Application of Physics to moving bodies

NEWTON’S LAWS OF MOTION

Newton’s First Law of motion: If the engine of a moving car is switched off, the car is suddenly brought to a rest by friction and air resistance. If such opposing forces were absent, it is believed that a body, once set in motion, would go on moving for ever with a constant speed in a straight line. That is, a force is not at all needed to keep a body moving with uniform velocity so long as no opposing forces or force act on it.

It was Galileo (1564-1642) who proposed this idea which arose from his two inclined planes experiments in which he found that a ball once allowed to roll down one smooth slope, it rose very nearly to the same height on the other. He felt that only friction stopped the ball from reaching exactly the same height on the second slope that it had started from on the first. He predicted that if the second plane was horizontal and if friction was absent altogether, the ball would go on moving for ever (or until a force stopped it).

Newton (1642-1727) developed further on Galileo’s work and virtually started from the point where Galileo had left and consequently, went into laying the foundation of his celebrated three laws of motion, the first law of course, being a summary of Galileo’s ideas. It states that: “Every body continues to be in a state of its rest or uniform motion in a straight line unless, being compelled by an external force to act otherwise.”

The question we should ask about a moving body is not ‘what keeps it moving’, but ‘what changes or stops its motion?’ The smaller the external force opposing a moving body, the smaller is the force needed to keep it moving with a uniform velocity.

Newton’s Second Law: This law states that: “The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts or applied.” What we can deduce from this law is that the acceleration (the rate of change of velocity) of a body is directly proportional to the unbalanced force acting on it and is inversely proportional to its mass whereas, the direction of acceleration shall be the same as that of the force. The simple mathematical equation for Newton’s second law is given as: F= ma.

Everyday Physics in Newton’s second law:

Newton’s Third Law: The genesis of this law is contained in the natural fact that forces never occur singly but always in pairs as a result of the action between two bodies. For example, when you step forward from rest your foot pushes backwards on the earth and the earth exerts an equal but opposite force forward on you. This simply boils down to the fact that in every case in nature, two bodies and two forces are involved. As in the above example, the small force that you exert on the large mass of the earth, gives no noticeable acceleration to the earth, but the equal force that the earth exerts on your comparatively a very much smaller mass, causes you to accelerate. But remember that the equal and opposite forces do not act on the same body, of course; if they did, there could never be any resultant forces and hence, acceleration would be impossible because; they could have simply amounted to canceling out each other.

This behaviour of forces is summoned up by Newton’s third law of motion which clearly states that: “To very action there is an equal and opposite reaction.” Say for example, If a body A exerts a force on a body B, then B exerts an equal and opposite force on A along the same line of action.

Everyday Physics in Newton’s third law of motion:

You really need to appreciate the third law and the effect of friction when stepping from a rowing boat. You push backwards on the boat and, although the boat pushes you forwards with an equal force, it is itself now moving backwards (because friction with the water is slight); this reduces your forward motion by the same amount – and you might fall in! Similarly,

If a gun is fired, a recoil is felt – so called a sort of a ‘kick’; the forward thrust of a projectile is matched by the backward thrust of the gun.

How Rockets work?

The principle of rocketry & Newton’s third law of motion:

The motion of a rocket is much like the motion of a balloon loosing air such that the escaping air from the balloon becomes a backward movement balanced equally by the forward movement of the balloon. Exactly similar is the phenomenon that governs the working of rockets and the science of rocketry as such and this is what that remains to be the essence of Newton’s third law of motion which states that for every action, there is an equal and opposite reaction.

The flow of the gas through the nozzle of a rocket that lies at its rear end produces a pushing force what we call as thrust away from the flow of exhaust gases from its nozzle. The said pushing force or forward thrust is produced as a consequence of the burning of the rocket fuel, better called as propellant that may be as solid or liquid propellant. In the rockets, using liquid propellant, the fuel that is generally a mixture of liquid oxygen and hydrogen is burnt in a separate chamber in the presence of an oxidizer being stored in a separate chamber and thus, both are burnt in a separate combustion chamber such that the force with which the exhaust of the gases from the fuel burning spurt out of the nozzle, an equal amount of forward thrust, the rocket will gain and hence, proving Newton’s third law of motion in exactness.

The Force of Friction

What is Friction? Friction is the resistance offered to the moving bodies or to the movement of one material against another. It could be any two materials one can think of.

