SOUND
Origin of Sound
A vibrating body produces sound. When a gong of a bell is struck with a hammer, sound is produced. The bell is set into vibration and sound is propagated through air. These vibrations reach the ear and the eardrum is set into vibration. The vibrations are communicated to the brain. By touching the gong with the hand. One can feel the vibration of the gong. Similarly the cycle bell produces sound due to the vibrations produced by the gong. When the cycle bell is induced with hand, the vibrations are stopped and the bell does not produce sound. If a pith ball pendulum is held in contact with the edges of a vibrating gong, the sound is produced.
A tuning fork is set into vibrations by striking its prongs against a rubber pad. These vibrations of the prong of the tuning fork can be see. Similarly, vibrating strings, air columns, vibrating plates etc, produce sound.
Material Medium is a Necessity
It can be proved by means of an experiment that a material medium is a necessity for the propagation of sound waves. In the absence of a medium, no sound waves can travels.
Wave Motion
It is a form of disturbance, which travels through the medium due to the repeated periodic motion of the particles of the medium about their mean positions, the disturbance being handed over from one particle to the next. When a stone is dropped into a pond containing water, waves are produced at the point where the stone strikes the water in the pond. The waves travel outward; the particles of water vibrate only up and down about their mean positions Water particles do not travel along with the wave.
Characteristics of wave motion
It is a disturbance produced in the medium by the repeated periodic motion of the particles of the medium.
(1) Only the wave travels forward whereas the particles of the medium vibrate about their mean positions.
(2) There is a regular phase change between the various particles of the medium. T particle ahead starts vibrating a later than a particle just preceding it.
The velocity of the wave is different from the velocity with which the particles of the medium, are vibrating about their mean positions. The wave travels with a uniform velocity whereas the velocity of the particles is different at different positions. It is maximum at the mean position and zero at the extreme position of the particles.
Transverse Wave Motion
In this type of wave motion, the particles of the medium vibrate at right angles to the direction of propagation of the wave.
To understand the propagation of transverse waves in a medium consider nine particles of the medium and the circle of reference The particles are vibrating about their mean positions, up and down and the wave is traveling from left to right The disturbance takes T/8 seconds to travel from one particle to the next.
(1 ) At t = 0, all the particles are at their mean position.
(2) After T/8 second the particle 1 travels a certain distance upward and the disturbance reaches particles 2.
(3) After 2T/8 seconds particle 1 has reached its extreme position and the disturbance has reached particle 3.
(4) After 3T/8 seconds particle 1 has completed 3i8 of its vibration and the disturbance has reached particle 4.
(5) In this way after T/2 seconds, particle 1 has come back to ~s means position The disturbance has reached particle 5.
In T seconds, the particles one, five and nine are at their mean positions of the particles after 5T/8, 6T/8, 7T/8 and T seconds
Longitudinal Wave Motion
In this type of wave motion, the particles of the medium vibrate along the direction of the propagation of the wave. Consider nine particles of the medium and the circle of the reference. The wave travels from left to right and the particles vibrate about their mean positions. After T/8 seconds, the particle 1 goes to the right and completes 1/8 of it vibration. The disturbance reaches the particle 2. After T/4 second the particle 1 has reached its extreme right position and complete ¼ of its vibration and the particle 2 completers 1/8 of its vibration. The disturbance reaches the particles 3. The process continues.
The wave has reached particle 7. Here 1 and 9 are again in the same phase. Here particles 1, 5 and 9 are at their mean positions. The particles 1 and 3 are close to the particle 2. This is the position of condensation. Similarly particles 9 and 8 are close to the particle 7. This is also the position of condensation or compression. On the other hand particles 4 and 6 are far away from the particle 5. This is the position of rarefaction. Hence in a longitudinal wave motion, condensation and rarefaction are alternately formed.
Wavelength It is the distance traveled by the wave in the time in Which
particle of the medium completes one vibration. It is also defined as the distance between two nearest particles in the same phase.
The distance AB is equal to the wavelength l.
Frequency: It is the number of vibrations made by a particle in one second.
Amplitude: It is the maximum displacement of the particle from its mean position of rest.
Time period: It is the time taken by a particle to complete one vibration. suppose frequency = n
Time taken to complete n vibrations = 1 second
Time taken to complete 1 vibration = 1/n second
From the definition of time period, time taken to complete one vibration is the time period (T)
\T = 1/n or n T = 1
Frequency x time period = 1.
Vibration It is the to and fro motion of a particle from one extreme position to the other and back again. It is also equal to the motion of a particle from the mean position to one extreme position, then to the other extreme position and finally back to the mean position.
Phase It is defined as the ratio of the displacement of the vibrating particle at any instant to the amplitude of the vibrating particle or it is defined as the fraction of the time interval that has elapsed since the particle crossed the mean position of rest in the positive direction or it is also equal to the angle swept by the radius vector since the vibrating practical last crossed its mean position of rest.
Relation between Frequency and Wavelength
Velocity of the wave is the distance travelled by the wave in one second. velocity = distance /Time
Wavelength (l) is the distance travelled by the wave in one time period (T). Velocity = wavelength = l
Time period T
But, frequency x time period = 1
n x T = 1
T = 1
n
v = l = l
T 1/n
Laws of Transverse Vibration of Strings:
There are three laws of transverse vibration of strings:
(1 )The fundamental frequency is inversely proportional to the length of the string.
n a 1/l
(2)The fundamental frequency is directly proportional to the square root of the stretching force or tension.
n a T
(3)The fundamental frequency is inversely proportional to the square root of the mass per unit length.
n a 1/Öm
Combining the above three laws, n a 1/lÖ (T/m)
n = k/l Ö(T/m) (OR)
The value of the constant k =1/2
\n = 1 Ö (T/m)
2l
Echo
The repetition of the sound produced due to reflection by a distant extended surface like a cliff, hill, well, building etc. is called an echo. The effect of sound on the human ear remains for 1/10 of a second. If the sound is reflected back in a time less than 1/10 th of a second, no echo is heard. Suppose, a person produces a sound and this sound is reflected from an obstacle at a distance x. The time taken by the sound to travel to the obstacle and back is t.
t = 2x
v
Here V = 340 meters/second
X = vt = 340 x 0.1 = 17metres
2 2
In means that if the distance between the source of sound and the obstacle is less than 17 meters (56ft) no echo (repetition) is heard. But echo is heard if the distance is more than 17 meters.
If a person is standing in between two hills and produces a sound, the sound is reflected again and again from the two hills and successive echoes are heard.
Eg.1. The distance between particles on a sting is 10cm. Determine the
phase difference in terms of the phase angle of oscillations, if the speed is 100 m/s.
v = 100 m/s.
n = 400 Hz.
A = v/n=100/400 = 0.25m,
x = 10 cm = 0.1 m.
f = 2p x/l = 2l. 0.1/0.25 = 0.8p radians.
2. A body vibrating with a certain frequency sends wave 15 cm long through a medium A and 20 cm long through a medium B. The velocity of waves in A is 1200 cm/s. Find the velocity in B.
Suppose the frequency = n. In the first frequency = n.
l1= 15 cm , v1 = 1200m/s.
v1= n l1
n=v1/l = 1200/15 = 80
the second case: n =80, l2= 20 cm , v2=? .
v2 = nl2. = 80 x 20 = 1600cm / s
3. A thunderclap was heard 5.5 s later than the accompanying light flash was seen. How far away did the flash occur? Velocity of sound = 350 m/s.
v= 350 m/s. t= 5.5 sec.
S= v x t = 350 x 5.5 = 1925 m.
4. The velocity of sound in air at 16 0C is 340 m/s. Find the wavelengths in air of a note of frequency 680 at 160°C and 51 0C.
(a) At 16°C suppose the wave length = l1
\V1 = 340 m/s.
n= 680
V1= n l1
l1 = V1/n = 340/680 = 0.5m
(b) At 51 ° C, suppose the wavelength = l2
t1 = 16 0C, V1 = 340 m/s.
2 = 51 0C, V2 = ? .
v2 = Ö(273 +t2)
v1 Ö(273+16)
V2 = 360 m/s.
l 2 = V2/n = 360/380 = 0.53 m
5. The velocity of sound at normal temperature and pressure is 332 m/s. Find velocity of sound at 819°C.
t1 = 00C V1 = 332 m/s. t2 = 8190c V2 = ?
V2 = Ö(273+819)
V1 Ö 273
V2 = 664m/s.
6. The disc of a siren contains 64 holes and is made to rotate 240 times/s. Calculate the Frequency of the note emitted.
Frequency = N,
Number of holes = h,
Number of rotations/s = n,
N = n x h.
240 x 64. = 15360Hz
7. The disc of siren having a circle of 40 holes, rotates uniformly 500 times in 1 minute.24 seconds. Find the frequency of the note emitted and its wavelength in air, if the velocity of sound in air is 34000 cm/s.
Frequency N,
Number of holes = h =40.
Number of rotations/s = n = 500/84.
N= n x h.
40 x 500/84. = 15360.
but V =Nl
l = v/n = 34000/238.1 = 142.8 cm.
(a) A note produces 4 beats/seconds with a tuning fork of frequency 512h and 6 beats/seconds with a tuning fork of frequency 514Hz. Find the frequency of the note.
