….. (i)
u = F(s)/R
u is the constant of proportionality, which depends upon the nature of the surfaces of the two surfaces in contact. It is known as the coefficient of friction. It is only a number without any unit. We know that the normal reaction is directly proportional to the weight of the block, therefore,
R = W = mg
Substituting the value of R in equation (i)
=> Fs = umg
Rolling Friction
If we set a heavy spherical ball rolling, it experiences an opposing force called rolling friction. When a body rolls over a surface, the force of friction is called rolling friction. Rolling friction is much less than the sliding friction. This is because the surfaces in contact are very much less.

KINEMATICS

DEFINITION “It is the branch of Physics which deals with description of motion without reference to any opposing or external force”.
MOTION
“When a body changes its position with respect to its surrounding so the body is said to be in the state of motion”.

TYPES OF MOTION
There are three types of motion:
1, Linear or Translatory motion
2, Rotatory motion
3, Vibratory motion
1. Linear or Translatory Motion
If a body moves in a straight path so the body is to be in Linear motion or Translatory motion.
Example
A bus is moving on the road, A person is running on the ground.
2. Rotatory Motion
If a body spins or rotates from the fixed point ,so the body is to be in Rotatory motion.
Example
The blades of a moving fan, The wheel of a moving car.
3. Vibratory Motion
To and fro motion about the mean point so the body is to be in Vibratory motion.
Example
Motion of a spring.
REST
“When a body does not change its position with respect to its surrounding so the body is said to be in the state of rest”.

Example
A book is laying on the table,A person is standing on floor,A tree in the garden.
SPEED
“The distance covered by a body in a unit time is called speed.”
OR
“The rate of change of distance is called speed.”
FORMULA
Speed = Distance/Time
or V = S/t
UNIT
The S.I unit of speed in M.K.S system is Meter/second.
or m/s
Kinds Of Speed
1. Uniform Speed
If a body covers an equal distance in equal interval of time so the body is said to be in uniform speed.
2. Variable speed
If a body does not cover an equal distance in equal inteval of time so the body is said to be in variable speed.
VELOCITY
“The distance covered by a body in a unit time in a particular direction is called velocity.”

OR
“The rate of change of displacement is called speed.”
OR
“Speed in a definite direction is called velocity.”
FORMULA
Velocity = Displacment/Time
or V = S/t
UNIT
The S.I unit of Velocity in M.K.S system is Meter/second.
or m/s
Kinds Of Velocity
1. Uniform Velocity
If a body covers an equal distance in equal interval of time in a Constant direction so the body is said to be in uniform Velocity.
2. Variable Velocity
If a body does not cover an equal distance in equal interval of time in a particular direction so the body is said to be in variable velocity.
ACCELERATION
“The rate of change of velocity is called acceleration.”
OR
“Acceleration depends upon the velocity if the velocity continously increases or decreases the accelerattion will be produced.”
1. Positive Acceleration
If the velocity continously increases then the acceleration will be positive.
2. Negative acceleration
If the velocity continously decreases then the acceleration will be negative.
FORMULA
Acceleration = change of velocity/Time
or a = (Vf-Vi)/t
UNIT
The S.I unit of Velocity in M.K.S system is Meter/second+square
or m/S2
EQUATION OF MOTION
The relationship of initial velocity, final velocity, acceleration, time,and linear distance.
FIRST EQUATION OF MOTION
suppose an object moves with initial velocity “Vi” in a time “t” and covers a distance “S” in an acceleration “a” and the final velocity of an object becomes “Vf”
According to the defination of the acceleration “The rate of change of velocity is called acceleration”
i.e. Acceleration = Change of velocity/time
=> a = Vf – Vi/t
DERIVATION
a = Vf – Vi/t
at = Vf – Vi
or Vf = Vi + at
SECOND EQUATION OF MOTION
According to the definition of the acceleration “The rate of change of velocity is called acceleration”.
i.e. Acceleration = Change of velocity/time
=> a = Vf – Vi/t
at = Vf – Vi
or Vf = Vi + at ————-(1)
Substituting the average velocity:
Vav = (Vi + Vf)/2 ———–(2)
The distance covered by the body in a unit:
S = Vav/t
Putting the value of Vav from equation 2:
S = [(Vi + Vf)/2] * t
Putting the value of Vf from equation 1:
S = [(Vi + Vi + at)/2] * t
S = [(2Vi + at)/2] * t
S = (Vi + at/2} * t
S = (Vit + 1/2at2) {Here 2 is the square of the time “t”. Dont write this sentence in the examination}
THIRD EQUATION OF MOTION
According to the definition of the acceleration “The rate of change of velocity is called acceleration”.
Acceleration = Change of velocity/time
=> a = (Vf – Vi)/t
=> at = Vf – Vi
or t = (Vf – Vi)/a ————-(1)
Subsituting the average velocity:
Vav = (Vi + Vf)/2 ———–(2)
We know that:
Vav = S/t
=> S = Vav * t
Putting the value of Vav from equation 2 and value of t from eq 1:
S = [(Vi + Vf)/2] * [(Vf-Vi)/a]
S = Vi2 – Vf2/2a since {(a+b) (a-b) = a2 – b2}
or 2as = Vf2 – Vi2
ACCELERATION DUE TO GRAVITY OR FREE FALLING OBJECTS
“Galileo was the first scientist to appreciate that, neglecting the effect of air resistance, all bodies in free-fall close to the Earth’s surface accelerate vertically downwards with the same acceleration: namely 9.8 m/s2″
Example
If a ball is thrown vertically upward, it rises to a particular height and then falls back to the ground. However this is due to the attraction of the earth which pulls the object towards the ground”
CHARACTERISTIC OF FREE FALLING BODIES
1, When a body is thrown vertically upward, its velocity continously decreases and become zero at a particular height During this motion the value of acceleration is negative and Vf is equal to zero (a = -9.8m/s2 , Vf = 0).
2, When a body falls back to the ground , its velocity continously increases and become maximum at a particular height During this motion the value of acceleration is positive and Vi is equal to zero (a = 9.8m/s2 , Vi = 0).
3, Acceleration due to gravity is denoted by a and its value is 9.8m/s2 .
4, Equation of motion for the free-falling bodies be written as,
Vf = Vi + gt
h = Vit + 1/2 gt2
2gh = Vf2 – Vi2

