NUMERICALS ON SIMPLE HARMONIC MOTION

1. A simple harmonic motion is represented by by    x = 10 sin (20t + 0.5), 

Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in in metres and time in seconds. 

2. A body oscillates with SHM according to the equation, 

x = (5.0 m) cos [(2π rad/s)t + π/4]

At t = 1.5 s, calculate (a) displacement, (b) speed and (c) acceleration of the body. 

3. The equation of a simple harmonic motion is given by , 

y = 6 sin 10π t + 8 cos 10π t, where y is in cm, and t in seconds. Determine the amplitude, period and initial phase. 

4. A body oscillates with SHM according to the equation :

x(t) = 5 cos (2 πt + π/4)

Where t is in second, and x in metres. Calculate, 

(a) displacement at t = 0

(b) time period, (c) initial velocity

5. A spring of force constant  800 N/m has an extension of 5 cm. What is the work done in increasing the extension from 5 to 15 cm?

6. A body executes SHM of time period 8 s. If its mass be 0.1 kg, its velocity 1 second after it passes through its mean position be 4 m/s, find its (i) kinetic energy (ii) potential energy and (iii) total energy. 

7. A particle is executing SHM of amplitude A. At what displacement from the mean position, is the energy half kinetic and half potential?

8. What is the length of a second pendulum? 

(A second pendulum is a pendulum with a time period of 2 s). 

LECTURE 1: CLASS 12: ATOMS

CLASS - X : ELECTRIC POWER AND HEATING EFFECT OF ELECTRIC CURRENT

LECTURE - 1: CLASS - X: MAGNETIC EFFECT OF ELECTRIC CURRENT

LECTURE - 1 : CLASS IX : SCIENCE : CHAPTER 4 : WORK AND ENERGY

WORK:

What is done when a force produces motion. 

The work done by a force on a body depends on two factors. 

(i) magnitude of the force, and

(ii) distance/displacement through which the body moves in the direction of force. 

Work done in moving a body is equal to the product of force exerted on the body and the distance/displacement moved by the body in the direction of the force.

Work = Force x distance/displacement moved the direction of force.

W = F x S

Unit of work

The SI unit of work is Joule.

1 joule of work= When a force of 1 Newton moves a body through a distance of 1 m in its own direction then the work done is known as 1 Joule. 

Work is a scalar quantity.

Work done against gravity

Whenever work is done against gravity, the amount of work done is equal to the product of weight of the body and the vertical distance through which the body is lifted. 

Work done in lifting a body = weight of body x vertical distance

W = m x g x h = mgh

W= work done, m= mass of the body, g = acceleration due to gravity, h = height through which the body is lifted. 

1. How much work is done by a force of 10 N in moving and objects through a distance of 1 m in the direction of force?

Soln. We know work done W = F x s

Here, F = 10 N , s = 1 m

So, Work done = 10 x 1 J = 10 J

2. Calculate the work done in lifting 200kg of water through a vertical height of 6 m (g = 10 m/s²).

Soln. We know work done against gravity, 

W = mgh

Here, mass of water, m = 200 kg

Acceleration due to gravity, g = 10 m/s²

And height, h = 6 m

W = 200 x 10 x 6 = 12000 J = 12 kJ

3. A car weighing 1000 kg and travelling at 30 m/s stops at a distance of 50 m decelerating uniformly. What is the force exerted on it by the brakes? What is the work done by the brakes?

WORK DONE BY A FORCE ACTING OBLIQUELY

When the movement of the body is at an angle to the direction of the applied force, then the work done in pulling the body will be equal to the horizontal component of the force (F cosθ) and the displacement of the body. 

W = F cosθ x s

F = applied force, 

θ= angle between the direction of force and the direction of motion, 

s = displacement. 

When the force acts at right angles to the direction of motion (zero work)

When the displacement of the body is perpendicular (at 90°) to the direction of force no work is done.

W = F cosθ x s  

θ = 90°  but cos 90° = 0

W = 0

To keep a body moving in a circle there must be a force acting on it is directed towards the centre this force is called centripetal force. The work done on a body moving in a circular path by the centripetal force is zero.

The work done in the case of earth moving around the sun is zero as well as the work done in the case of a satellite moving around the earth is also zero. 

Work done when the force acts opposite to the direction of motion (negative work)

If the angle between the direction of force and the direction of motion is 180° , then the work done is negative. 

As cos θ = cos 180° = - 1

W = F cos 180° x s = - F x s

Positive, Negative and Zero Work

The work done by a force can be positive, negative or zero. 