In the first case:
Frequency of the tuning fork = 512 Hz
Beats/sec = 4
.'. Possible frequencies of the ote are 512 + 6 = 516 Hz
or 512 -4 = 508 Hz
In the second case:
Frequency of the tuning fork = 514 Hz
Beats/sec = 6
Possible frequencies of the note are 514+6 = 520 Hz or 514-6
= 508Hz
As the frequency of 508Hz common in both, the only possible frequency of the 4 note = 508Hz
9. A tuning fork and a siren produce 18 beats in 3s. The siren has 16 holes and is making 960 revolutions per minute. If the speed of the siren is reduced, the two notes will be in unison. Find the pitch of the tuning fork.
There are 18 beats in 3 seconds.
Beats/sec = 6
Number of holes h = 16
Revolutions per minute = 960
\ Revolutions per second n =
Frequency of the sound produced by the siren = n x h = 16 x 16
= 256 Hz
\ Frequency of the tuning fork is either
256 + 6 = 262 (or) 256 -6 = 250-6=250Hz,
10. The prongs of a tuning fork A, originally in unison with a tuning fork B, are found. Now tuning fork on being sounded together produce 2 beats/sec. What is the frequency of A after filling with water, if the frequency of B is 250 cycles/sec.
Frequency of A =250 cycles/sec.
Frequency of B = 250 cycle/sec.
Beats after A is filled 2 cycles/sec.
Since the frequency increases after filling, frequency of A =250 + 2
= 252 cycles/sec
Wednesday, June 18, 2008
yogendra
Heat is defined as energy in transit.
The temperature of a system can be defined as the property that determines whether or not the body is in thermal equilibrium with the neighboring systems. If a number of systems are in thermal equilibrium, a single numerical vale called the temperature can represent this common property of the system. It means that if two systems are not in thermal equilibrium, they are at different temperatures.
Thermometry
The branch of heat relating to the measurement of temperature (degree of hotness) of a body is called thermometry. Thermometer is the instrument used to measure the temperature of a body.
Types of Thermometers. There are different kinds of thermometers
(i) Liquid thermometers. These thermometers are based on the principle of change in volume of a liquid with change in temperature. Mercury and alcohol thermometers are based on this principle.
(ii) Gas thermometers These are based on the principle of change in pressure or volume with change in temperature, Eg: Callendar's constant pressure thermometer, constant volume hydrogen thermometer, etc.
(iii) Resistance thermometers. These are based on the principle of change in resistance with change in temperature, Eg: platinum resistance thermometer.
(iv) Thermo-electric thermometers: These are based on the principle of thermo-electricity, Eg :- production of thermo -EME in a thermo-couple when the two junctions are at different temperatures.
(v) Radiation thermometers: These are based on the quantity of heat radiations emitted by a body Ex: -furnaces. These instruments are known as pyrometers.
(vi) Vapour pressure thermometers: These are based on the principle of change of vapour pressure with change in temperature. These are used to measure low temperatures, Ex:- helium vapour pressure thermometer, etc.
Celsius. Fahrenheit and Reaumur Relation:
C = F -32 = R
100 180 80
Relation between Celsius. Kelvin. Fahrenheit and Rankin Relation:
C -0 = F -32 = K -273 = R
100 180 100 80
Specific Heat
When a body is heated, its temperature rises. If 100gm of copper and 100gm of water are heated by similar burners for the same time, the rise in temperature is not the same in the two cases. The rise in temperature depends on the quantity of heat given to the body and the nature of its material. Let Q be the quantity of heat given to a body of mass m and let the rise in temperature be e. Then, Q = mse
Where s is a constant that depends upon the nature of the substance. S is called the specific heat of the substance.
Calorie It is the quantity of heat required to raise the temperature of one gram of water from 14.5° to15.5° C. This is the standard unit recommend by International Committee of Pure Physics.
For ordinary purposes, the specific heat of water is taken as 1, but specific heat of water is not 1 at all temperatures. For practical purposes calorie may be defined as the amount of heat required to raise the temperature of 1 gm of water through 1° C.
Kilogram Calorie It is the amount of heat required to raise the temperature 1 kg of water through 10 c.
1 kg calorie = 1000 calories.
British Thermal Unit It is the amount of heat required to raise the temperature of 1 pound of water through 10F. 1 BTU = 252 calories.
Therm It is the amount of heat required to raise the temperature of 105 pounds of water through 10F.
1 Therm = 2.52 x 107 calories.
Pound Calorie It is the amount of heat required to raise the temperature of 1 pound of water through 10c.
1 pound calories = 453.6 calories.
UNITS OF HEAT
Unit
Quantity of water
Rise in temp
Relation
Calorie
1gm
10c
= 1 calorie
Kg Calorie
1kg
10c
= 1000 calories
BTU
1 pound
10 F
= 252 calories
Therm
105pound
10 F
= 2.52 x 107 calories
Pound Calorie
1 pound
10c
= 453.6 Calories
Specific Heat Specific heat is defined as the quantity of heat required to raise the temperature of one gram of a substance through 10c. The specific heat of a substance is not constant and it is different at different temperatures. Ordinarily, the specific heat determined is the mean specific heat, Suppose, m is the mass of the substance, s is the mean specific heat and if Q units of heat is required to raise its temperature from q1 to q2 , then the mean specific heat
s = Q / m(q2 - q1)
For qualitative work, if dQ heat is given to raise the temperature of m grams of substance through dq.
dQ = m s dq
s = 1 x dq
m x dt
The unit of specific heat is ‘cal/g0 c
Thermal Capacity It is the quantity of heat required to raise the temperature of the whole of the substance through 10C. Let the mass of the substance be m and its specific heat s
Thermal capacity = m x S x 1
= ms calories.
Water Equivalent It is the amount of water that will absorb the same quantity of heat as the substance for the same rise in temperature. Let the mass of the substance be m, specific heat s and rise in temperature q.
Q = mse
If the water equivalent = W
Q = W x 1 x q
W x 1 x q = mse (OR) W = ms grams
Water equivalent is numerically equal to the thermal capacity but the unit of water equivalent is gram and that of thermal capacity is calorie.
Change of State
A substance can exit three states viz. Solid, Liquid and Gas. The particular state of a substance depends on its temperature. According to the kinetic theory, the molecules of a substance in the solid state have less degree of freedom than a substance in the liquid or gaseous state. The molecules are more free to move in the gaseous state. The change in state can be brought about by supplying or withdrawing heat from the substance. Ice is the solid state of water. By supplying heat to ice, it can be changed into water. Similarly by supplying heat to water, it can be converted into the gaseous state (steam). This is true for all substances. Even permanent gases like oxygen, nitrogen, hydrogen etc can be liquefied at low temperatures.
For a given substance the change of state takes place at a fixed temperature and pressure. When the substance changes from the solid to the liquid state, the heat supplied at the constant temperature (called melting point) is used to overcoming the forces of intermolecular attraction. The mean molecular distance increases and the molecules from the liquid to the gaseous state at a fixed temperature (called the boiling point) and pressure. The heat supplied is used in increasing the mean molecular distance. The molecules become free to move about in the whole space available to them.
Latent Heat of Fusion
Take small pieces of ice in a beaker. Fix a thermometer to note the temperature of ice in the beaker. Heat the beaker slowly. Ice melts but the thermometer does not show any rise in temperature. When the whole of ice has melted the temperature of water rises and the thermometer indicates it. During the process of conversion from ice to water (change of state from solid to liquid) the heat supplied is used to change the state of ice from solid state to liquid state. This heat is called latent heat. Latent means hidden i.e.. Which is not indicated by the thermometer.
It has been found that one-gram of ice takes 80 calories of heat to get it converted to water. This heat is called latent heat of fusion of ice. Its unit is 'cal/gram'.
Latent heat of a substance is defined as the amount of heat required change the state of one gram of substance from solid to liquid without any change in its temperature.
Law of Fusion
(1) Every substance changes its state from solid to liquid at a particular temperature (under normal pressure) called the melting point.
(2) As long as the change of state takes place there is no change in temperature.
(3) One gram of every substance requires a definite quantity of heat for change of state from solid to liquid and it is called the latent heat of fusion of that substance. It is different for different substance.
(4) Some substances show increase in volume on melting e.g., wax, ghee, etc. While some other substances show decrease in volume on malting e.g., ice
(5) The melting point of those substance which decrease in volume on melting, is lowered with increase in pressure.
(6) The melting point of those substance which increase in volume on melting, is increased with increases in pressure.
Note
(1) Ice decreases in volume on melting and its melting point is lowered with increases in pressure.
(2) The melting point or solidification point is the same for a substance.
Laws of Boiling
(1) Every liquid changes its state from liquid to its vapour at a particular temperature (under normal pressure) called the boiling point.
(2) As long as the change of state takes place, there is no change in temperature.
(3) One gram of every liquid requires definite quantity of heat for change of state from liquid to vapour and it is called the latent heat of vaporization of that liquid. Latent heat is different for different substances.
(4) All liquids show increase in volume on vaporization.
(5) The boiling point of a liquid increase with increase in pressure of a liquid.
(6) The liquid can boil at a lower temperature under reduced pressure.
Latent Heat of Vaporization
The latent heat of vaporization of a liquid is the amount of heat required to convert one gram of the liquid into vapour without any change in temperature. For water, latent heat of vaporization is 537 cals/grm at a pressure of 75cm of Hg. Latent heat of vaporization is different for different substances.