The force of friction has such a utility in our life that many of the jobs and activities we carry on in our life would have been just impossible without friction being involved therein. Without friction, the belts of machines would slip, nails and screws wouldn’t hold, feet would not grip the floor or pavement and wheels of our automobiles would just spin without making things move anymore. Interestingly at the same time, in many cases, especially in machines, we actually try to reduce friction as much as possible. Why? The simple answer is to reduce the maximum wear and tear of the machine or its parts and to optimize the energy efficiency that is being used to run the machine.

So far the nature of friction in different material bodies is concerned, in the case of solid things; the friction is caused mainly by unevenness in the surfaces that touch each other. Thus, more smoother these surfaces are, the less will be the friction. Interestingly enough, friction between unlike materials is less than that between substances of the same kind. So, when we lubricate the surfaces say, when we oil the bearings of machines, we actually reduce the friction by substituting liquid friction for solid friction. The most common of the frictions we observe around are between solids which predominantly are of two kinds called as sliding and rolling friction.

The rolling friction is generally and invariably less than the sliding friction. That is why, the wheel was one of the man’s greatest inventions ever because; it made it possible to substitute rolling friction for sliding friction in pulling loads.

Consider the following analogy to understand the implications of substituting the rolling friction for sliding friction that man has achieved by inventing the wheel.

Suppose a large and heavy stone is being carried over a rough surface. It would take perhaps a dozen men to drag the same over the same surface by sliding friction. Now, if we put the same stone on rollers, it might then take just six men to pull the same stone over the same rough surface. Taking it further, if the same stone is now put on a cart provided with two wheels, it is very likely that only four men might do this job comfortably because, by using the cart, we now have passed on the so called sliding friction to the axle of the wheels and rolling friction over the same rough surface. In the next possibility, we now grease the axles and alternatively make the rough road smooth, quite likely that now only two men can pull the cart without much fuss. And lastly, we have now provided the cart wheels with ball bearings and thus, only one man can now move the same stone with much ease and comfort! This is how the friction has facilitated and does facilitate the many going-on in the material world.

Connecting concepts: Why do the airplanes or ships are being made the way they are? From what all that has been described above, it does not anywhere indicate to mean that the friction has a role to play in the solid objects only. In fact, water and air does create friction and in order to restrict or minimize the same, we have the body of our airplanes being streamlined to reduce the air resistance or so called air friction. In the same vein, the boats are being shaped the way they are so as to cut down water friction when a boat is being plied over the water surface….

The force of “Gravitation” & “Gravity

What is Gravitation?

Gravitation is the force of attraction that acts between all objects because of their mass – that is, the amount of matter they are made of. Because of gravitation, objects that are on or near the earth are pulled toward it. The gravity of the moon and the sun causes the ocean tides on the earth. Gravitation holds together the hot gases in the sun. It keeps the planets in their orbits around the sun, and it keeps all the stars in our galaxy in their orbits about its centre. The gravitational attraction that an object has for objects near it is called the ‘force of gravity’.

Although the effects of gravity are easy to see yet, an explanation for gravitational force has puzzled people for centuries. The ancient Greek philosopher Aristotle taught that heavy objects fall faster than light ones. This view was accepted for many centuries. But in the early 1600’s, the Italian scientist Galileo introduced a different view of gravity. According to Galileo’s theory, all objects fall with the same acceleration (rate of change of velocity), unless air resistance or some other force slows them down.

Ancient astronomers studied the motions of the moon and the planets. But these motions were not correctly explained until the late 1600’s, when the English scientist Sir Isaac Newton showed that there is a connection between the forces that attracts objects to the earth and the way the planets move.

Newton’s theory of gravitation: It says that the gravitational force between two objects is proportional (related directly) to the size of their masses. That is, larger the mass, larger shall be the force of attraction between such two objects. The theory refers to mass rather than weight because; the weight of an object on the earth is really the strength of the earth’s gravity on that object. On different planets, the same object would have different weights, but its mass would always be the same. Also, the gravitational force is inversely (oppositely) propositional to the distance between the centers of gravity of the two objects squared (multiplied by itself). For example, if the distance between the two objects doubles, the force, between them becomes a fourth of its original strength.

