Chapter 1 Physical Environment Force Active Without Contact Force Active Without
Contact Introduction
A force which can be exerted by an object even from a distance (without touching each other) is called a non-contact force or force active without contact.
There is no physical contact between the object which exerts the force and the object on which the force is exerted. Examples of non-contact type forces are Gravitational force and Electro- static force.
The force exerted by a magnet is called the magnetic force. The magnetic force acts even from a distance. Hence, the magnetic force is also a force that is active without contact.
Gravity and Gravitation
To explain the causes of the various natural phenomena, such as planetary motion, the fall of Gravitation is the mutual attractive force between any two material bodies in the universe that have mass.
The gravitational force that acts between the earth and any other object nearer to it is called gravity. In other words, gravity is the earth’s gravitational pull on a body lying on or near it.
The gravitational force between two bodies is a force of attraction that acts even if the two objects are not connected by any means.
For example, it is the gravitational force between the sun and the earth which holds the earth in its orbit around the sun.
Since this force acts on objects from a distance (without there being a physical Sir Isaac Newton proposed the Law of Universal Gravitation to calculate the magnitude of such attractive forces. The law is also known as Newton’s law of Universal Gravitation.
Newton’s law of universal gravitation states that any two bodies in the universe attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The attractive force (F) between any two bodies having masses “m,” and “m”, separated by a distance “r” acts along the line joining the centres of two bodies and has the magnitude, F = Gm¹m²
where G is called Universal Gravitational Constant. The constant “G” is called “universal” because it does not depend on the mass of the bodies or the medium in which they are placed.
Also, it is not affected by heat, light, magnetic or electric fields etc. It is independent of the presence of other bodies.
contact), therefore, gravitational force or gravity is an example of non-contact force.
objects towards Earth’s surface, etc. scientists and
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1. The Law of Universal Gravitation
Sir Isaac Newton proposed the Law of Universal Gravitation to calculate the magnitude of such attractive forces. The law is also known as Newton’s law of Universal Gravitation.
philosophers put forward different hypotheses. But now we know that all these phenomena are the manifestations of gravity and gravitation.
That the weight of a body should be regarded as a force of attraction between the earth and that body, was an idea by Newton and some of his contemporary scientists.
It is the amount of gravitational force with which the earth pulls all the bodies near it. This is the reason that raindrops fall on the earth from the sky or shredded tree leaf falls on the ground.
Earth’s pull has been utilized in making spring balance, which measures the weight of the objects. Until the seventeenth century, the laws governing the celestial motions (e.g. planetary motions, revolving of the earth around the sun, etc.)
Were considered quite different from the laws practically governing the motions of the bodies on the earth. It was Sir Isaac Newton, who first pointed out that both motions might have the same origin.
The attractive force (F) between any two bodies having masses “m” and “m”, separated by a distance V’ acts along the line joining the centres of two bodies and has the magnitude,
where G is called Universal Gravitational Constant.
The constant “G” is called “universal” because it does not depend on the mass of the bodies or the medium in which they are placed.
Also, it is not affected by heat, light, magnetic or electric fields etc. It is independent of the presence of other bodies.
2. Unit of Universal Gravitational Constant (G)
A century after Newton’s death, astronomer William Herschel (1738 1822) discovered instances of far-distant stars that revolved around each other in strict accordance with Newton’s law of universal gravitation.
From the Law of Universal Gravitation, we have learnt that the gravitational force,
or,
Hence, a unit of G in SI unit is Newton.m² /kg² (that is, Newton.metre2 per kg² or N.m² /kg² )
And in CGS system unit of G is dyn.cm² /g² (that is , dyne.centimetre2 per gram² or dyne.cm² /g² )
3. Value of G
The value of G, as has been calculated from various experiments, in SI unit is 1011 N.m² /kg² and in
CGS unit is6.67/108 dyne.cm² /g²
In 1798, the English scientist Henry Cavendish (1731 1810) devised an experiment to determine the value of “G”. What he obtained is a value very close to this.
From the mathematical expression of the law of Universal Gravitation, we find that for a pair of two-point objects of masses “m,” and “m”, the force of gravitation decreases as “r” (which is the distance between the two objects) increases.
Since G is a constant, F will be zero only when ” is infinitely large. So we can consider that F will always be a number other than zero, however large the value of “may be.