Conduction Is the process in which heat is transmitted from one point to the other through the substance without the actual motion of the particles? When one end of a metal bar is heated, the molecules at the hot end vibrate with higher amplitude (kinetic energy) and transmit that heat energy from one particle to the next and so on. However the particles remain in their mean positions of equilibrium. (This process of conduction is prominent in the case of solids. The property of transmission of heat has been used in Davy's safety lamp. Materials having less conductivity e.g. granite, brick walls boiler etc. The space between the two walls of a thermos flask is evacuated because vacuum is a poor conductor of heat. The air enclosed in the woolen fabric helps in protecting us from cold because air is a poor conductor of heat.
Convection is the process in which heat is transmitted from one place to the other by the actual movement of the heated particles. It is prominent in the case of liquids and gases. Land and sea breezes, and trade winds are formed due to convection. Convection plays an important part in ventilation; gas filled electric lamps and heating of buildings by hot water
circulation.
Radiation is the process in which heat is transmitted from one place to the other directly without the necessity of the intervening medium. We get heat radiations directly from the sun without affecting the intervening medium. Heat radiation's can pass through vacuum. Their properties are similar to light radiations.
Examples
1. Find the value of absolute zero of the Fahrenheit scale.
F –32 = A –273
180 100
Here A = 0
F = -180 x 273 + 32
100
= -456.40F
2. There is a certain temperature which has the same reading on both centigrade and Fahrenheit thermometers. Find the temperature.
F -32 = A -273
180 100
Here F = C = x
\ x – 32 = x
180 100
(OR)
x –32 = 9/5x
\ x = -40
\-400C = -40 0F
3. A faulty thermometer has its fixed points marked 5 and 95. What is the correct temperature in centigrade when this thermometer records 59?
Let the reading on the centigrade thermometer be °c
C = R-L.F.P.
100 P.-L.F.P.
\ c = 59-5
100 95-5
c = 54
100 90
C = 600C
4. A certain mass of gas exerts a pressure of 72 cm of mercury at 2~C. It is heated at constant volume and the pressure observed after some time is 90cm of mercury. Calculate the temperature.
Here P1 = 72 cm of Hg P2 = 90cm of Hg
V1 = V V2 = V
T1 = 273 + 27 = 3000 A0 T 2 = ?
P2 v2 = p1 v1 (OR) 90v = 72v
T2 T1 T2 300
T2 = 90 x 300 = 3750A = 020c
72
5. Calculate how much steam from water boiling at 100 0C will just m 200gm of wax at 15°C. (Melting point of wax = 550C, S.P. Latent heat of fusion of x = 35 cal/gm)
Suppose mass of steam = m
Mass of wax = 200gm
Sp. Heat of wax = 0.7
Latent heat of wax = 35 cal/gm
Initial temperature of wax = 150C
Melting point of wax = 550C
Heat required to rise the temperature of wax from 150C to550C
= 200 x 0.7 x (55 -15) = 5600 cal
Heat required to melt wax at 550C = 200 x 35 = 7000 cal
Total heat gained by wax = 5600 + 7000 = 12,600 cal
Heat lost by steam = m x 540 + m (100- 55)
= 540m + 45m = 585m
Heat lost = Heat gained
585m = 12,600
m = 21.54gm
6. How much ice at 00C would a kilogram of steam at 1000C melts, if the resulting water is at 00C ? Latent heat of ice = 80cal/gm and latent heat of steam = 536 cal/gm.
Mass of ice = M gm
Mass of steam = 1 kg = 1000 gm
Temper of stem = 1000 C
Final temp = 00C
Heat gained by ice = M x 80 cal
Heat lost by ice steam = 1000 x 536 + 1000 x 100
= 636000cal
Heat gained = Heat lost
80 M = 636000
M = 7950 gm
= 7.95kg
7. A piece of metal weighing 60 gm at 100C was immersed in a current of steam 1000C . Calculate the amount of steam condensed. Specific heat of the metal is 0.1 cal/gm - 0C and latent heat of steam is 540 cal/gm.
M = 60gm
S = 0.1 cal/gm - 0C
T1 = 100C
T2 = 100°C
Heat taken by the metal = MS(T 1 -T 2)
= 60 x 0.1 (100 -10)
= 540 cal.
Suppose the mass of steam condensed = m grams
Latent heat of steam,
L = 540cal/gm .
\Heat lost by steam,
m L = m x 540
Heat gained = Heat lost
540 = 540m
\m = 1 gm
(OR) Hence, the mass of steam condensed = 1 gram.
8. An electric heater rod is dipped in a vessel containing water at 00C. The electric rod produces heat at the rate of 3000J/s. The vessel with its contents is maintained at 00 C by adding ice at the rate of 9 g/s. Calculate the specific latent heat of fusion of ice. If the total heat capacity of the water, the vessel and its contents is 12000j/K, at what rate does the temperature start rising when the supply of ice is stopped.
(1) Here H = 3000J/s
m = 9 g/s = 9 x 10-3 kg/ s
H = mL
L = H/m
L = 3000
9 X 10 -3
L = 3.33 x105 J/Kg.
(2) When the supply of ice is stopped, let the rate of rise of temperature be q k/s
w = 12000J/Kg
H = 3000 J/s
H = Wq
q = H/W
q = 3000
12000
q = 0. 25Kg/s.
9. lt is found that 65,45,000 cal of heat are transmitted per minute across a sheet of silver 10cm square and 1 mm thick, with a difference of temperature between its faces 1100C. Find the coefficient of thermal conductivity of silver.
Q = 65,45,000 cal, time t=1 min = 60sec
Each side of the square = 10cm
\Area of cross-section
A = 1 mm = 1/10cm, q1 -q2 = 1100C
Q = kA(q1 -q2 ) t
D
(OR)
K = Q x d = 65,45,000 x 1
A (q1 -q2)t 10 x 100 x 110 x 60
= 0.99
10. Estimate the rate at which ice would melt in a wooden box 2cm thick and of inside measurements 100 x 60 x 60 cm. Assuming that the external temperature, is 30oC and K for wood = 0.0004.
Thickness of the box = d = 2cm
q1 = 300c
q2 = 00c
(q1-q2) = 300c
Surface area of the box
A = 2 x 100 x 60 + 2 x 60 x 60 + 2 x 100 x 60
= 31200 sq cm
Q = kA(q1 -q2 ) t
D
= 0.0004 x 31200 x 30 x 1
2
= 187.2 cal
Suppose the amount of ice melted = m grams
Q = 80 m
M = 2.34 grams
11. The height of Niagra falls is 50 meters. Calculate the difference between the temperature of water at the top and the bottom of the falls. (J=4.2 x 107 ergs/cal) h = 50meters = 5000 ergs
suppose difference of temperature = o C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x e calories W = JH
suppose difference of temperature = u C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x q calories
W = JH
M x 980 x 5 000 = 4.2x107 x m x q
q = 980 x 5000
42 x107
12. A 12kg mass falls through 23mm on to the ground and bounces to a height of 0.50.? Assuming that all the potential energy to is used in heating up the mass, 'calculate the temperature rise. Take specific heat capacity of the material as 600 joules/kg0C and the force of gravity on 1kg = 10 Newton.
M = 12kg
S = 600joules/kg -0C
h1 = 23mm
q = ?
h2 = 0.50 mm
g = 10 m/s2 (given)
Loss in potential energy = Mg (h1 – h2)
= 12 x 10(23- 0.50)
= 2700joules
= Msq
= 2700joules
\q = 2700 = 0. 375 0C.
12x600
Eg.13. Convert 50°C into Farenheit and 68°F into Centigrade. (HMT -1995)
Eg.14. Why is better to wear dark clothes in winter and bright clothes in summer. (HMT -1995)
Eg.15.A man has a temperature of 99.8° F what will be the thermometer shows if it measures temperature in degrees Celsius? (HMT-1994)
Eg.16. A measuring unit of power
Eg.17. The velocity of light is
(a) 313 m/sec (b) 330 m/s (c) 303 m/s (d). none Of these
The temperature of a system can be defined as the property that determines whether or not the body is in thermal equilibrium with the neighboring systems. If a number of systems are in thermal equilibrium, a single numerical vale called the temperature can represent this common property of the system. It means that if two systems are not in thermal equilibrium, they are at different temperatures.
Thermometry
The branch of heat relating to the measurement of temperature (degree of hotness) of a body is called thermometry. Thermometer is the instrument used to measure the temperature of a body.
Types of Thermometers. There are different kinds of thermometers
(i) Liquid thermometers. These thermometers are based on the principle of change in volume of a liquid with change in temperature. Mercury and alcohol thermometers are based on this principle.
(ii) Gas thermometers These are based on the principle of change in pressure or volume with change in temperature, Eg: Callendar's constant pressure thermometer, constant volume hydrogen thermometer, etc.
(iii) Resistance thermometers. These are based on the principle of change in resistance with change in temperature, Eg: platinum resistance thermometer.
(iv) Thermo-electric thermometers: These are based on the principle of thermo-electricity, Eg :- production of thermo -EME in a thermo-couple when the two junctions are at different temperatures.
(v) Radiation thermometers: These are based on the quantity of heat radiations emitted by a body Ex: -furnaces. These instruments are known as pyrometers.
(vi) Vapour pressure thermometers: These are based on the principle of change of vapour pressure with change in temperature. These are used to measure low temperatures, Ex:- helium vapour pressure thermometer, etc.
