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 (Pi) = m u
Final momentum of the body (Pf) = m v
Now, change in momentum of the body = Pf – Pi = 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 \(\left( {\because a = \frac{{(v\, - \,u)}}{t}} \right)\)