DYNAMICS

INTRODUCTION

In chapter 3, we discussed kinematics of moving bodies. In this chapter we will deal with dynamics of the bodies. Dynamics tells us answer to such question as: why do bodies move from rest and why do they accelerate or re accelerate? For such motion push or pull types external agency is required, which acts on a body in the motion either brings to the rest or external agency is required, which when acts on a body in a motion either brings it to  the rest or causes it to accelerate. On the other hand, if the external agency acts on a body at rest, the body will start to move. This pull or push is called force. Galileo Galilee (1564- 1642) studied the motion of bodies on an inclined plane and concluded that the body is continued to move with the same velocity if no external force acted on it. Later, Sir Isaac Newton (1642- 1727) studied the problem of motion in detail and enunciated three laws of motion, which cover the motion of all bodies- big or small. The three laws are named after him.

1.   NEWTON’S LAWS OF MOTION

The following three laws of motion were originally formulated by Newton and were first published in 1686.

1.   First law of motion: Every body continuous in its rest or of uniform motion in a straight line, unless external force act on it.

2.   SECOND LAW OF MOTION: The rate of momentum of a body is directly proportional to the impressed force and takes place in the direction in which the force acts.

3.   THIRD LAW OF MOTION: Action and reaction are always equal and opposite to each other.

2.   INTERPRETATION OF THE FIRST LAW

The first law of motion has two parts:

I)                Every body continues in its state of rest, unless external force acts on it.

II)            Every body continues in its state of uniform motion in a straight line, unless external force acts on it.

The first parts of the law are experienced everyday, because a body lying on a table continues to remain there until it is pushed (or pulled).

The second part of the law may seem contrary to our common experiences. A rolling ball comes to rest after sometimes. It should be realized that the ball comes to rest because of air- resistance and also due to the friction from the surface it rolls on.

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ELASTICITY

      

INTRODUCTION

Every thing around us, with us and without us is matter. Everything in the materials world consists of matter. Atmosphere, air, water, trees, rocks, flesh, blood, bones, etc are the examples. Matter is every where in nature. It occupies the space and knowledge about it can be obtained using our organs of sense and instrument. It has mass and/or possesses energy. It is not spirit.

Matter is composed of particles called molecules and atoms. The size of the typical molecules is about 3×10ˉ10 m. Mechanical properties of matter are the topics our study in this and in the following two chapters.

The quantity of matter is a given substance is called it mass. Mass remain same even when its volume, shape or size change due to the external force, provided we don’t loose matter in the process. For example, substance like wool, cotton, rubber etc. can be compressed or stretched by Applying external force. But their masses do not change. Liquid and gases also flow, but their mass remains constant.

Constituents if matter

Matter is made up of a very large number of molecules. Each kind of matter has its own distinctive molecules. A molecule, in general, is composed of smaller particles called atoms. Atoms of elements were supposed to be invisible and were regarded as elementary particles with which all matter was assumed to be building up. In the beginning of the last century researches established the existence of more elementary particles, e.g. electrons, protons and neutrons. In the modern theory of matter an atom is made of a nucleus and electrons revolve around it. The nucleus is made of protons and neutrons.

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VAN DE GAFF GENERATOR

A Van d Gaff generator is a device for generating very high voltage and collecting extremely high amount of charge. It is based on of discharging action of points and accumulation charges by a large hollow spherical conductor. In 1929, Robert J. Van d Gaff designed these machines, which was later named after him.

It consists of a large hollow metallic dome mounted on an insulating stand. There are two types pulley, one inside the dome and other is near the bottom as shown in the figure 32.17. A belt of insulating materials, e.g. Silk, goes over the pulley. The lower pulley is driven by an electric motor (or, by hand for a small demonstration machines). There are two metals brushes having a number of sharp needles near the two pulleys. The needles are pointed towards the belt without touching it. The upper brush is connected to the metallic dome from inside whereas the lower brush is connected to a source of high positive potential.