Celsius. Fahrenheit and Reaumur Relation:
C = F -32 = R
100 180 80
Relation between Celsius. Kelvin. Fahrenheit and Rankin Relation:
C -0 = F -32 = K -273 = R
100 180 100 80
Specific Heat
When a body is heated, its temperature rises. If 100gm of copper and 100gm of water are heated by similar burners for the same time, the rise in temperature is not the same in the two cases. The rise in temperature depends on the quantity of heat given to the body and the nature of its material. Let Q be the quantity of heat given to a body of mass m and let the rise in temperature be e. Then, Q = mse
Where s is a constant that depends upon the nature of the substance. S is called the specific heat of the substance.
Calorie It is the quantity of heat required to raise the temperature of one gram of water from 14.5° to15.5° C. This is the standard unit recommend by International Committee of Pure Physics.
For ordinary purposes, the specific heat of water is taken as 1, but specific heat of water is not 1 at all temperatures. For practical purposes calorie may be defined as the amount of heat required to raise the temperature of 1 gm of water through 1° C.
Kilogram Calorie It is the amount of heat required to raise the temperature 1 kg of water through 10 c.
1 kg calorie = 1000 calories.
British Thermal Unit It is the amount of heat required to raise the temperature of 1 pound of water through 10F. 1 BTU = 252 calories.
Therm It is the amount of heat required to raise the temperature of 105 pounds of water through 10F.
1 Therm = 2.52 x 107 calories.
Pound Calorie It is the amount of heat required to raise the temperature of 1 pound of water through 10c.
1 pound calories = 453.6 calories.
UNITS OF HEAT
Unit
Quantity of water
Rise in temp
Relation
Calorie
1gm
10c
= 1 calorie
Kg Calorie
1kg
10c
= 1000 calories
BTU
1 pound
10 F
= 252 calories
Therm
105pound
10 F
= 2.52 x 107 calories
Pound Calorie
1 pound
10c
= 453.6 Calories
Specific Heat Specific heat is defined as the quantity of heat required to raise the temperature of one gram of a substance through 10c. The specific heat of a substance is not constant and it is different at different temperatures. Ordinarily, the specific heat determined is the mean specific heat, Suppose, m is the mass of the substance, s is the mean specific heat and if Q units of heat is required to raise its temperature from q1 to q2 , then the mean specific heat
s = Q / m(q2 - q1)
For qualitative work, if dQ heat is given to raise the temperature of m grams of substance through dq.
dQ = m s dq
s = 1 x dq
m x dt
The unit of specific heat is ‘cal/g0 c
Thermal Capacity It is the quantity of heat required to raise the temperature of the whole of the substance through 10C. Let the mass of the substance be m and its specific heat s
Thermal capacity = m x S x 1
= ms calories.
Water Equivalent It is the amount of water that will absorb the same quantity of heat as the substance for the same rise in temperature. Let the mass of the substance be m, specific heat s and rise in temperature q.
Q = mse
If the water equivalent = W
Q = W x 1 x q
W x 1 x q = mse (OR) W = ms grams
Water equivalent is numerically equal to the thermal capacity but the unit of water equivalent is gram and that of thermal capacity is calorie.
Change of State
A substance can exit three states viz. Solid, Liquid and Gas. The particular state of a substance depends on its temperature. According to the kinetic theory, the molecules of a substance in the solid state have less degree of freedom than a substance in the liquid or gaseous state. The molecules are more free to move in the gaseous state. The change in state can be brought about by supplying or withdrawing heat from the substance. Ice is the solid state of water. By supplying heat to ice, it can be changed into water. Similarly by supplying heat to water, it can be converted into the gaseous state (steam). This is true for all substances. Even permanent gases like oxygen, nitrogen, hydrogen etc can be liquefied at low temperatures.
For a given substance the change of state takes place at a fixed temperature and pressure. When the substance changes from the solid to the liquid state, the heat supplied at the constant temperature (called melting point) is used to overcoming the forces of intermolecular attraction. The mean molecular distance increases and the molecules from the liquid to the gaseous state at a fixed temperature (called the boiling point) and pressure. The heat supplied is used in increasing the mean molecular distance. The molecules become free to move about in the whole space available to them.
Latent Heat of Fusion
Take small pieces of ice in a beaker. Fix a thermometer to note the temperature of ice in the beaker. Heat the beaker slowly. Ice melts but the thermometer does not show any rise in temperature. When the whole of ice has melted the temperature of water rises and the thermometer indicates it. During the process of conversion from ice to water (change of state from solid to liquid) the heat supplied is used to change the state of ice from solid state to liquid state. This heat is called latent heat. Latent means hidden i.e.. Which is not indicated by the thermometer.
It has been found that one-gram of ice takes 80 calories of heat to get it converted to water. This heat is called latent heat of fusion of ice. Its unit is 'cal/gram'.
Latent heat of a substance is defined as the amount of heat required change the state of one gram of substance from solid to liquid without any change in its temperature.
Law of Fusion
(1) Every substance changes its state from solid to liquid at a particular temperature (under normal pressure) called the melting point.
(2) As long as the change of state takes place there is no change in temperature.
(3) One gram of every substance requires a definite quantity of heat for change of state from solid to liquid and it is called the latent heat of fusion of that substance. It is different for different substance.
(4) Some substances show increase in volume on melting e.g., wax, ghee, etc. While some other substances show decrease in volume on malting e.g., ice
(5) The melting point of those substance which decrease in volume on melting, is lowered with increase in pressure.
(6) The melting point of those substance which increase in volume on melting, is increased with increases in pressure.
Note
(1) Ice decreases in volume on melting and its melting point is lowered with increases in pressure.
(2) The melting point or solidification point is the same for a substance.
Laws of Boiling
(1) Every liquid changes its state from liquid to its vapour at a particular temperature (under normal pressure) called the boiling point.
(2) As long as the change of state takes place, there is no change in temperature.
(3) One gram of every liquid requires definite quantity of heat for change of state from liquid to vapour and it is called the latent heat of vaporization of that liquid. Latent heat is different for different substances.
(4) All liquids show increase in volume on vaporization.
(5) The boiling point of a liquid increase with increase in pressure of a liquid.
(6) The liquid can boil at a lower temperature under reduced pressure.
Latent Heat of Vaporization
The latent heat of vaporization of a liquid is the amount of heat required to convert one gram of the liquid into vapour without any change in temperature. For water, latent heat of vaporization is 537 cals/grm at a pressure of 75cm of Hg. Latent heat of vaporization is different for different substances.
Conduction Is the process in which heat is transmitted from one point to the other through the substance without the actual motion of the particles? When one end of a metal bar is heated, the molecules at the hot end vibrate with higher amplitude (kinetic energy) and transmit that heat energy from one particle to the next and so on. However the particles remain in their mean positions of equilibrium. (This process of conduction is prominent in the case of solids. The property of transmission of heat has been used in Davy's safety lamp. Materials having less conductivity e.g. granite, brick walls boiler etc. The space between the two walls of a thermos flask is evacuated because vacuum is a poor conductor of heat. The air enclosed in the woolen fabric helps in protecting us from cold because air is a poor conductor of heat.
Convection is the process in which heat is transmitted from one place to the other by the actual movement of the heated particles. It is prominent in the case of liquids and gases. Land and sea breezes, and trade winds are formed due to convection. Convection plays an important part in ventilation; gas filled electric lamps and heating of buildings by hot water
circulation.
Radiation is the process in which heat is transmitted from one place to the other directly without the necessity of the intervening medium. We get heat radiations directly from the sun without affecting the intervening medium. Heat radiation's can pass through vacuum. Their properties are similar to light radiations.
Examples
1. Find the value of absolute zero of the Fahrenheit scale.
F –32 = A –273
180 100
Here A = 0
F = -180 x 273 + 32
100
= -456.40F
2. There is a certain temperature which has the same reading on both centigrade and Fahrenheit thermometers. Find the temperature.
F -32 = A -273
180 100
Here F = C = x
\ x – 32 = x
180 100
(OR)
x –32 = 9/5x
\ x = -40
\-400C = -40 0F
3. A faulty thermometer has its fixed points marked 5 and 95. What is the correct temperature in centigrade when this thermometer records 59?
Let the reading on the centigrade thermometer be °c
C = R-L.F.P.
100 P.-L.F.P.
\ c = 59-5
100 95-5
c = 54
100 90
C = 600C
4. A certain mass of gas exerts a pressure of 72 cm of mercury at 2~C. It is heated at constant volume and the pressure observed after some time is 90cm of mercury. Calculate the temperature.
Here P1 = 72 cm of Hg P2 = 90cm of Hg
V1 = V V2 = V
T1 = 273 + 27 = 3000 A0 T 2 = ?
P2 v2 = p1 v1 (OR) 90v = 72v
T2 T1 T2 300
T2 = 90 x 300 = 3750A = 020c
72
5. Calculate how much steam from water boiling at 100 0C will just m 200gm of wax at 15°C. (Melting point of wax = 550C, S.P. Latent heat of fusion of x = 35 cal/gm)
Suppose mass of steam = m
Mass of wax = 200gm
Sp. Heat of wax = 0.7
Latent heat of wax = 35 cal/gm
Initial temperature of wax = 150C
Melting point of wax = 550C
Heat required to rise the temperature of wax from 150C to550C
= 200 x 0.7 x (55 -15) = 5600 cal
Heat required to melt wax at 550C = 200 x 35 = 7000 cal
Total heat gained by wax = 5600 + 7000 = 12,600 cal
Heat lost by steam = m x 540 + m (100- 55)
= 540m + 45m = 585m
Heat lost = Heat gained
585m = 12,600
m = 21.54gm
6. How much ice at 00C would a kilogram of steam at 1000C melts, if the resulting water is at 00C ? Latent heat of ice = 80cal/gm and latent heat of steam = 536 cal/gm.