But actually after a certain value of “, the value of F becomes very small and the force due to gravitation becomes insignificant. Another point needs to be clarified at this stage.
In the statement of the Law of Universal Gravitation, we have mentioned point mass and. the mathematical expression has been proposed accordingly.
But, when we consider celestial bodies like the earth, moon etc. which are not point masses, how can one use the above mathematical expression?
Actually, if the distance between the two objects is much more compared to the diameter of either of the objects, then the objects can be considered as point masses.
Besides this, the earth, moon, sun, stars, etc. have spherical shapes and their masses can be considered to be condensed at their geometric centre.
So, while considering the gravitational force between the earth and an object placed on the surface of the earth, the distance between them has to be taken as equal to the average radius of the earth (which is approximately 6370 kilometres).
4. Relation between ‘G’ and ‘g
The force of gravity (F) exerted by the earth on an object of mass 1 kg can be alternatively shown as follows:
Let, the mass of the earth = M kg Mass of the object = 1 kg Distance of the object from the earth’s centre, (r) = average radius of the earth = R
So, applying Newton’s law of gravitation, we can show that, Image-
Let us denote the force of gravity of the earth on an object of unit mass by “g”.
So,
Also, from the calculation (2) above, we see that the gravitational force with which the earth pulls an object of mass 1 kg is 9.797 Newton.
So, we can say that g= 9.797 Newton So, the force of gravity of earth on an object of mass “m” will be,
5. Motion (where ‘w’ is the weight of the object) and Acceleration due to Gravity
If we allow a ball to fall freely when released from a certain height, it falls vertically down on the surface of the earth.
It is our general observation that starting from rest, as the ball starts falling down, the speed of the ball increases with the passage of time.
So the ball falls down with acceleration. This acceleration is produced due to the action of the earth’s gravity.
The acceleration produced in an object due to the earth’s gravity is called acceleration due to gravity.
We already know that,
Force = mass x acceleration
or, F = m x a
When F is the force of gravity on an object of mass “m”, then,
So, we can show that the force of gravity on unit mass is equal to the acceleration due to gravity, denoted by “g”.
Acceleration due to gravity means the increase in velocity of a freely falling body with time which is caused by the force of gravity acting on it. ,
The value of ‘g’ varies from place to place. The average value of “g” in the SI unit is taken as 9.8 rp/s² and in the CGS unit 981 cm/s².
We have calculated earlier that g=GM/R² This means that magnitude of “g” at any point on the earth’s surface depends on the distance of that point from the centre of the earth.
The shape of the earth is not perfectly spherical. Hence, even if we place an object at sea level, the distance from the centre of the earth is not always the same, and it will be different at different places.
The value of “g” at the equator is 9.781 m/s² and that at the poles is 9.831 m/s². In Kolkata, the value of “g” is 9.788 m/s²; in New Delhi, it is 9.79 m/s²; in Mumbai, it is 9.786 m/s² and in Chennai, it is 9.784 m/s².
6. Difference and relation between Weight and Mass
The weight of a body (w) is the force with which the earth attracts it, whereas mass is the measure of the amount of matter in a body.
Now, Weight of a body = mass of the body x acceleration due to gravity or, w = m.g
SI unit of weight is the same as that of the force i.e., newton (N).
A weight of 1 kg mass is usually written as 1-kilogram weight (1 kg wt.). Similarly, the weight of a 10-gram mass is written as 10 g wt. and so on.
Some important points about the weight of a body:
- The weight of a body (w) can be zero if g is zero since mass (m) can not be zero.
- Since the value of g changes from place to place, therefore the weight of a body is not constant, i.e. it changes from place to place.
- Weight has magnitude and direction (towards the centre of the earth) both.
- At a given place, g is constant.
∴ At a given place w varies as mass (m). Thus weight is a measure of the mass of the body at a given place.
7. Value of acceleration due to gravity on the moon
The moon’s pull on an object on its surface is not the same as that of the earth. When an object is placed on the surface of the moon, the mass of the object (m) & G remains constant.
But the mass and radius of the moon are respectively 1/81 the 3/11 mass and the radius of the earth.
So, the mass of the M moon M = M/81 and the radius of the moon, r =3R/11 where M and R are the mass and radius of the earth respectively.
