how to derive newtons second formula of motion
Asked by s.sreeram
| 9th Dec, 2008,
06:35: PM
Newton's 2nd law of motion states that rate of change of momentum is directly proportional to the applied force and the change takes place in the direction of applied.
So accordingly, F = k dP / dt (here, k is the constant of proportionality)
Now, if a body of mass 'm' moving with initial velocity 'u' changes to final velocity 'v' in given time 't',
then, change in momentum ( dP ) = m ( v - u )
and rate of change of momentum ( dP/ dt ) = m ( v - u ) / t
now following from definition, F = k dP / dt = m ( v - u ) / t
or, F = K ma [ (v-u)/ t = a ]
when m= 1 kg , a = 1 m/s2 and F = 1 N,
K = 1
so, F = ma ; which is the formula or mathematical form of Newton's 2nd law of motion.
Answered by
| 9th Dec, 2008,
10:24: PM
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