Mass of ice = M gm
Mass of steam = 1 kg = 1000 gm
Temper of stem = 1000 C
Final temp = 00C
Heat gained by ice = M x 80 cal
Heat lost by ice steam = 1000 x 536 + 1000 x 100
= 636000cal
Heat gained = Heat lost
80 M = 636000
M = 7950 gm
= 7.95kg
7. A piece of metal weighing 60 gm at 100C was immersed in a current of steam 1000C . Calculate the amount of steam condensed. Specific heat of the metal is 0.1 cal/gm - 0C and latent heat of steam is 540 cal/gm.
M = 60gm
S = 0.1 cal/gm - 0C
T1 = 100C
T2 = 100°C
Heat taken by the metal = MS(T 1 -T 2)
= 60 x 0.1 (100 -10)
= 540 cal.
Suppose the mass of steam condensed = m grams
Latent heat of steam,
L = 540cal/gm .
\Heat lost by steam,
m L = m x 540
Heat gained = Heat lost
540 = 540m
\m = 1 gm
(OR) Hence, the mass of steam condensed = 1 gram.
8. An electric heater rod is dipped in a vessel containing water at 00C. The electric rod produces heat at the rate of 3000J/s. The vessel with its contents is maintained at 00 C by adding ice at the rate of 9 g/s. Calculate the specific latent heat of fusion of ice. If the total heat capacity of the water, the vessel and its contents is 12000j/K, at what rate does the temperature start rising when the supply of ice is stopped.
(1) Here H = 3000J/s
m = 9 g/s = 9 x 10-3 kg/ s
H = mL
L = H/m
L = 3000
9 X 10 -3
L = 3.33 x105 J/Kg.
(2) When the supply of ice is stopped, let the rate of rise of temperature be q k/s
w = 12000J/Kg
H = 3000 J/s
H = Wq
q = H/W
q = 3000
12000
q = 0. 25Kg/s.
9. lt is found that 65,45,000 cal of heat are transmitted per minute across a sheet of silver 10cm square and 1 mm thick, with a difference of temperature between its faces 1100C. Find the coefficient of thermal conductivity of silver.
Q = 65,45,000 cal, time t=1 min = 60sec
Each side of the square = 10cm
\Area of cross-section
A = 1 mm = 1/10cm, q1 -q2 = 1100C
Q = kA(q1 -q2 ) t
D
(OR)
K = Q x d = 65,45,000 x 1
A (q1 -q2)t 10 x 100 x 110 x 60
= 0.99
10. Estimate the rate at which ice would melt in a wooden box 2cm thick and of inside measurements 100 x 60 x 60 cm. Assuming that the external temperature, is 30oC and K for wood = 0.0004.
Thickness of the box = d = 2cm
q1 = 300c
q2 = 00c
(q1-q2) = 300c
Surface area of the box
A = 2 x 100 x 60 + 2 x 60 x 60 + 2 x 100 x 60
= 31200 sq cm
Q = kA(q1 -q2 ) t
D
= 0.0004 x 31200 x 30 x 1
2
= 187.2 cal
Suppose the amount of ice melted = m grams
Q = 80 m
M = 2.34 grams
11. The height of Niagra falls is 50 meters. Calculate the difference between the temperature of water at the top and the bottom of the falls. (J=4.2 x 107 ergs/cal) h = 50meters = 5000 ergs
suppose difference of temperature = o C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x e calories W = JH
suppose difference of temperature = u C = ? Mass of water = m
Work done (W) = mgh = m x 980 x 5000ergs
Heat produced (H) = mSe = m x 1 x q calories
W = JH
M x 980 x 5 000 = 4.2x107 x m x q
q = 980 x 5000
42 x107
12. A 12kg mass falls through 23mm on to the ground and bounces to a height of 0.50.? Assuming that all the potential energy to is used in heating up the mass, 'calculate the temperature rise. Take specific heat capacity of the material as 600 joules/kg0C and the force of gravity on 1kg = 10 Newton.
M = 12kg
S = 600joules/kg -0C
h1 = 23mm
q = ?
h2 = 0.50 mm
g = 10 m/s2 (given)
Loss in potential energy = Mg (h1 – h2)
= 12 x 10(23- 0.50)
= 2700joules
= Msq
= 2700joules
\q = 2700 = 0. 375 0C.
12x600
Eg.13. Convert 50°C into Farenheit and 68°F into Centigrade. (HMT -1995)
Eg.14. Why is better to wear dark clothes in winter and bright clothes in summer. (HMT -1995)
Eg.15.A man has a temperature of 99.8° F what will be the thermometer shows if it measures temperature in degrees Celsius? (HMT-1994)
Eg.16. A measuring unit of power
Eg.17. The velocity of light is
(a) 313 m/sec (b) 330 m/s (c) 303 m/s (d). none Of these
UNITS AND MEASUREMENTS
Units and Standards
In making a measurement of any physical quantity, some definite and convenient quantity of the same kind is taken as the standard, in terms of which the quantity as a whole is expressed. The conventional quantity used as the standard of measurement is called a unit. The unit of area is the area of a square each side of which is of unit length. Two Important Systems of Fundamental Units are there. They are
(1) The C. G. S. System (Metric System)
(2) The F.P.S. System (British System)
In the C.G.S. system C stands for 'Centimetre (cm.)' as the unit of length, G for 'Gram (gm.) as the unit of mass, and S for "Second (sec.) as the unit of time.
In the F. P.S. system, F stands for 'Foot (ft.)' as the unit of length, P for 'Pound (lb.)' as the unit of mass, and S for 'Second (sec.) as the unit of time.
In MKS System M stands for meter, K stands for kilogram, S stands for second.
SI: In this system there are seven fundamental quantities which are as shown below:-
Ser
No
Physical quantity
Name
symbol
1.
Length
Meter
M
2.
Mass
Kilogram
Kg
3.
Time
Second
Sec
4.
Temperature
Kelvin
K
5.
Luminous Intensity
Candle
Cd
6.
Electric current
Ampere
A
7.
Amount of substance
Mole
mol
Speed
The rate of change of position a body irrespective of direction is called Speed.
Speed = Distance traveled = s meters
Time taken t seconds
= s/t m/sec
Speed is a scalar quantity i.e., it has magnitude only.
Velocity
The rate of change of position of a body in a particular direction is called velocity. It is measured by the distance covered in a particular direction per unit time measures it.
Velocity = Distance covered (in particular direction)
Time
\V = s meters = s m/s
T seconds t
Velocity is a vector quantity i.e., it posses both magnitude and direction.
Uniform Velocity
If a body covers equal distances, in a particular direction, in equal intervals of time, however small, it is said to move with uniform velocity.
Consider a truck moving along Delhi Road. This truck is covering equal distances (5 meters) in equal intervals of time (sys, 1 second) in the same direction. Therefore truck is moving with a uniform velocity. In this case, velocity of truck. = 5m/1s = 5ms-1
Variable Velocity
If a body covers unequal distances in a particular direction, in equal intervals of time however small, it is said to move with a variable velocity.
It should be noted that even if a body covers equal distances in equal intervals of time, but changes its direction, it is said to possess variable velocity.
Average Velocity
The average velocity of moving body during a given interval of time is measured by the total distance traveled divided by total time taken.
Average velocity = Total distance traveled
Total time taken
Acceleration
The rate of change of velocity is called acceleration. change of velocity per unit time.
Acceleration = Change in velocity (OR) a = v - u
Time t
Where a = Acceleration of body
u = Initial velocity
v = Final velocity
t = Time taken for the velocity to change from u to v.
Acceleration has magnitude as well as direction; therefore it is a vector quantity.
Newton's First Law of Motion.
" If a body is at rest, it will continue to remain at rest until it is acted upon by some external agency. "
Force.
It is defined as that external agency that changes or tends to change the state of rest or of uniform motion of a body in a straight line.
The first law of motion is also called the "Law of Inertia" inertia is the inability of a material body to change by itself its state of rest or of uniform motion in a straight line.
Newton's Second Law of Motion.
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.
Momentum.
It is the quantity of motion of a body. It is the product of mass and velocity. It is a vector quantity.
Momentum = mass x velocity. The units of momentum are:(1) In C.G.S. units, g-cm/s (2) In rationalized units, kg-m/s.
Newton's Third Law of Motion.
According to Newton's third law of motion, to every action there is always an equal and opposite reaction.
Centrifugal Force.
Centrifugal force. When a body is rotating on a circular path, it has a tendency to move along a tangent. If a body A leaves the circular; path at any instant, for an observer B who is not sharing the motion along the circular path (i.e., a body B standing outside the reference circle), the body A appears to fly off tangentially at the point of release. For an observer C, who is sharing the same circular motion as that of the body A, the body A appears to be at rest before it is released. According to C, when A is released, it appears to fly off radically away from the center. It appears to the body C as if the body A has been thrown off along the radius away from the center by some force. This inertia force is known as centrifugal force'. Its magnitude is mv2/r. It is not a force of reaction. Centrifugal force is a fictitious force and holds good in rotating frame of reference.