So, the Force of gravitation of the moon is only 1/6th of that of the earth.
We know that the weight of a body (w) is the force (Fmoon) with which the earth attracts it. So, for an object of mass “m”, we can write, F=m.g (where “g” is the acceleration due to gravity on earth).
When the same object is placed on the moon’s surface, the force (Fmoon) with which the moon attracts it is, F= m.gmoon (where the moon is the acceleration due to gravity on the moon).
Hence, we can show that Fmoon / F = g moon /g
But we have shown that Fmoon F = 1/6. Hence, gmoon/g=1/6
That means acceleration due to gravity on the surface of the moon is about l/6th of that on the surface of the earth.
8. Falling Bodies
Due to gravity, ail bodies lying within a certain distance above the earth, come down when they are released.
It is seen, usually, that a lighter body, e.g., a piece of paper, descends more slowly than a heavier object e.g., a piece of stone.
This is because when a body Is falling on the earth, the air resists its motion. When the heavier stone is falling,
Its weight prevails over the resistance offered by air So it comes down more quickly than the lighter object, which cannot overcome the resistance of air appreciably.
But, we should note that in absence of air, when there is no resistance, all bodies of different masses come down at the same time.
In fact, Galileo, the famous Italian scientist, demonstrated this phenomenon through an experiment in public.
From the top of the leaning tower of Pisa, Galileo simultaneously released two spheres of equal volume but of different masses (one made of wood and the other made of iron).
One was much lighter than the other. The people gathered there to witness this experiment saw that both spheres touched the ground almost at the same time.
Laws of Freely Falling Bodies
If you drop a stone from a cliff, in addition to gravity, air resistance acts on it. Hence not all bodies fall down freely.
When a body is falling on earth due to gravity in absence of air, there is no resistive force, and it is called a free-falling body.
A body is thus said to be falling freely or in a state of free fall when it is under the influence of gravity alone and no other force acts on it.
When bodies are in free fall, the acceleration due to gravity acting on them is the same and is independent of their masses.
Galileo established three laws for freely falling objects. The laws are:
1. In a vacuum, all bodies starting from rest fall with equal rapidity.
2. In a given time, the velocity acquired by a body falling freely from rest is directly proportional to time.
(This means that the speed of a freely falling body increases with the increase in the time of fall).
3. The distance traversed by a body falling freely from rest is directly proportional to the square of the time. (This means that the distance traversed by a freely falling body increases with the increase in time of fall)
Newton’s Guinea And Feather Experiment Newton’s Guinea And feather Experiment
Newton’s Guinea and feather experiment Newton’s Guinea and feather experiment proves the 1st law as mentioned above.
Newton in his experiment used a hollow glass tube in which a guinea and a feather were introduced.
When the tube was inverted with air in it, the coin was found to come down earlier than the feather.
After that, the air was drawn out from the tube and again the tube was inverted. Both the guinea and the feather this time were seen to fall at the same time.
So, we find that, in absence of any opposing forces, like air resistance, gravity causes all bodies (heavier or lighter) to fall simultaneously if they start to fall simultaneously from rest.
This means the earth always produces the same acceleration on every object.
10. Common Facts Due To The Action Of Gravity
1. It is our common experience that when an object is thrown vertically upward, its speed decreases with increasing altitude. Ultimately at a certain altitude, the speed becomes zero.
Then the direction of motion is altered and it comes back to the earth again. Acceleration due to gravity is directed towards the centre of the earth. So, while moving upwards, speed decreases with increasing altitude.
When the object starts falling down, acceleration occurs due to gravitational pull, and hence, the speed of fall increases with the time of fall.
2. If the same object is thrown upwards (as a projectile), making an acute angle (0) with the ground, under the action of gravity the direction and speed of the projectile will continuously change as
Moving along a curved path, the projectile ultimately comes back to the ground after traversing some horizontal distance.
3. If a stone is thrown with greater and greater force, then a situation will arise when the object will not return to the earth due to balancing between its velocity and gravitational pull by the earth.
It will then start revolving around the earth. During its revolution around the earth, along a path of circular trajectory, its velocity will change continuously due to changes in its direction
4. Artificial satellites: Man-made objects which revolve (or orbit) around the earth in outer space are called artificial satellites.