1. Work done is positive when a force acts in the direction of motion of the body.

2. Work done is negative and a force acts opposite to the direction of motion of the body.

3. Work done is zero when a force acts at right angles to the direction of motion of the body. 

Examples of positive, negative and zero work

1. We kick a football lying on the ground, then the football stars moving. Here,  we have the applied force in the direction of the motion of football. So the work done on the football in this case is positive.

2. A football moves on the ground slows down gradually and ultimately stops. This is because a force due to friction of the ground acts on the football. The force of friction acts in a direction opposite to the direction of motion of football. So in this case the work done by the force of friction on the football is negative.

3. The satellite move around the earth in a circular path. In this case, the gravitational force of earth acts on the satellite at right angles to the direction of motion of satellite. So the work done by the Earth on the satellite moving around it in circular path is zero.

ENERGY: The ability to do work is called energy. The amount of energy possessed by a body e is equal to the amount of work it can do to where its energy is released. Energy is a scalar quantity. 

UNIT OF ENERGY: The SI unit of energy is Joule (J). The energy required to do one joule of work is called 1 Joule of energy. 

1 kilo Joule (1 kJ) = 1000 J

DIFFERENT FORMS OF ENERGY:

The main forms of energy are

1. Kinetic energy, 2. Potential energy, 3. Chemical energy, 4. Heat energy, 5. Light energy, 6. Sound energy, 7. Electrical energy, 8. Solar energy, 9. Nuclear energy.

KINETIC ENERGY: The energy of a body due to its motion is called Kinetic energy. 

Formula for kinetic energy:

If a body of mass m starts to move from rest to a velocity v, then its kinetic energy is equals to 

K.E. = ½mv²

Proof of the kinetic energy:

If a body of mass m starts to move from rest to a velocity v, 

Work = Force x Displacement

W = F x s

But we know v² = u² + 2as

u = 0, v² = 2as => s = v²/2a

Again , F = ma

W = F x s = ma x v²/2a = ½mv²

*If the mass of a body is doubled, its kinetic energy also gets doubled. 

If the mass of a body is halved, is kinetic energy also gets halved. 

The velocity of a body is doubled, its kinetic energy becomes four times. If the velocity of a body is halved, then its kinetic energy becomes one fourth. 

As the kinetic energy of a body depends on its mass and velocity, therefore heavy bodies moving with high velocities have more kinetic energy. 

POTENTIAL ENERGY: 

The energy of a body due to its position or change in shape is known as potential energy. 

A body may possess energy even when it is not in motion due to its position or shape. 

The sum of the potential and kinetic energies of a body is called its mechanical energy. 

Formula for potential energy

Work done on a body against a force, is stored in the body as potential energy. 

Therefore, workdone on a body against gravitational force will be stored as the gravitational potential energy (U). 

Suppose a body of mass m has been raised to a height h from the ground against gravitational force. The workdone occurs against gravitational force equal to the weight of the body mg. 

Workdone, W = force x displacement

W = mg x h = mgh

POWER:

Power is defined as the rate of doing work. Therefore, power is equals to work done/time taken. 

If W work is done in t time, then power P = W/t

Hence, we can say power is equals to work done per unit time. 

When work is done, an equal amount of energy is consumed. Therefore, power can also be defined as the rate at which energy is consumed. Power is a scalar quantity. 

Q. Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work’.

A. Suma is swimming in a pond.

B. A donkey is carrying a load on its back.

C. A wind-mill is lifting water from a well.

D. A green plant is carrying out photosynthesis.

E. An engine is pulling a train.

F. Food grains are getting dried in the sun.

G. A sailboat is moving due to wind energy.

Answer:

A. Suma is swimming in a pond: - She is pushing the water in the backward direction, which is an action performed by her.

However, due to reaction, the water pushes her in the forward direction. Work is done by Suma.

B. A donkey is carrying a load on its back: - In this case, force of gravity on the load is acting in the downward direction, whereas the displacement will be in the horizontal direction i.e., the force and displacement are perpendicular to each other.

There is no displacement in the direction of the force of gravity, and therefore no is work done as there is no displacement.

C. A wind-mill is lifting water from a well: - The work is done by the wind mill in lifting the bucket of water from the well. The work is done against the force of gravity.

D. A green plant is carrying out photosynthesis: - No work done is done in this case. As both force and displacement are 0.

E. An engine is pulling a train: - In this case, an engine is pulling a train parallel to the ground.

The force exerted by the engine is in the direction of displacement of the train.

Thus, the force and displacement are in the same direction. Therefore, work is done.

F. Food grains are getting dried in the sun: - No work is done in this case as food grains remain at rest.

G. A sailboat is moving due to wind energy: - The force exerted by the wind on the sail move the boat in the direction of force, hence, positive work is done by wind energy

LECTURE - 2 : CLASS VIII : SCIENCE : CHAPTER 18 : POLLUTION OF AIR AND WATER

WATER POLLUTION: 

What is water pollution?