Expressed in the form of an equation, the gravitational force F=Gm¹m²/r² where ‘G’ is the universal gravitational constant, and ‘r’ is the distance between two bodies of masses m₁ and m₂ respectively.  

The universal gravitational constant (G) has its value determined at 6.67 x 10^-11. Incidentally and curiously enough, the value of G has so far been found to be the same in all parts of the universe.

This force i.e. gravitational force of attraction is always present between two bodies although, in many situations, when two bodies are extremely small and the distances are very small, this force is negligible in strength as compared to other forces (the electromagnetic force, the strong forces and the weak forces).

Newton published his theory of gravitation in 1687. Until the early 1900’s, scientists observed only one phenomenon that disagreed with the predictions of Newton’s theory. This was the motion of the planet Mercury, but factually, the disagreement was very small.

What is ‘Gravity’?

Gravity is the gravitational force between the earth (or other planet or satellite) and a body near its surface. This gravitational force (gravity) is measured as the weight of the body on earth (or planet). The term ‘gravity’ thus, must be used in a different sense from that of the term ‘gravitation’. While gravitation is a phenomenon which gives rise to a force of attraction between all bodies. Whereas, gravity is the measurable effect of the phenomenon of gravitation between a body and a planet. This implies that the term gravity is invariably being used to express the weight of a body on a planet. The weight of an object however, can also be expressed in terms of the acceleration due to gravity (g) experienced by a body near the earth’s surface.

Connecting concepts: How does a Body Fall Through Space?

Gravitation is the force which pulls every object in the universe towards every other object in the universe. It is the force that makes a body fall through space towards the earth.

It was not until the time of Galileo (1564-1642) that any effort was made to measure the effect of gravity. It was believed until that time that the speed with which a falling object struck the ground from any height depended, but on the weight of the object. In order to confirm this belief, Galileo went on to perform a small experiment.

Galileo dropped objects of different weights from the leaning tower of Pisa to show how the “force” of gravity caused them to fall & whether heavier objects fall earlier than the lighter ones.  He showed that a heavy weight and a light weight object when dropped together, reached the ground at the same time.

Galileo also rolled a ball down a slope slowly enough to measure its position at definite times. He found that the increase in the speed of the ball was proportional to the time it was rolling. This means that, at the end of two seconds, it was traveling twice as fast as at the end of one second, and, at the end of three seconds, it was traveling three times as fast, and so on.

He also found that the distance it traveled was proportional to the square of the time it spent traveling. (The square of a number is the number multiplied by itself). So at the end of two seconds, it was four times as far as at the end of one second. At the end of three seconds, it was nine times as far away, and so on. Taking a cue from Galileo’s discoveries and revealations,

Sir Issac Newton made the next great discoveries about gravitation. Newton assumed that the force which attracts any body towards the earth should grow less as the distance grows greater. Out of his studies and the observations of others came, Newton’s Law of Universal Gravitation. The basic idea of this law is that: “If the mass (amount of matter) of one of the two attracting bodies is doubled, the gravitational attraction will also be doubled; but if their distance apart is doubled, the force of gravitational attraction between such two bodies will be only one-fourth as great.”

Albert Einstein who finally came on the scene and attempted to answer the same predominant question “What is gravity?” by explaining that it is due to the shape of four-dimensional space-time. This is a very complicated theory requiring utmost scientific training to understand. His latest theory is related the gravitational “field”, to the electric, magnetic and electromagnetic fields. But we can say and attribute this to the frailty of human mind that actually, no one has yet been able to explain exactly what gravity is to everyone’s satisfaction.

We do know, however to the extent that the acceleration (increase in speed) caused by gravity is 10 metres per second each second. That means the speed of a falling body is increased 10 metres per second for each second it is falling. At the end of one second, it is dropping at a speed of 10 metres per second; at the end of two seconds, 20 metres per second; and so on. At the end of the first second, a falling object will be 5 metres down; at the end of two seconds, 20 metres, and at the end of 3 second, 45 metres.     

Application of Physics to ‘Space technology’

A spacecraft may make several kinds of trips into space. It may be launched into orbit around the earth, rocketed to the moon, or sent past a planet. For each trip the spacecraft must be launched at a particular velocity (speed and direction). The job of the launch vehicles is to give the spacecraft this velocity. If the spacecraft caries a crew, the spacecraft itself must be able to slow down and land safely on the earth.

