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Wednesday, 11 September 2019

HEIGHTS AND DISTANCES

          The topic of height and distance in trigonometry is an important topic in competitive examinations point of view. Generally we have seen the problems where the height of a building is given and then from the top of this building the angles of elevation or depression are given for another building and we have to find the height of the second building. In this article we will cover these type of problems.

There are certain terms associated with the heights and distances which are described as follows:

Angle of Elevation: Let us consider a situation where a person is standing on the ground at point ‘O’ and he is looking at an object which is at some height (above the level of his eye) say the top of the building (P). The line joining the eye of the person with the top of the building is called the line of sight. The angle made by the line of sight with the horizontal line is called Angle of Elevation.
In this figure the line of sight is making an angle θ with the horizontal line. This angle is the angle of elevation.
Angle of elevation of P from O = AOP

Angle of Depression: Now let us take another situation where the person is standing at some height (O) with respect to the object he is seeing (P). In this case the line joining the line of sight of the man with the object is called the line of sight. The angle made by the line of sight with the horizontal line is called angle of depression.
 In the above figure ‘θ’ is the angle of depression.

Note: The angle of elevation is equal to the angle of depression.

The questions on this topic require some basic knowledge of Trigonometry. We should be aware of the basic trigonometric ratios and their values.
          Let us recall that the ratios of the sides of a right angled triangle are called trigonometric ratios. These are sine, cosine, tangent, cosecant, secant and cotangent.
Let the ΔABC is a right angled triangle.

Then Sin θ = Opp/Hyp = AB/CB
Cos θ = Base/Hyp = AB/CB
Tan θ = Opp/ Base = AB/AC
Cosec θ = CB/AB
Sec θ = AB/BC
Cot θ = AC/AB

Also we should know the values of these trigonometric ratios of some common angles as given in the following table:

0°
30°
45°
60°
90°
Sin
0
1/2
1/√2
√3/2
1
Cos
1
√3/2
1/√2
1/2
0
Tan
0
1/√3
1
√3
Infinite
The values in the given table will be useful while solving the questions on height and distances.
After going through some examples we will learn how to measure the height and how to find the distance.

Friday, 25 January 2019

Electrification of a Body (or) Electrification processes of bodies

          A body can be charged or electrified in many ways; the methods are discussed below:
a. Charging by friction
b. Charging by conduction or contact
c. Charging by induction
d. Electrification byh heating
e. Electrification by pressure

a. Charging by friction: When two nutral bodies are rubbed against each other, due to friction one of them losses electrons and hence gets positively charged and the body that ains electrons gets negetively charged.
Experiment: Take a small piece of uncharged plastic rod and cloth, rub against each other this will result both of them get charged. Same thing will happen between rubber rod and fur, Glass rod and silk cloth.

b. Charging by conduction: When a charged body is brought in direct contact with an uncharged body (or nutral body), it shares its charge with it. Thus the uncharged body becomes charged.

c. Charging by Induction: The process of temporary electrification of an initially neutral conductiong body (induced) by bringing a charged body (inducer) close to it without making any actual contact between the bodies is known as charging by induction.

d. Electrification by heating: Certain bodies, when heated, is electrified by presenting contrary electricities names in two diametrically opposite points. The phenomenon is called pyroelectric phenomenon. It is more common in crystalls, such as Tourmaline.

e. Electrification by pressure: Certain bodies, when compressed, is electrified, displaying electricities names against the ends. The phenomenon is called piezoelecttric phenomenon. It is also ore common in crystals, such as Tourmaline, Calcite, and Quartz. 

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Static Electricity

          Electricity is the phenomenon of flow of electric charges. The study related to the charges, when they are at rest is called as "Static electricity". Static electricity generates through friction.
          Greeks found that amber when rubbed with fur attracts small objects. The substances which on rubbing acquire the nature to attract lite objects are called as charged or electrified. The charged bodies possess electric charges by virtue of which they interact with each other. This force of interaction is called as "Electric force".

Some examples of static electricty are:

1) When we brush Dry hair with a plastic comb static electricity is produced. If we done it in a dark room we can also notice sparkles.
2) Similarly when we pass a comb through the dry hair, the hair will starts moving or stand.
3) We rub a plastic pen or a comb and placed near small pieces of paper they will get attracted.
4) Lightining is the best example of static electricity. Lighting causes due to the positive and negetive charges in the cloud.
5) We even can bend a stream of water using static electricity.


Uses:
There are several practical uses of static electricity, they are

1) Spray painting for car parts
          The spray nozzle is connected to a negetive electrode by this we can charge each droplet of paint. The car body parts is given a positive charge. When the paint is sprayed from a paint gun, the sprayed particles of paint will attracted by the car body parts. There are several more advantages by this method painting they are : (a) Paint goes to the charged body part not to the uncharged or nutral flor,  (b) Paint only attracted by body parts so less wastage, (c) there is no need of skilled labour for painting (d) the paint will distibuteded evenly so job will look neater.

2) Pollution control
          Static electricity is used in pollution control. Static charge is given to the dirt particles in the air and opposite charge is given to the collector. By this the dirt particles which are present in the air are attraced by the collector and pollution is controlled. These devices are called as "Electro static precepitators". Factories and thermal power plants use this kind of technique to reduce pollution coming from their smoke chimnies.

3) In photo copier







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