The contamination of water of rivers, lakes and ponds etc with unwanted and harmful substances is called water pollution. 

What are water pollutants?

The unwanted and harmful substances which make the water contaminated are called water pollutants.

Major water pollutants:

The major pollutants which cause water pollution are sewage, fertilizers, pesticides and industrial wastes. Hot water from power plants and industries is also considered a pollutant.

Sources of water pollution:

There are several sources of water pollution. They are as follows.

1. Dumping of untreated sewage into rivers causes water pollution.

2. Use of fertilizers in agriculture causes water pollution.

3. Use of pesticides in agriculture causes water pollution.

4. Discharging of untreated industrial wastes into rivers and lakes causes water pollution.

Harmful effects of common pollutants

1. Untreated sewage from homes

The waste water containing human excreta and carried in sewers or underground pipes is called sewage. Sewage contains several harmful microorganisms such as bacteria, protozoa, fungi, viruses and parasites which cause serious diseases in humans. The drinking of river water contaminated with can cause water borne diseases such as typhoid diarrhoea dysentery and jaundice.

2. Fertilisers used in agriculture

The water pollution caused by fertilizers used in agriculture decreases the amount of dissolved oxygen in water bodies and leads to the death of fish and other aquatic animals. 

3. Pesticides used in agriculture

The farmers use toxic chemicals called pesticides on standing crops in the fields to protect them from pests and diseases. Some of these pesticides dissolve in rain water and run into rivers, lakes and ponds and pollute their water. This poisonous pesticides kill the aquatic animals like fish. The non biodegradable pesticides in the polluted water are absorbed by aquatic plants. This aquatic plants are then eaten by aquatic animals like fish. During this pesticides are transferred from aquatic plants to fish and when a person eats the fish grown in this polluted water the pesticides present in the fish enter his body and damage his health.

4. Untreated industrial wastes

The toxic chemicals present in industrial wastes are the compounds of harmful metals such as Mercury, lead, arsenic, nickle and cadmium. The water of rivers and lakes polluted with toxic industrial waste can kill fish and other aquatic animals which live in this river or lake. The toxic metal compounds present in this polluted water can enter the human body through the food chain like eating fish grown in this polluted water. They can damage our nervous system and cause diseases such as blood poisoning and cancer.

Harmful effects of water pollution

The various harmful effects of water pollution are as follows.

1. Drinking of water polluted with untreated sewage can cause diseases such as Cholera, Typhoid, Diarrhoea, Dysentery and Jaundice.

2. Water of rivers and lakes polluted with fertilizers can cause the death of aquatic animals like fish.

3. Water of rivers and lakes polluted with pesticides can kill aquatic animals like fish and also damage our health through food chain.

4. Water of rivers and lakes polluted with toxic industrial waste kills the aquatic animals like fish damages our nervous system and causes diseases such as blood poisoning and cancer.

Controlling water pollution

The various ways of controlling our minimising water pollution are as follows.

1. Sewage should be treated properly at sewage treatment plants to make it harmless before discharging it into nearby rivers.

2. Farmers should use correct amounts of fertilizers and pesticides in the fields so that excessive amounts of these harmful agricultural chemicals are not washed into the rivers, lakes and ponds.

3. All the industries should treat the toxic wastes produced by them suitably to make them harmless before discharging them into rivers.

4. Water pollution prohibition laws which exist for the industries producing toxic chemical waste should be implemented strictly by the concerned authorities.

5. Garbage or household wastes should not be thrown into open drains, rivers, lakes or ponds. Dead bodies should not be thrown into rivers. Dead bodies should be cremated or buried properly to prevent pollution of water.

6. People should be made aware of the harmful effects of water pollution so that they may co-operate and help in preventing it. 

Conservation of water

As there is scarcity of fresh water in our country, we should conserve water by using it carefully, economically and avoiding is wastage. The various ways to conserve water or save water at home are as follows.

1. Turn off the tap immediately after use. Get the leaking taps repaired immediately.

2. Brush your teeth by filling water in a mug. Leaving the tap running while brushing the teeth may waste several litres of water.

3. Wash the utensils by filling water in a basin and not under the running tap. 

4. Use water from washing rice, pulses, vegetables and fruits after wearing the plants at home. 

5. Do not use the full flash from the cistern in the toilet when a half flush is sufficient.

Potable Water

The water which is safe for drinking is called potable water. 

Ways to make water potable

The various methods which can be used to make water potable are as follows. 