When a car is turning round a corner, the persons sitting inside the car experience an outward force. This is due to the fact that the passengers provide no centripetal force.
Applications
1.Sugar crystals are separated from molasses with the help of a centrifuge.
2.ln cream separators, when the vessel containing the milk is rotated at high speed, the lighter cream particles collect around the axis of rotation while the skimmed milk moves away from the axis.
3. In drying machines, the wet clothes are rotated at high speed. The water particles fly off tangentially through the holes in the wall of the outer vessel.
4.Honey is also separated from bees wax with the help of a centrifuge.
5. Analysis of blood samples.
Centripetal Force
It is defined as the force, which acts towards the center along the radius of a circular path on which the body is moving with a uniform velocity.
Work
The term 'work' by itself does not convey any meaning in physics. Work is either done on a body or by a body. Therefore the complete term is
(I) Work done on a body
(II) Work done by a body.
In everyday life the term work is attributed to numerous acts eg: lifting a load, going up a hill, coming down the hill, stopping a moving ball, bullet hitting a target etc.
Work done is equal to the product of the force and distance moved by the body along the direction of the force.
W=F x S
Units of Work
W = F x S = Force x distance,
MKS. UNITS Work is Joule
CGS .UNITS Work is ergs.
Power
Power is defined as the rate of doing work.
Power = work done I Time
Units of power = watt in MKS
= ergs/s in CGS , =HP in FPS.
Energy
Energy of a body is defined as its capacity to do work. In physics there are many forms of energy e.g. heat, light, sound, magnetic, electric, potential etc, In mechanics we are mainly concerned with the two forms of energy of a body viz. Kinetic energy and potential energy.
Kinetic Energy
It is energy possessed by a moving body
Magnitude of Kinetic Energy
Consider a body of mass M moving with a velocity v. A retarding force F is applied on the body to bring it to rest. Let the body move a distance S before coming to rest and the retardation be a.
o –V2 = 2(-a)S
\ a = v2
2s
Retardation force = Ma = Mv2
2s
Kinetic energy = ½ M v2
Potential Energy
It is the mechanical energy possessed by a body due to its position or distortion. At the ground level, the potential energy of a body is zero. Suppose there is a body of mass M at a height h above the ground.
This body can do work = Mg x h when allowed to fall freely. Therefore its capacity to do work = Mgh and its potential energy = Mgh.
A compressed spring and stretched wire have potential energy spring in a watch after winding possesses potential energy. Any body subjected to deforming forces possesses potential energy.
Unit of Energy
Energy has the same units as that of work.
Law of Conservation of Energy
The total energy of a body remains constant. Only one form of energy changes into another form.
Potential Energy + kinetic Energy = Constant.
Simple Machines
In modern age, in every instrument or mechanism, we come across some simple devices. These devices are levers, pulleys, screw jack, wedge, inclined plane etc. These devices are called simple machines. If a tyre of a car is to be replaced, the screw jack is used to lift the car. Loading of trucks and goods wagons is done. with a plank serving as an inclined plane. Scissors, pair of tongs, forceps, punching machine etc., work on the principle of levers. Knife works on the principle of a wedge.
Simple machines are those where the effort is applied at a more convenient point in a more convenient direction.
Principle of Work
Whenever effort is applied on a machine and the point of application moves through a certain distance, work is said to be done on the machine. This work done on the machine is called input. The load or resistance overcome is moved through a certain distance and the machine does this work. Work done by the machine is called output. In an actual machine, there is always some loss of energy due to friction etc. Therefore the output is always less than the input. According to the principle of work, in a perfect machine.
Output = Input
Mechanical advantage
It is defined as the rate of resistance overcome to the effort applied.
MA = w = Resistance overcome
p Effort applied
Velocity ratio:
It is defined as the ratio of the distance moved by the effort applied to the distance moved by the resistance overcome,
VR = D/d = Distance moved by the effort
Distance moved by the resistance overcome
Efficiency It is defined as the ratio of output to input.
Output = W x d
Input = p x D
Efficiency h = Output = W x d = W/P = MA
Input P x D/d VR
\Efficiency = Mechanical Advantage
Velocity Ration
Mechanical advantage = efficiency x velocity ratio,
MA is a ratio of two forces,
VR is a ratio of two distances,
"h" is a ratio of two works done by the machine and on the machine.
In a perfect machine,
Output = Input and h = 1
\ Mechanical advantage = Velocity ratio
Lever
Lever is a rigid bar, which is capable of rotating about a fixed point called the fulcrum. The perpendicular distance between the fulcrum and the direction in which the effort is applied is called the power arm or effort arm. The perpendicular distance between the fulcrum and the direction of the load or resistance overcome or weight overcome is called the weight arm or the resistance arm.
Consider a lever AB, capable of a rotating about the fulcrum F . effort applied. If the lever is in equilibrium, p x BF = W x AF (OR)
Effort x effort arm = Load x arm
There are three types of levers. They are
(1) Class I Levers Here the fulcrum F is in between load Wand effort P.
According to the principle of lever,
P x a = w x b
W/P = a/b
(1) a>b, p will be less than W, Mechanical advantage is greater than 1.
(2) If a = b, p = W Mechanical advantage is equal to 1.
(3) If a
(2) Class II Levers
Here load W is in between the fulcrum F and the effort p, p
AF = a and BF = b
According to the principle of lever,
P x a = w x b
W/P = a/b
Here a is always greater than b. Therefore, less effort is applied to overcome a heavy load. The Mechanical advantage is always greater than 1.
(3) Class III Lever
Here effort p is in between the fulcrum F and the load W.
AF = a and BF = b
According to the principle of lever ,
W/P =a/b
Here a is always less than b. Therefore, more effort has to be applied to overcome a small load the mechanical advantage is always less than 1.
Ex:- Fire tongs, fore arm used for lifting load on the palm, forceps in the weight box and fishing rod.
Note:- The three types of levers can be remembered as follows:
FWP in levers three Must each in turn, the center be.
It means that, in class I levers F is in the middle, in class II levers, W is in the middle and in class III levers, p is in the middle.
Eg.1. A stone is thrown vertically upwards with a velocity of 24.5 m/s (1) calculate the highest height which it rises. (2)Calculate also the time it takes to reach the highest point.
u = 24.5 m/s. v=o, h=? , g=-9.8 m/s2.
V2-U2 = 2as. 0- 24.52=2.(-9.81 ).h, h= 30.625 m.
(2), v= u + at, t = 24.5/9.8 = 2.5 sec.
Eg.2. A body is thrown vertically upwards and rises to a height of 10 meters Calculate (1 ) the velocity with which the body was thrown upward and (2) the time it takes to reach the highest point.
u =?, v= 0, h =10 m,
g= -9.8 m/s2. V2-U2 = 2as, 0- (u)2=2.(-9.81 ).10,
u = 14 m/sec. 2.v= u- gt, t= 14/9.8 =1.43 sec.
Eg.3. A projectile weight 45 kg is fired from a gun weight 8000 kg with velocity of 500m/s . Find the velocity of recoil of the gun?
Here m=200 kg, M=8000 kg, u=500 m/sec,
v=? MV = m v, V = m v/M = 12.5 m/sec,
Eg.4. A motor car of mass 25 quintals is moving with a velocity of 36 kmph. By application of breaks it is brought to rest in a distance of 25 mtrs. Find the average force of resistance in newton.
M =25 quintals = 2500 kg,
u= 36 kmph, u= 10 m/sec, s= 25 mtr,
v=o, F= ? V2-U2 = 2as.
0 – 102=2.(a).h, a= -2 m/sec2, Force of resistance,
F= ma. = 2500 x 2 = 5000N.
Eg.5 Physical quantities, formulas and units.
Sr.No
Physical quantity
Formula
Units
1.
Velocity
Displacement
m/sec.
2.
Acceleration
Velocity/time
m/sec2,
3.
Force
Mass x acceleration
kg or Newton
4.
Work
Force x distance
kg-m
5.
Power
Work / time
kg-m/sec.
6.
Pressure
Force/ area
kg/m2.
7.
Stress
Force/ area
kg/m2
8.
Moment
Force x distance
kg-m.
9.
Torque
Force x distance
kg-m.
10.
Couple
Force x distance
kg-m.
11.
Effort
Force
kg.
12.
Energy
Capacity to do work
kg-m
Eg.6. What is the work done by a man in carrying a suitcase weight 30 kg over head when he travels a distance of 1 in (1) vertically and (2). Horizontal direction.
(1) Distance moved in vertical direction = 10 m.
Work done = mgh = 30 x 9.8 x 10 = 2940 Joules.
(2). Since a force has no component at right angles to it, therefore, component of mgh in the horizontal direction = F = mg cos90°=0,
Eg. 7 .A man whose mass is 60 kg walks up to the top of building whose height is 15 m above the street level?
(1) How many joules of work has he done.
(2) What is the increase in his potential energy,
m= 60 kg, g= -9.8 m/.sec2.
(1) work done = 60 x 9.8 x 15 joules.
(2). Increase in p .E = work done = 60 x 9.8 x 15 =8820 Joules.