Aryabhatta (the first artificial satellite successfully launched by India), Bhaskara, Rohini, INSAT-1A etc. are some of the satellites launched by India.
Artificial satellites are “thrown” with a very great speed and they revolve around the earth. Moon is a natural satellite of the earth and also revolves around the earth following the same principle.
5. Escape Velocity: When a body is projected upwards, it comes down to the earth after some time due to the earth’s gravitational attraction.
So, one may think, whether it is possible to throw a body with such a velocity, that the body will not return to the earth again.
For an object to escape from the earth and never return, it must be launched with a velocity, which will take the body beyond the gravitational field of the earth. Such velocity is known as Escape Velocity”.
It Is defined as the least velocity with which a body must be thrown vertically upwards In order that it may just escape the gravitational pull of the earth. The value of escape velocity is estimated to be 11.2 km/s or approximately 7 mile/s.
Electrostatic Force and Charge
1. Introduction to static electricity
When a plastic ruler is rubbed against dry hair or a woollen sweater for some time and then brought near to the small pieces of paper, we find that the paper pieces are flying towards.
The plastic ruler and sticking to it, as if the ruler is attracting them like a magnet, although they are not in contact with each other.
Another example of such a phenomenon is that a metal knife or blade does not attract pieces of Thermocol.
But immediately after cutting a sheet of thermocol with that knife or blade, it attracts small pieces of thermocol.
When an inflated balloon is rubbed against a woollen sweater, it sticks to the sweater.
So it is found that if knife or blade or plastic ruler etc.
are rubbed with another object for some time, and only then do they acquire the capability of attracting other objects.
It is interesting to note that ancient Greeks knew that when amber, a fossilized gum, is rubbed against wool, it acquired the property of attracting light objects like small leaves, dry straw etc.
Dr William Gilbert in the seventeenth century showed that glass on rubbing against silk, ebonite on rubbing against cat’s skin or sealing wax on rubbing against wool also acquire this property.
The substances which develop this property are said to be charged or electrified and the process is called electrification.
The formation of “charges” is evident from the following example. In winter, when we take off our clothes (made from synthetic materials like nylon, terylene, etc.) in darkness, we may see sparks (caused by electrical charges) fly off our bodies.
Similarly, if we comb dry hair in darkness while standing in front of a mirror, we will see sparks coming out from the hair.
So, we have found that a number of different objects can be charged by rubbing them with suitable materials. Let us now understand the nature of the electric charge produced on the objects.
Coulomb’s Law
We have just learnt that like charges repel each other and unlike charges attract each other. Attraction or repulsion occurs due to a force called electrostatic force.
The force exerted by an electrically charged object is called electrostatic force. An electrically charged object can exert an electrostatic force on an uncharged object or another charged object.
The electrostatic force can be exerted by a charged object on another object from a distance (even when they are not in contact with each other). So, an electrostatic force is an example of a non-contact force.
French scientist Charles Augustin invented the following formula to calculate the magnitude of force existing between two charged particles.
where, F is the electrostatic force of attraction or repulsion between two particles having the amount of charge q1 and q2on them, separated by a distance “r”. “k” is a constant whose value depends on the nature of the intervening medium between the two charged particles.
For example, the value of “k” is different for dry air, water and vacuum.
The unit of “F” is dyne (in the CGS system); [Symbol = ‘dyn’]. The unit of “r” is cm (in the CGS system) and the unit of charge is e.s.u. or statcoulomb.
∴The unit of “k” is dyne.cm² /(e.s.u)² according to the CGS system.
If the electrostatic force of repulsion between two like point-charges separated by a distance of 1 cm in a vacuum is 1 dyne, then the charge on each point-charge is 1 e.s.u. or 1 statcoulomb.
If vacuum (or air) is the medium and the quantities are measured in the CGS system, then k = 1.
SI unit of charge is coulomb; a unit of force is Newton; a unit of V’ is metre. So the unit of “k” is Newton.m² / (Coulomb)².
If the electrostatic force of repulsion between two like point-charges separated by a distance of 1 m in a vacuum is 9 x 109 Newton, then the charge on each point-charge is 1 coulomb.
