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can you tell me the newton second law of motion derivation
Asked by Viswanathan | 18 Sep, 2019, 11:27: PM
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,

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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