Scalar and Vectors

SCALAR

"Scalar quantity are those physical quantity which are completely specified by their magnitude express with suitable unit. They do not require any mention of the direction for complete their specification is called scalar quantity."

OR

" Scalar quantity are those physical quantity which require magnitude , express with suitable unit only is called scalar quantity."


CHARACTERISTICS OF SCALAR QUANTITY

1, Scalar quantity can be added,subtracted,multiplied,divided according to the ordinary algebraic rule.

2, Two scalars are equal if they have same unit.

REPRESENTATION

It can be represented by the numbers with decimals. (positive negative)


EXAMPLE

Mass,Distance,Temperature,volume,speed e.t.c

VECTOR

"VECTOR quantity are those physical quantity which do not require only their magnitude express with suitable unit. But they also require a particular direction for complete their specificaton is called vector quantity."

OR

" vector quantity are those physical quantity which require magnitude , express with suitable unit as well as proper direction is called vector quantity."


CHARACTERISTICS OF VECTOR QUANTITY

1, vector quantity can not be added,subtracted,multiplied, divided according to the ordinary algebraic rule.

2, It can be added,subtracted,multiplied,divided according to the some special rules like head and tail rule,Graphical method e.t.c.

3, vector always treats as positive.

REPRESENTATION

It can be represented by an arrow with headline. The length of an arrow represents its magnitude and the headline represents the direction of the vector(figure 1.1)

-------------------------------------&gt;
(figure 1.1)

EXAMPLE

Weight,Displacement,Velocity,Acceleraton,Torque,Momentum e.t.c

ADDITION OF A VECTOR

"The process of combining of two or more vector to produce a signal vector having the combinig effect of all the vector is called the resultant of the vector and this process is known as the addition of a vector".


HEAD AND TAIL RULE

Suppose we have two vector A and B having the different magnitude and direction.

1, First of all chose a suitable scale and representation of all the vector have been drawn on the paper.

2, Put all the vector for finding the resultant of given vector such that the head of the first vector join the tail of the second vector.

3, Now join the tail of the first vector with tail of the second vector such that it join the two vector with head to head and tail to tail by another.

4, The new vector R will be the resultant of the given vector.

5, It can be measured by the Dee or any suitable mean.This method is called the head and tail or tip to tail rule


RESOLUTION OF A VECTOR

"The process of splitting up of a signal vector into two or more vector is called the resolution of a vector"

OR

"The process of splitting up of a signal vector into its components is called the resolution of a vector"
  RECTANGULAR COMPONENTS

A vector which is not along x-axis or y-axis it can be resolved into infinite number, but generally a vector can be resolved into its components at a right angle to each other
 
MATHEMATICALLY PROVED
suppose a vector F is denoted by a line AB which makes an angle @ with horizontal surface OX. From a point A draw perpendicular to the horizontal surface OX.