Eg.8. The value of "g" is maximum at (HMT 1993)
(a) At earth's surface (b), At earth center (c) At hill top (d) At hill top
Eg.9. If a ball thrown up, the highest point will be______________
Eg.10.0ne HP is equal to _______________ watts
Eg.11. Length, mass, time, are ________________
Eg.12. Static friction is always less than the dynamic friction (T/F)
Units and Standards
In making a measurement of any physical quantity, some definite and convenient quantity of the same kind is taken as the standard, in terms of which the quantity as a whole is expressed. The conventional quantity used as the standard of measurement is called a unit. The unit of area is the area of a square each side of which is of unit length. Two Important Systems of Fundamental Units are there. They are
(1) The C. G. S. System (Metric System)
(2) The F.P.S. System (British System)
In the C.G.S. system C stands for 'Centimetre (cm.)' as the unit of length, G for 'Gram (gm.) as the unit of mass, and S for "Second (sec.) as the unit of time.
In the F. P.S. system, F stands for 'Foot (ft.)' as the unit of length, P for 'Pound (lb.)' as the unit of mass, and S for 'Second (sec.) as the unit of time.
In MKS System M stands for meter, K stands for kilogram, S stands for second.
SI: In this system there are seven fundamental quantities which are as shown below:-
Ser
No
Physical quantity
Name
symbol
1.
Length
Meter
M
2.
Mass
Kilogram
Kg
3.
Time
Second
Sec
4.
Temperature
Kelvin
K
5.
Luminous Intensity
Candle
Cd
6.
Electric current
Ampere
A
7.
Amount of substance
Mole
mol
Speed
The rate of change of position a body irrespective of direction is called Speed.
Speed = Distance traveled = s meters
Time taken t seconds
= s/t m/sec
Speed is a scalar quantity i.e., it has magnitude only.
Velocity
The rate of change of position of a body in a particular direction is called velocity. It is measured by the distance covered in a particular direction per unit time measures it.
Velocity = Distance covered (in particular direction)
Time
\V = s meters = s m/s
T seconds t
Velocity is a vector quantity i.e., it posses both magnitude and direction.
Uniform Velocity
If a body covers equal distances, in a particular direction, in equal intervals of time, however small, it is said to move with uniform velocity.
Consider a truck moving along Delhi Road. This truck is covering equal distances (5 meters) in equal intervals of time (sys, 1 second) in the same direction. Therefore truck is moving with a uniform velocity. In this case, velocity of truck. = 5m/1s = 5ms-1
Variable Velocity
If a body covers unequal distances in a particular direction, in equal intervals of time however small, it is said to move with a variable velocity.
It should be noted that even if a body covers equal distances in equal intervals of time, but changes its direction, it is said to possess variable velocity.
Average Velocity
The average velocity of moving body during a given interval of time is measured by the total distance traveled divided by total time taken.
Average velocity = Total distance traveled
Total time taken
Acceleration
The rate of change of velocity is called acceleration. change of velocity per unit time.
Acceleration = Change in velocity (OR) a = v - u
Time t
Where a = Acceleration of body
u = Initial velocity
v = Final velocity
t = Time taken for the velocity to change from u to v.
Acceleration has magnitude as well as direction; therefore it is a vector quantity.
Newton's First Law of Motion.
" If a body is at rest, it will continue to remain at rest until it is acted upon by some external agency. "
Force.
It is defined as that external agency that changes or tends to change the state of rest or of uniform motion of a body in a straight line.
The first law of motion is also called the "Law of Inertia" inertia is the inability of a material body to change by itself its state of rest or of uniform motion in a straight line.
Newton's Second Law of Motion.
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction of the force.
Momentum.
It is the quantity of motion of a body. It is the product of mass and velocity. It is a vector quantity.
Momentum = mass x velocity. The units of momentum are:(1) In C.G.S. units, g-cm/s (2) In rationalized units, kg-m/s.
Newton's Third Law of Motion.
According to Newton's third law of motion, to every action there is always an equal and opposite reaction.
Centrifugal Force.
Centrifugal force. When a body is rotating on a circular path, it has a tendency to move along a tangent. If a body A leaves the circular; path at any instant, for an observer B who is not sharing the motion along the circular path (i.e., a body B standing outside the reference circle), the body A appears to fly off tangentially at the point of release. For an observer C, who is sharing the same circular motion as that of the body A, the body A appears to be at rest before it is released. According to C, when A is released, it appears to fly off radically away from the center. It appears to the body C as if the body A has been thrown off along the radius away from the center by some force. This inertia force is known as centrifugal force'. Its magnitude is mv2/r. It is not a force of reaction. Centrifugal force is a fictitious force and holds good in rotating frame of reference.
When a car is turning round a corner, the persons sitting inside the car experience an outward force. This is due to the fact that the passengers provide no centripetal force.
Applications
1.Sugar crystals are separated from molasses with the help of a centrifuge.
2.ln cream separators, when the vessel containing the milk is rotated at high speed, the lighter cream particles collect around the axis of rotation while the skimmed milk moves away from the axis.
3. In drying machines, the wet clothes are rotated at high speed. The water particles fly off tangentially through the holes in the wall of the outer vessel.
4.Honey is also separated from bees wax with the help of a centrifuge.
5. Analysis of blood samples.
Centripetal Force
It is defined as the force, which acts towards the center along the radius of a circular path on which the body is moving with a uniform velocity.
Work
The term 'work' by itself does not convey any meaning in physics. Work is either done on a body or by a body. Therefore the complete term is
(I) Work done on a body
(II) Work done by a body.
In everyday life the term work is attributed to numerous acts eg: lifting a load, going up a hill, coming down the hill, stopping a moving ball, bullet hitting a target etc.
Work done is equal to the product of the force and distance moved by the body along the direction of the force.
W=F x S
Units of Work
W = F x S = Force x distance,
MKS. UNITS Work is Joule
CGS .UNITS Work is ergs.
Power
Power is defined as the rate of doing work.
Power = work done I Time
Units of power = watt in MKS
= ergs/s in CGS , =HP in FPS.
Energy
Energy of a body is defined as its capacity to do work. In physics there are many forms of energy e.g. heat, light, sound, magnetic, electric, potential etc, In mechanics we are mainly concerned with the two forms of energy of a body viz. Kinetic energy and potential energy.
Kinetic Energy
It is energy possessed by a moving body
Magnitude of Kinetic Energy
Consider a body of mass M moving with a velocity v. A retarding force F is applied on the body to bring it to rest. Let the body move a distance S before coming to rest and the retardation be a.
o –V2 = 2(-a)S
\ a = v2
2s
Retardation force = Ma = Mv2
2s
Kinetic energy = ½ M v2
Potential Energy
It is the mechanical energy possessed by a body due to its position or distortion. At the ground level, the potential energy of a body is zero. Suppose there is a body of mass M at a height h above the ground.
This body can do work = Mg x h when allowed to fall freely. Therefore its capacity to do work = Mgh and its potential energy = Mgh.
A compressed spring and stretched wire have potential energy spring in a watch after winding possesses potential energy. Any body subjected to deforming forces possesses potential energy.
Unit of Energy
Energy has the same units as that of work.
Law of Conservation of Energy
The total energy of a body remains constant. Only one form of energy changes into another form.
Potential Energy + kinetic Energy = Constant.
Simple Machines
In modern age, in every instrument or mechanism, we come across some simple devices. These devices are levers, pulleys, screw jack, wedge, inclined plane etc. These devices are called simple machines. If a tyre of a car is to be replaced, the screw jack is used to lift the car. Loading of trucks and goods wagons is done. with a plank serving as an inclined plane. Scissors, pair of tongs, forceps, punching machine etc., work on the principle of levers. Knife works on the principle of a wedge.
Simple machines are those where the effort is applied at a more convenient point in a more convenient direction.
Principle of Work
Whenever effort is applied on a machine and the point of application moves through a certain distance, work is said to be done on the machine. This work done on the machine is called input. The load or resistance overcome is moved through a certain distance and the machine does this work. Work done by the machine is called output. In an actual machine, there is always some loss of energy due to friction etc. Therefore the output is always less than the input. According to the principle of work, in a perfect machine.
Output = Input
Mechanical advantage
It is defined as the rate of resistance overcome to the effort applied.
MA = w = Resistance overcome
p Effort applied
Velocity ratio:
It is defined as the ratio of the distance moved by the effort applied to the distance moved by the resistance overcome,
VR = D/d = Distance moved by the effort
Distance moved by the resistance overcome
Efficiency It is defined as the ratio of output to input.
Output = W x d
Input = p x D
Efficiency h = Output = W x d = W/P = MA
Input P x D/d VR
\Efficiency = Mechanical Advantage
Velocity Ration
Mechanical advantage = efficiency x velocity ratio,
MA is a ratio of two forces,
VR is a ratio of two distances,
"h" is a ratio of two works done by the machine and on the machine.
In a perfect machine,
Output = Input and h = 1
\ Mechanical advantage = Velocity ratio
Lever
Lever is a rigid bar, which is capable of rotating about a fixed point called the fulcrum. The perpendicular distance between the fulcrum and the direction in which the effort is applied is called the power arm or effort arm. The perpendicular distance between the fulcrum and the direction of the load or resistance overcome or weight overcome is called the weight arm or the resistance arm.
Consider a lever AB, capable of a rotating about the fulcrum F . effort applied. If the lever is in equilibrium, p x BF = W x AF (OR)
Effort x effort arm = Load x arm
There are three types of levers. They are
(1) Class I Levers Here the fulcrum F is in between load Wand effort P.