1. Water can be filtered to make it potable by using porcelain candle filter or electric water filter. 

2. Water can be made absolutely safe for drinking by boiling for sufficient time.

3. Chlorination is a commonly used chemical method for purifying water.

Pollution of river Ganga

The water of river Ganga has been highly polluted because the villagers, town, and cities which are situated on the banks of this very long river through large quantities of garbage, untreated sewage, toxic industrial vestige, dead bodies of infants and many other harmful things directly into the river. 

GANGA ACTION PLAN

WWF has found that Ganga is one of the most polluted rivers in the world. At present, the pollution level in many stretches of river Ganga is so high that no aquatic animals like fish etc can survive in it. The river is said to be dead at those places. An ambitious plan to cleanse the highly polluted river Ganga and save it, was launched in 1985. It is called Ganga action plan. The aim of Ganga action plan is to reduce the pollution level in the water of river Ganga. However, the increasing population and industrialization has already damaged this mighty and sacred river beyond repair.

LECTURE - 3 : CLASS VIII : SCIENCE : CHAPTER 15 : SOME NATURAL PHENOMENA

SEISMIC ZONES OR FAULT ZONES:

The weak zones of earth's crust which is more prone to earthquakes are called seismic zones. It is also known as fault zones. 

In India, the areas most affected or threatened by earthquakes are Kashmir, Western and central Himalayas, the whole of North-east, Rann of Kutch, Rajasthan and Indoh gangetic plane. Some areas of South India is also prone to earth-quakes. 

SEISMOGRAPH: THE EARTHQUAKE MEASURING INSTRUMENT.

Seismograph is an instrument which measures and records the magnitude of an earthquake in terms of the shock waves it produces. 

Construction of Seismograph or Seismometer:

A seismograph consists of a heavyweight like a heavy metal ball suspended from a support with the help of a strong wire. The support is attached to the base of the seismograph and the base is rigidly fixed to a solid rock on the surface of the earth. A pen is attached to the the lower end of the hanging heavyweight.  It is used to draw graphs on the graph paper which is wrapped around a rotating drum. When earthquake occurs the pen draws graphs on the graphsheets due to the oscillation of the heavy object. From this graph we can measure earthquakes.

FOCUS AND EPICENTER OF EARTHQUAKE:

The place inside the earth's crust where the earthquake is generated, is called 'focus' of the earthquake. 

The point on earth's surface directly above the focus is called epicenter. 

MAGNITUDE OF EARTHQUAKE AND RICHTER SCALE:

The magnitude or intensity of an earthquake is expressed on the Richter Scale.

In a Richter scale 1 to 12 numbers are assigned to express the magnitude of an earthquake. 

Suppose the magnitude of an earthquake is 3 on the Richter scale, and magnitude of another Earthquake is 4 on the Richter scale, then the second earthquake is 10 times more intense than first earthquake. 

The magnitude of earthquake having 4 in Richter Scale is ten times more than the magnitude of the Earthquake having 3 on the Richter scale.

The Earthquakes having magnitudes higher than 7 on the Richter Scale are called destructive Earthquake. 

PROTECTION AGAINST EARTHQUAKE:

Earthquakes are highly destructive and it cannot be predicted. Therefore, we should always take some precaution against earthquake.

1. All the houses and other buildings in seismic zones should be designed and constructed in such a way that they can with stand measure earthquake tremors.

2. In highly systemic areas the use of mud and timber for building houses is better than using heavy construction materials. 

3. The cupboards and shelves should be fixed to the world's so that they do not fall easily when shaking occurs during an earthquake. Glass bottles should not be placed on high shelves and heavy objects should be placed low to the ground.

4. The objects such as heavy mirrors, photo frames, wall clocks and water heaters should be mounted securely on the world at such places in the house that they do not fall on the people in the house in the event of an earthquake.

5. All buildings should have fire fighting equipment in working order because some buildings may catch fire during an earthquake due to electric short circuits. 

PRECAUTIONS TAKEN WHEN EARTHQUAKE OCCURS:

A. If we are at home when an earthquake occurs.

We should take the following precautions.

1. We should take shelter under a study table for a kitchen counter and stay there till the shaking due to earthquake stops and we should cover our head with hands.

2. We should stay away from tall and heavy objects so that if they topple they may not for on us. We should also stay away from glass windows that may shatter due to vibrations.

3. If we are in bed, we should just move on the bed to be close to a wall but not get up from the bed. We should protect our head with a pillow.

B. If we are outdoors when an earthquake occurs.

We should take the following precautions.

1. We should stay at a clear spot away from buildings, trees and overhead power lines etc. We should also seat on the ground.

2. If we are in a car or bus, we should not come out of it. The car or bus should be driven slowly to a clear spot away from buildings, trees and overhead electric wires etc. We should not come out of the vehicle till the tremors stop.