Concept of Force

 Force is the (physical) quantity which can change its initial state of a mass body whether in the uniform motion or at the rest. 

        From daily experience, we observed that the motion of a body is the net result of interaction with other bodies around it. So, a net interaction in quantitatively produced as the concept of the term 'force'; e.g.- When a player kicks the football, the football starts to move along the direction of the feet of the player. This football behaves in the motion state is due to the net result of interaction of the player with it. Here the football gets a rapid change in its initial momentum of the football due to the interaction of the player's feet with it. This suddenly change in momentum is directly related to a net quantity which produced by the player's feet termed as 'force', and gets the football in a motion state as a net result of action and reaction, (Every action has an equal and opposite reaction - Newton's 3rd Law). 

        Inertia is the property of restriction to change its original state for all substances; beginning from the smallest substances to the huge body, Universe which we consider as the infinite large. Any substance or body has its own inertia, and it can changed its original position only if an external net force which can overcome this restriction (i.e.,inertia) is applied. From this observation, we can concluded the Newton's 1st Law which is also known as 'Law of Inertia'.-- 'A mass body always tends to retain its original state or position'. So, a body required a net force to displace its initial position; e.g.,- a cubic wooden blog where laid on the floor can not displace its position unless you pushed or pulled, here such physical activity or quantity of push or pull is responded as the force.         

        According to Newton's 2nd Law of motion, a mass body can't change its initial state unless an external net force is applied. In other word, a mass body with the uniform motion can change its initial momentum when an external net force is applied. Hence the change in momentum is directly depend to the applied net force. 

         It is also stated that the rate of change of momentum of a mass body with the uniform motion is equal to the applied net force. 

Mathematically, it is expressed as 

Initial momentum, p1=mv1  

Final momentum,  p2=mv2   

where, m is a constant, v1 is the initial velocity, and v2 is the final velocity. 

Change in momentum = p2 - p1 = m(v2-v1)= ma ,    a= acceleration=change in velocity = v2 - v1 

The external applied net force is given by 

               f = ma 

Or,  also 

   f = dp/dt =ma,     p=mv , a=dv/dt 

      =d(mv)/dt = m dv/dt = ma 

International System of Units of a net force is Newton. It is denoted by the letter "N".  

When    m=1kg, a= 1 m/s^2                     Here,  ^ is used as an exponential symbol.

             f= 1kg*1 m/s^2                                       * is denoted the symbol of multiplication operator.

              = 1 kg m / s^2 = 1 Newton or N

It can concluded that 'when a mass body of 1 kg gets an acceleration of 1 m/s^2, then this produced net force is said to be 1 Newton or 1 N'. The unit 'Newton' is MKS (metre,kilogram,second) system of dimension of the force. In CGS (centimetre, gram, second) and FPS (feet, pound, second) systems, the units of the force are dyne and poundal respectively.   

Frame of Reference -  A set of  coordinate axes which attached to a specified body. It is also called as a  'reference frame'. In other words, a system relative to hich the motion of any object is described is called a frame of reference. There were considered two reference frames, viz- a) inertial frame of reference and b) non-inertial frame of reference. 

a) inertial frame of reference ---- (unaccelerated frames); if the frames are unaccelerated when relative with an unaccelerated  body, then the frames are said to be inertial frame of references. Example- our house is moving along with the surface of earth when it rotates about its rotational axis. Here this rotational heavenly body, i.e., the 'earth' is the inertial frame of reference.  

        From such an inertial frame of reference, we might be pictured a mass body is at the rest or in the motion. If the displacement or position of a mass body changes with an inertial frame of reference in an equal interval of time, then we can say that the mass body is in the motion or a motion state. On the other hand; if the mass body can not changed its initial position or displacement with the inertial reference frame in an interval of time, then it is said to be the mass body is at the rest. 

b) non-inertial frame of reference ---- ( accelerated frames); if the frames get an acceleration when relative with an unaccelerated body, these frame of references are said to be non-inertial frame of references. Example- In case of the earth revolves around the sun; if the sun is taken as at the rest, then the earth is said to be non-inertial frame of reference, because the earth moves along an elliptical path or orbit around the sun; i.e., the earth does not move with a constant linear velocity or speed around the sun. 

        According to Kepler's law of planetary motion, "the areal velocity of the radius vector with an elliptical path is a constant", i.e., the earth moves with a constant areal displacement in the equal interval of time  around the sun, though the earth consider to keep at a focus of the elliptical orbit. Since an elliptical path have two foci, the linear velocity of the earth will not a constant along the orbit, it will vary with an equal interval of time due to the earth sweeps out equal areas in equal times. So, here we considered the earth as non-inertial frame of reference.  

Thus, we need a reference frame when we measure a distance, or to determine whether a body is in the motion or at the rest. Every heavenly body or spaceship which found in our universe have a relative motions; if we assumed a mass body gets an acceleration from a reference body, then the mass body behaves in the motion state, i.e., an external net force is acted to the mass body and get a change in its initial momentum. If the average speed of its relative motion is constant, then the heavenly bodies characteristics as a rest state; a classical example is taken here that, if you sit at a seat in a moving bus, the person who sat at the front of you does not change to his position as running the bus. Here the relative displacement between you and him does not change as the bus moves continuously. This is pointed that you and him is at the rest within the bus, but the bus is in the moving or motion state if you reference the things outside the bus. Thus we can easily pictured whether a mass body is at the rest or in the motion.     


                                                                                                                  to be continue .......... 



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