According to the principle of lever,
P x a = w x b
W/P = a/b
(1) a>b, p will be less than W, Mechanical advantage is greater than 1.
(2) If a = b, p = W Mechanical advantage is equal to 1.
(3) If a
(2) Class II Levers
Here load W is in between the fulcrum F and the effort p, p
AF = a and BF = b
According to the principle of lever,
P x a = w x b
W/P = a/b
Here a is always greater than b. Therefore, less effort is applied to overcome a heavy load. The Mechanical advantage is always greater than 1.
(3) Class III Lever
Here effort p is in between the fulcrum F and the load W.
AF = a and BF = b
According to the principle of lever ,
W/P =a/b
Here a is always less than b. Therefore, more effort has to be applied to overcome a small load the mechanical advantage is always less than 1.
Ex:- Fire tongs, fore arm used for lifting load on the palm, forceps in the weight box and fishing rod.
Note:- The three types of levers can be remembered as follows:
FWP in levers three Must each in turn, the center be.
It means that, in class I levers F is in the middle, in class II levers, W is in the middle and in class III levers, p is in the middle.
Eg.1. A stone is thrown vertically upwards with a velocity of 24.5 m/s (1) calculate the highest height which it rises. (2)Calculate also the time it takes to reach the highest point.
u = 24.5 m/s. v=o, h=? , g=-9.8 m/s2.
V2-U2 = 2as. 0- 24.52=2.(-9.81 ).h, h= 30.625 m.
(2), v= u + at, t = 24.5/9.8 = 2.5 sec.
Eg.2. A body is thrown vertically upwards and rises to a height of 10 meters Calculate (1 ) the velocity with which the body was thrown upward and (2) the time it takes to reach the highest point.
u =?, v= 0, h =10 m,
g= -9.8 m/s2. V2-U2 = 2as, 0- (u)2=2.(-9.81 ).10,
u = 14 m/sec. 2.v= u- gt, t= 14/9.8 =1.43 sec.
Eg.3. A projectile weight 45 kg is fired from a gun weight 8000 kg with velocity of 500m/s . Find the velocity of recoil of the gun?
Here m=200 kg, M=8000 kg, u=500 m/sec,
v=? MV = m v, V = m v/M = 12.5 m/sec,
Eg.4. A motor car of mass 25 quintals is moving with a velocity of 36 kmph. By application of breaks it is brought to rest in a distance of 25 mtrs. Find the average force of resistance in newton.
M =25 quintals = 2500 kg,
u= 36 kmph, u= 10 m/sec, s= 25 mtr,
v=o, F= ? V2-U2 = 2as.
0 – 102=2.(a).h, a= -2 m/sec2, Force of resistance,
F= ma. = 2500 x 2 = 5000N.
Eg.5 Physical quantities, formulas and units.
Sr.No
Physical quantity
Formula
Units
1.
Velocity
Displacement
m/sec.
2.
Acceleration
Velocity/time
m/sec2,
3.
Force
Mass x acceleration
kg or Newton
4.
Work
Force x distance
kg-m
5.
Power
Work / time
kg-m/sec.
6.
Pressure
Force/ area
kg/m2.
7.
Stress
Force/ area
kg/m2
8.
Moment
Force x distance
kg-m.
9.
Torque
Force x distance
kg-m.
10.
Couple
Force x distance
kg-m.
11.
Effort
Force
kg.
12.
Energy
Capacity to do work
kg-m
Eg.6. What is the work done by a man in carrying a suitcase weight 30 kg over head when he travels a distance of 1 in (1) vertically and (2). Horizontal direction.
(1) Distance moved in vertical direction = 10 m.
Work done = mgh = 30 x 9.8 x 10 = 2940 Joules.
(2). Since a force has no component at right angles to it, therefore, component of mgh in the horizontal direction = F = mg cos90°=0,
Eg. 7 .A man whose mass is 60 kg walks up to the top of building whose height is 15 m above the street level?
(1) How many joules of work has he done.
(2) What is the increase in his potential energy,
m= 60 kg, g= -9.8 m/.sec2.
(1) work done = 60 x 9.8 x 15 joules.
(2). Increase in p .E = work done = 60 x 9.8 x 15 =8820 Joules.
Eg.8. The value of "g" is maximum at (HMT 1993)
(a) At earth's surface (b), At earth center (c) At hill top (d) At hill top
Eg.9. If a ball thrown up, the highest point will be______________
Eg.10.0ne HP is equal to _______________ watts
Eg.11. Length, mass, time, are ________________
Eg.12. Static friction is always less than the dynamic friction (T/F)
Cooking
Cooking is an act of preparing food for eating. It encompasses a vast range of methods, tools and combinations of ingredients to improve the flavour or digestibility of food. It generally requires the selection, measurement and combining of ingredients in an ordered procedure in an effort to achieve the desired result. Constraints on success include the variability of ingredients, ambient conditions, tools and the skill of the individual cooking. The diversity of cooking worldwide is a reflection of the myriad nutritional, aesthetic, agricultural, economic, cultural and religious considerations that impact upon it. Cooking requires applying heat to a food which usually, though not always, chemically transforms it, thus changing its flavor, texture, appearance, and nutritional properties. Cooking proper, as opposed to roasting, requires the boiling of water in a receptacle, and was practiced at least since the 10th millennium BC with the introduction of pottery. There is archaeological evidence of roasted foodstuffs, both animal and vegetable, in human (Homo erectus) campsites dating from the earliest known use of fire some 800,000 years ago.[citation needed]
Cooking is an act of preparing food for eating. It encompasses a vast range of methods, tools and combinations of ingredients to improve the flavour or digestibility of food. It generally requires the selection, measurement and combining of ingredients in an ordered procedure in an effort to achieve the desired result. Constraints on success include the variability of ingredients, ambient conditions, tools and the skill of the individual cooking. The diversity of cooking worldwide is a reflection of the myriad nutritional, aesthetic, agricultural, economic, cultural and religious considerations that impact upon it. Cooking requires applying heat to a food which usually, though not always, chemically transforms it, thus changing its flavor, texture, appearance, and nutritional properties. Cooking proper, as opposed to roasting, requires the boiling of water in a receptacle, and was practiced at least since the 10th millennium BC with the introduction of pottery. There is archaeological evidence of roasted foodstuffs, both animal and vegetable, in human (Homo erectus) campsites dating from the earliest known use of fire some 800,000 years ago.[citation needed]
yogendra
Games
Card game, 1895.
A game is a structured or semi-structured recreational activity, usually undertaken for enjoyment (although sometimes for physical or vocational training). A goal that the players try to reach and a set of rules concerning what the players can or cannot do create the challenge and structure in a game, and are thus central to its definition. Known to have been played as far back as prehistoric times, games are generally distinct from work, which is usually carried out for remuneration. Because a wide variety of activities are enjoyable, numerous types of games have developed. What creates an enjoyable game varies from one individual to the next. Age, understanding (of the game), intelligence level, and (to some extent) personality are factors that determine what games a person enjoys. Depending on these factors, people vary the number and complexity of objectives, rules, challenges, and participants to increase their enjoyment. Games generally involve mental and/or physical stimulation. For this reason, they are beneficial after a large meal or a long and tedious task, but counterproductive if played immediately before sleeping.[citation needed] Many games help develop practical skills and serve as exercise or perform an educational, simulational or psychological role & also roaming.
Card game, 1895.
A game is a structured or semi-structured recreational activity, usually undertaken for enjoyment (although sometimes for physical or vocational training). A goal that the players try to reach and a set of rules concerning what the players can or cannot do create the challenge and structure in a game, and are thus central to its definition. Known to have been played as far back as prehistoric times, games are generally distinct from work, which is usually carried out for remuneration. Because a wide variety of activities are enjoyable, numerous types of games have developed. What creates an enjoyable game varies from one individual to the next. Age, understanding (of the game), intelligence level, and (to some extent) personality are factors that determine what games a person enjoys. Depending on these factors, people vary the number and complexity of objectives, rules, challenges, and participants to increase their enjoyment. Games generally involve mental and/or physical stimulation. For this reason, they are beneficial after a large meal or a long and tedious task, but counterproductive if played immediately before sleeping.[citation needed] Many games help develop practical skills and serve as exercise or perform an educational, simulational or psychological role & also roaming.
Kumar
New Delhi: As inflation has touched 8.75%, the highest level during the UPA regime, Finance Minister P Chidambaram today said the rate of price rise is high prompting the Reserve Bank of India (RBI) to tighten money supply.
"Inflation is high. RBI must take steps, and it has taken," Chidambaram told reporters after meeting the top brass of Central Bank of India.
This was the first statement from the Finance Minister after the Reserve Bank hiked its short-term lending rate by 0.25% to 8% putting pressure on interest rates.
Inflation has soared to 8.75% for the week ended May 31. It is set to cross the 9% mark when data is released on June 20.
The previous high during the UPA regime was 8.33% as per the provisional figure for the week ended August 28, 2004.
"Inflation is high. RBI must take steps, and it has taken," Chidambaram told reporters after meeting the top brass of Central Bank of India.
This was the first statement from the Finance Minister after the Reserve Bank hiked its short-term lending rate by 0.25% to 8% putting pressure on interest rates.
Inflation has soared to 8.75% for the week ended May 31. It is set to cross the 9% mark when data is released on June 20.
The previous high during the UPA regime was 8.33% as per the provisional figure for the week ended August 28, 2004.
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