The line AB represents its vertical component and it is denoted by Fy.The line OB represents its horizontal component and it is denoted by Fx. Now in the triangle AOB

Sin@= AB/OA {sin@= Perpendicular/Hypotenuse}

or sin@= Vy/V

or Vy= V sin@

Similarly


Cos@= OB/OA {sin@= Base/Hypotenuse}

or Cos@= Fx/F

or Vx= V Cos@

For the triangle

Tan@= AB/OB {Tan@= per/hyp)

or Tan@= Vy/Vx

or @=Tan-1 =Vy/Vx

SUBTRACTION OF A VECTOR

"It is defined as the Addition of A to the negative of a B is called the subtraction of a vector (A-B)"

Measurements

Definitions
1. Meter

The length of the path traveled by light in vacuum in 1/299,792,458 of a second is known as meter.
Length is a fundamental unit used for measurements of length, distance and height. It is equal to the distance between two marks on a Platinum-Iridium bar kept at 0 C in International Bureau of Weight and Measurements (IBWM) near Paris.

2. Kilogram

The mass of a Platinum-Iridium cylinder kept at 0 C in International Bureau of Weight and Measurements (IBWM) near Paris is considered to be 1 kilogram.
Kilogram is a fundamental unit used for measurements of mass.

3. Second

It is equal to the duration of 9,192,631,770 periods of radiation of Cesium-133 in ground state.

Fundamental Units

The international system of units is based on seven independent units known as Fundamental or Basic Units. These are given below:

1. Meter (m): length, distance, height (l)
2. Kilogram (kg): mass (m)
3. Second (s): time (t)
4. Ampere (A): electric current (I)
5. Kelvin (K): temperature (T)
6. Mole (mol): amount of substance (n)
7. Candela (cd): luminous intensity (Iv)

Derived Units

The units that require two or more basic measurements of same units or different fundamental units for its definition are called derived units.

1. Square meter (m2): area (A)
2. Cubic meter (m3): volume (V)
3. Hertz (Hz): frequency (v)
4. Kilograms per cubic meter (kg/m3): mass density (p)
5. Meter per second m/s: speed velocity (V)
6. Radians per second (rad/s): angular velocity (w)
7. Meters per second square (m/s2): acceleration (a)
8. Newton (N) (kg.m/s2): force (F)
9. Pascal (Pa) (N/m2): pressure (P)
10. Joule (J)(N.m): work (W), energy(E), quantity of heat (q)
11. Watt (W) (J/s): power (P)
12. Coulomb (C) (A.s): quantity of electric charge (Q)
13. Volt (V) (W/A): potential difference (V), electromotive force (E)
14. Ohm (Omega): electric resistance (R)
15. Farad (F)(A.s/V): capacitance (C)
16. Weber (Wb)(V.s): magnetic flux (@)
17. Henry (H) (V.s/A): inductance (E)
18. Volts per meter (V/m): electric field strength (E)
19. Newton per coulomb (N/C): electric field strength (E)
20. Tesla (T) (Wb/m2): magnetic flux density (B)
21. Ampere per meter (A/m): magnetic field strength (H)
22. Joules per kilogram Kelvin: (J/kg.K) specific heat (Q)

Vernier Callipers

A vernier calipers is an instrument that is used to measure the length, diameter and depth of solid substances accurately up to 0.1mm. A vernier calipers has two scales, the main scale (MS) and vernier scale (VS). The vernier scale (VS) slides over the main scale (MS).

Vernier Count (VC)

The smallest measurement that can be made with the help of a vernier calipers is known as least count of vernier calipers or vernier count (VC). Least count of the vernier calipers is calculated by

L.C = Value of Smallest Division of MS/Total Number of Divisions on VS

Micrometer Screw Gauge

A screw gauge is an instrument that is used to measure thickness of a wire, glass, plastic and metal sheets accurately up to 0.01mm. A micrometer screw gauge has two scales, the main scale (MS) and the circular scale (CS). The circular scale rotates over the main scale.

Least Count (LC)

The smallest measurement that can be made with the help of a screw gauge is known as least count of screw gauge. Least count of the screw gauge is calculated by:
L.C = Pitch of the Screw / Total number of divisions of CS
where pitch is the distance between two consecutive threads of the linear screw.

Physical Balance

A physical balance is an instrument that is used to find the mass of an object. Actually, it is the lever of the first kind with equal arms.

Stop Watch

A stop watch is an instrument that is used to measure accurately the time interval for any physical event. It can be used to measure the fraction of a second.

Measuring Cylinder

A measuring cylinder is a glass cylinder of uniform area of cross section with a scale in cubic centimeter or millimeter marked on it. It is used to measure the volume of a liquid