NEWTON’S SECOND LAW OF MOTION

NEWTON’S SECOND LAW OF MOTION
1.    The rate of change of momentum of a body is directly proportional to the external force and the change in momentum takes place in the direction of the force.
2.    Newton’s second law of motion leads to a formula useful for measuring force.  \(\overrightarrow F = m\overrightarrow a \).
3.    Force is a vector.  It is always in the direction of change in momentum. Force is also always in the direction of acceleration.
4.    SI unit of force is newton (N).  If a force acting on a mass of 1 kg produces in it an acceleration of 1 m s^-2 in its direction, it is called a newton. 
5.    CGS unit of force is dyne.  If a force acting on a mass of 1 gm produces in it an acceleration of 1 cm s^-2 in its direction, it is called a dyne.
6.    One newton = 10⁵ dyne.
7.    Gravitational units of force:  kilogram weight (kg.wt) and gram weight (gm.wt) are called the gravitational units of force. 1 kg.wt or kg. f = 9.8 N,  
    1 gm.wt or gm.f = 980 dyne.
8.    To calculate a force ‘F’, there are several useful variants of the formula .
9.     \(F= {mv-mu \over t}\)   ,    10.\(F = m{dv \over dt}\) s    ,       11. \(F = v{dv \over dt}\)  

Derivation of F = ma : Consider a body of mass ‘m’ moving with initial velocity u. Let a force F acts on the body for time ‘t’ so that the velocity of the body after time ‘t’ is v
   
 Initial momentum of the body (P_i) = m u
Final momentum of the body (P_f) = m v
Now, change in momentum of the body = P_f – P_i = mv – mu = m (v – u)
Time taken for this change in momentum = (t – 0) = t
Rate of change of momentum = \(\frac{{change\,\,of\,\,momentum}}{{time\,\,taken}}\) =\(\frac{{m\,\,(v\, - \,u)}}{t}\) = m a       \(\left( {\because a = \frac{{(v\, - \,u)}}{t}} \right)\)