Overcoming gravity is the biggest problem in getting into space. Gravity pulls everything to the earth and gives objects their weight. A rocket overcomes gravity by producing thrust (a pushing force). Thrust, like weight, can be measured in newtons or pounds. To lift a spacecraft, a rocket must have a thrust greater than its own weight and the added weight of the spacecraft. The extra thrust accelerates the spacecraft. That is, it makes the spacecraft go faster and faster until it reaches the velocity needed for its journey.

Rocket engines create thrust by burning large amounts of fuel. As the fuel burns, it becomes a hot gas. The heat creates an extremely high pressure in the gas. The gas leaves the rocket engine at high speed through the rocket nozzle. The reaction force created by the acceleration of the gas particles leaving the rocket engine causes the forward push on the rocket. This forward push on the rocket is the thrust, which is strong enough to lift the rocket from the ground.

Rocket fuels are called propellants. Liquid-propellant rockets work by combining a fuel, such as kerosene or liquid hydrogen, with an oxidizer, such as liquid oxygen (LOX). The fuel and oxidizer burn violently when mixed. Solid-fuel rockets use dry chemicals as propellants.

Engineers rate the efficiency of propellants in terms of the thrust that 1 kilogram of fuel can produce in one second. This measurement is known as the propellant’s specific impulses. Liquid propellants have a higher specific impulse than most solid propellants. But some, including LOX and liquid hydrogen, are difficult and dangerous to handle. They must be loaded into the rocket just before launching. Solid propellants are loaded into the rocket at the factory, and are then ready to use.  

Escaping Earth’s Gravity: What is Escape Velocity?

The moon lies within the earth’s gravity. But at the moon’s distance, the force of gravity is very weak. A spacecraft launched at 40,200 kilometers per hour – just 1,100 kilometers per hour greater than the speed necessary to reach the moon – can escape the influence of the earth’s gravity. The speed of 40,200 kilometers per hour which corresponds to 11.2 kilometers per second is called escape velocity. A spacecraft sent at this speed then comes under the influence of the sun’s gravity rather than Earth’s gravity which it has already escaped of and thus, goes into orbit around the sun; close to the earth’s orbit around the Sun.

The earth itself circles the sun in its orbit with a speed of 29.8 kilometers per second. A spacecraft launched form the earth also travels this fast in relation to the sun. The craft’s escape velocity is used up in getting away from the earth. It does not affect the speed of the spacecraft around the sun. Escape velocity can send the spacecraft into orbit around the sun. But it cannot send the craft to a planet.

Connecting concepts: How does an astronaut feel weightlessness and float about in his space craft?   

An astronaut orbiting the earth in a space vehicle with its rocket motors off is sometimes described a being ‘weightless’. If weight means the pull of the earth on a body, then the statement, although commonly used, is misleading. A body is not truly weightless unless it is outside the earth’s (or any other) gravitational field, whereas, in fact, it is the gravity only that keeps an astronaut and his vehicle in orbit.

On earth, we are made aware of our weight because, the ground (or whatever that supports us) exerts an upward push on us as a result of the downward push that our feet exert on the ground. It is in fact, this upward push essentially which makes us ‘feel’ the force of gravity.

An astronaut in an orbiting space vehicle is not unlike a passenger in a freely falling lift. The astronaut is moving with constant speed along the orbit, but since he is traveling in a circle he has a centripetal acceleration, which is of the same value as that of his space vehicle and is equal to “g” at that height. The walls of the vehicle exert no force on him; he is thus, unsupported and floats about with no apparent weight and hence, he appears to be ‘weightless’. To be strictly accurate, we should not apply the term ‘weightless’ to him, however, unless by weight we were to mean the force exerted on (or by) a body by (or on) its support.

Connecting concepts: Why do we feel weightlessness in a free falling lift?

When a lift suddenly stars upwards the push of the floor on our feet increases and we fell heavier, on the other hand, if the support is reduced when the lift starts moving downwards we seem to be lighter. In fact we judge our weight from the upward push exerted on us by the floor. If our feet are completely unsupported we experience weightlessness. Passengers in a lift which had a continuous downward acceleration equal to g would get no support from the floor, since they too would be falling with the same acceleration as the lift. There would be no upward push on them and they would feel to sensation of weight.