Newton’s laws of motion:
For centuries the problem of motion and its causes was a central theme of natural philosophy,an early name for what we call physics.It was not until the time of Galileo and Newton,however,that dramatic progress was made.Isaac Newton,born in England in the year of Galileo’s death,is the principal architect of classical mechanics.He carried to full fruition the ideas of Galileo and others who preceded him.His three laws first presented (in 1686) in his philosophiae Naturalis principia mathematica,usually called the principia.In his principia Newton stated the three fundamental laws of motion,which are the basis of Newtonian mechanics.
Before Galileo’s time most philosopher’s thought that some influence or “force” was needed to keep a body moving.They thought that a body was in its “natural state” when it was at rest.For a body to move in a straight line at constant speed,for example they believed that some external agent had to continually propel it ;otherwise it would”naturally” stop moving.
If we wanted to test these ideas experimentally we would first have to find a way to free a body from all influences of its environment or from all forces.This is hard to do,but in certain cases we can make the forces very small.If we study the motion as we make the forces smaller and smaller,we shall have some idea of what te motion would be like if tyhe external forces were truly zero.
Let us place our test body,say a block,on a regid horrizontal plane.If we let the block slide along this plane,we note that it gradually slows down and stops.This observation was used,in fact,to support the idea that motion stopped when the external force ,in this case the hand initially pushing the block ,was removed.We can argue against this idea,however,by reasoning as follows.Let us repeat our experimental,now using a smoother block and a smoother plane and providing a lubricant.We note that the velocity decreases the more slowly than before.Let us used still smoother blocks and surfaces and better lubricants.We find that the block decreases in velocity at a slower and slower rate and travels farther each time before comming to rest.Youmay have experimented with an air track,on which objects can be made to float on a film of air; such a device comes close to the limit of no friction,as even a slight tap on one of the gliders can send it moving along the track at a slow and almost constant speed.We can now extrapolate and say that if all friction could be eliminated the body would continue indefinately in a straight line with constant speed.An external force is needed to set the body in motion,but no external force is needed to keep a body moving with constant velocity.
It is difficult to find situation in which no external force acts on a body.The force of gravity will act on an object on or near the earth,and resistive forces such as friction on air resistance oppose motion on the ground or in the air.Fortunately ,we need not go to the vacuume of distant space to study motion free of external force,because,as for as the overall translational motion of the body is concerned,there is no distintion between a body on which no external force acts and a body on which the sum or resultant of all the external force is zero.We usually refer to the resultant of all the forces acting on the body as the “net” force.For example ,the push of our hand on the sliding block can exert a force that contracts the force of friction on the block,and an upward force of the horizontal plane contracts the force of gravity.The net force on the block can then be zero,and the block can move with constant velocity.
This principal was adopped by newton as the first of his three laws of motion:
Newton’s first law:
“Consider a body on which no net force acts.If the body is at rest,it will remain at rest.If the body is moving with constant velocity it will continue to do so.”
Newton’s first law is really a statement about reference frames.In general,the acceleration of a body depends on the reference frame relative to which it is measured.However,the laws of classical mechanics are valid only in a certain set of reference frames,namely,those from which all observors would measure the same acceleration for a moving body.Newton’s first law helps us to identify this family of referance frames if we express it as follows:
“If the net force acting on the body is zero,then it is possible to find a set of reference frames in which that body has no acceleration.”
The tendency of a body to remain at rest or in uniform linear motion is called inertia,and newton’s first law is often called the law of inertia.The reference frames to which it applies are called inertial frames.You will recall from that discussion that observers in different inertial reference frames (moving with constant velocity relative to one another) all measure the same value of acceleration.Thus there is no just one frame in which the acceleration happens to be zero;There is a set of all inertial frames in which the acceleration is zero.
If there is a net interaction between the body and objects present in the environment,the effect may be to change the “natural’ state of the body’s motion.To investigate this,we must now examine carefully the concept of force.
Newton’s second law of motion:
Newton’s second law of motion deals with situations when a net force is acting on a body.It states that:
“When a net force acts on a body,it produces acceleration in the body in the direction of the net force.The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass.”
If a force produces an acceleration a in a body of mass m,then we can state mathematically that as:
a ∝ F
and a ∝ 1/m
or a ∝ F/m
or F ∝ ma
Putting k as proportionality constant we get
F= kma …..(1)
In SI units ,the value of k comes out to be one.Thus equation (1) becomes:
SI unit of force is newton (N).According to newton’s second law of motion:
“One newton (1N) is the force that produces an acceleration of 1ms-2 in a body of mass of 1 kg.Thus,a force of one newton can be expressed as:
1N = 1kg ×1ms-2
or 1N =1kgms-2
Newton’s Third law of motion:
Newton’s third law of motion deals with the reaction of a body when a force acts on it.Let a body A exerts a force on another body B ,the body B reacts against this force and exerts a force on body A.The force exerted by body A on B is the action force whereas the force exerted by body B on A is called the reaction force.Newton’s third law of motion states that:
“To every action there is always an equal but opposite reaction.”
According to this law,action is always accompanied by a reaction force and the two forces must always be equal and opposite.Note that action and reaction forces act on different bodies.
Consider the books lying on a table as shown in figure.The weight of the books is acting on the table in the downward direction.This is the action,The reaction of the table acts on the books in the upward direction.
Consider another example.Take an air filled balloon is set free,the air inside it rushes out and the balloon moves forward.In this example,the action is by the balloon that pushes the air out of it when set free.The reaction of the air which escapes out from the balloon acts on the balloon forward.A rocket moves on the same principle.When its fuel burns,hot gases escape out from its tail with a very high speed.The reaction of these gases on the rocket causes it to move opposite to the gases rushing out of its tail,