Because of the high electric field near the needles of the lower brush, the air molecules become charged due to discharging action of points and air in between begins to conduct. The positive charge forms those needles leak through those sharp ends and reaches the belt. The belt moves upwards and carries those sharp ends and reaches the belt. The belt moves upward and carries those charges up. When it reaches the upper brush needles, induction takes place and their interior of the dome develops negative charges and outer surface becomes positively charged to the same extent. Since the upper brush needles are connected to the interior of the dome, the positively charges on the belt are neutralized by the discharging action of those brushes. Thus, electricity neutral belt moves down on other side of the pulley. However, the outer part of the dome accumulates positive charges.

Thus, these machines continuously transfer positive charge of the sphere. Potential (we will study about it in the next chapter 34) of the dome increases continuously as the belt moves and its value may reach higher as 10^6 V until dielectric breakdown stars. After that, it can not be charged further as the air starts to conduct as this potential and charges leak to the earth or nearby metal through air. However, it is possible to increase further the amount of charge on the dome if we enclose it in a highly evacuated chamber.

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CONDUCTOR AND INSULATOR

All the materials are classified into two types- conductor and insulators- based on their ability to conduct charges.

a)   CONDUCTOR

Materials through which electricity (charge) can pass easily is called conductors. Metals, mercury, acidic water, human body, earth etc. are conductors of electricity. These can be charged by friction but the charges they gain don’t remain localized and spread over the whole surface.

 In metals outermost electrons in the atoms are almost free and may move throughout the metal. They are not bound to any particular atom. They can be treated as free electrons. They are the actual carries of electricity in metal. For example, 1c.c. of copper contain approximately 10^23 free electrons! That is why metals are good conductor of electricity. Silver is a very good conductor, so are copper, gold and aluminum.

INSULATOR

There are some materials which don’t allow   electricity to pass through them. Those are called insulators. Glass, wood, ebonite, silk, rubber, sculpture, air etc are insulator or non conductor of electricity. These can gain charges by friction but the charges cannot move to other parts and remain localized.

SURFACE DENSITY OF CHARGES

We saw that the charges distribute themselves over the outer surface of a conductor. But their distribution is not uniform over the surface. The distribution of charges on a surface is characterized by surface charge density at a point on the surface. It is defined as the amount of charge per unit area of this surface surrounding the point. If q is the amount of charge and a is the small area over which the charge is spread, the surface density of charge is given by

σ= q/a

It depends on the shape of the surface of conductor. If the surface has large curvature at some points, the accumulation of charge there is also large. For uniform curvature of the surface, the charge distribution is also uniform. It is also greatly affected by the presence of other conductor in the neighborhood.

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MEASUREMENT OF CHARGE

We can measure electric charge on a charged body with the help of a simple apparatus called electroscope. There are two types of electroscope and they can be used to measure charges and find their nature.

(a)           PITH- BALL ELECTROSCOPE

(b)          GOLD LEAF ELECTROSCOPE

(a)           PITH- BALL ELECTROSCO                                 A pith- ball electroscope consists of a pith- ball        suspended from a support by a single silk fiber) fig 32.6). Pith is a light and spongy materials extracted from the stream of some plants. If it is gilded (overlaid with thin covering of gold) it works better. To test whether the body has got charge it is brought near an uncharged pith- ball. The pith ball will be attracted towards it. If it touches the pith ball, they will be repelled. The repulsion is due to same kinds of charges shared after touching the body, To find the type of charge on it, the pith- ball is charged by known type. Suppose the pith ball is charged positively. The body whose nature of charge is to be determined is brought near. It will be repelled if it is positively charged and will be attracted if it has negatively charges on it.

(b)          THE GOLD- LEAF ELECTROSCOPE (GLE)

This is a sensitive instrument. It can be used to detect charge and its nature. It can also give us a roughly the amount of charges on the body. That is why it is commonly used for demonstration. A typically gold leaf electroscope is shown in the figure32.7.

It consists a vertical metal rod, with a metal disk on top, going inside through an insulated hole on the top lid of a glass box. The lower end of the rod has two thin gold leaves attached to it (Aluminums foils can also be used). The sensitivity of this instrument can be increased by passing two strips of tin foil on the inner side of the glass panes facing the leaves. The tin- foils cover the level of gold leaves and pass down to the base of the instrument so that the electroscope can be grounded. The utility of these foils is to cancel any influence due to outside charges.

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