For all practical purposes, ‘k’ is taken to be equal to 9 x 109 Nm² /C2 according to the SI system. From Coulomb’s law, we realize that,
1. Keeping the distance between the two point charges fixed, if the amount of charge on the point charges increases, the electrostatic force also increases.
For example, if the amount of charge on one point- charge is doubled and the amount of charge is tripled on the other, the electrostatic force will be increased by (2 x 3) times or 6 times.
2. Keeping the number of charges on two point-charges fixed, if the distance between them is increased, the electrostatic force will decrease and vice versa.
For example, if the distance between the two point charges is halved, the electrostatic force will be increased Similarly, if the distance between them is doubled, the electrostatic force will be (1/2)2 or l/4th of the former.
Electrification Due To Rubbing
We already know that All things are made up of atoms.
An atom consists of three types of subatomic particles – electron, proton and neutron. (The only exception is the hydrogen atom which does not have a neutron.)
Electron has a unit negative charge on them, a proton has a unit positive charge and a neutron is uncharged.
In an atom, sum total of the positive charge of all the protons is equal to the sum total of the negative charge of all electrons. So an atom is neutral, which means the net charge in an atom is zero.
Protons and neutrons form the central core of the atom, commonly called the nucleus. The electrons revolve around the nucleus in fixed orbits.
Electrons close to the nucleus are strongly held by electrostatic attraction. But the electrons away from the nucleus experience less attractive force and so electrons in the outermost orbit are loosely held.
When two objects (say A and B) are rubbed against each other, the loosely held electrons in the outermost orbit of one object (say, A) come out and are transferred to the other object (B).
After losing electrons, A has less number of electrons than the number of protons in its nucleus. So A becomes positively charged.
After gaining electrons, the number of electrons of B becomes more than the number of protons in its nucleus. So, B becomes negatively charged.
The number of electrons lost by A is equal to the number of electrons gained by B. So, equal but opposite charges are produced simultaneously in the two objects.
This transfer of electrons from one body to another takes place when these two bodies are rubbed and the cause of electron transfer is friction between the two bodies.
The process of charging a body is known as electrification and when it is done by rubbing one body over the other, it is called electrification by friction. The charge thus obtained is called frictional charge.
Charging A Body By Induction
Let us consider brushing dry hair with a plastic comb. After that, the comb is placed near small pieces of paper and we find that they are attracted.
We have learnt that opposite charges attract each other. The plastic comb can acquire a charge due to rubbing with dry hair.
But the small pieces of paper have not undergone any such rubbing. So, how can they acquire charges?
Actually, an uncharged object becomes charged when it is brought closer to any charged object.
This can be explained as follows.
Suppose a positively charged body (say, A) is brought nearer to an uncharged body (say, B). The negatively charged sub-atomic particles of B are attracted towards A and the positively charged sub-atomic particles of B are repelled by A.
As a result, the end closer to A becomes negatively charged and the other end of B becomes positively charged. Hence the positively charged A attracts the negatively charged end of B.
The process by which an uncharged body gets two electrically opposite ends when held near a charged body is called INDUCTION and the uncharged body is then said to be induced.
The charges on body B that are towards body A in, i.e. negative charges in this case, are called bound charges and the charges that are away from body A, i.e. positive charges in this case,
When the charged plastic comb is held near the pieces of paper, they are induced and get attracted to the plastic comb.
Motion due to Electrostatic Force From Newton’s law, we know that a change in the velocity of an object occurs due to the application of external force and acceleration takes place towards the direction of the applied force.
Similarly, we have learnt that like charges attract each other and opposite charges repel each other. This attraction and repulsion are also a kind of force.
Such force is termed an electrostatic force. The motion produced by electrostatic force can be found in the case of negatively charged electrons revolving around the positively charged nucleus inside an atom.
The nucleus contains positively charged protons. Since electrons and protons are oppositely charged while moving,
electrons are attracted towards the nucleus and the direction of their motion is bent towards the centre of the atom.
The planets revolving around the sun resemble this situation, but here the force of attraction is gravitational.
There is also a resemblance between the mathematical expression of the law of universal gravitation and Coulomb’s law.
But we should remember that “m” is replaced by “q” in the case of the latter. Also in the case of gravitation, the forces are always attractive whereas electrostatic force may either be attractive or repulsive.