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CBSE Class 11-science Answered

can you tell me the newton second law of motion derivation  
Asked by Viswanathan | 18 Sep, 2019, 11:27: PM
answered-by-expert Expert Answer
Newton's second law states that  rate of change of momentum of a body is directly proportional to the applied force and
takes place in the direction in which the force acts.
 
Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv
i.e. its initial momentum p = m v changes by Δp = m Δv .
 
According to the Second Law,  begin mathsize 12px style F space proportional to space fraction numerator increment p over denominator increment T end fraction space space space space o r space space space F space equals space k space fraction numerator increment p over denominator increment T end fraction end style

where k is a constant of proportionality.
Taking the limit Δt → 0, the term Δp/ΔT becomes differential co-efficient  dp/dt  of p with respect to t.
 
Thus F = k (dp/dt)  ...............................(1)
 
if mass is not changing, we have dp/dt = m(dv/dt). 
 
Also we have (dv/dt) = a, where a is acceleration of the body which is subjected to force F.
 
Hence Eqn.(1) becomes   F = k m (dv/dt) = k m a ...................(2)
 
Let us choose units system as SI units and define 1 unit force as 1 Newton that produces acceleration 1 m/s2 on unit mass 1 kg.
 
Then k will become 1.
 
Finally, we write eqn.(2) in SI units as,   F = m a
 
Answered by Thiyagarajan K | 19 Sep, 2019, 07:52: AM
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