Question

Explain the Mathematical formation of Second law of Motion or Newton's Second law

Answer 1

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According to the Second law the rate of change in momentum of a body in per unit time is directly proportional to the unbalanced force acting on it.


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Consider a body of mass (m) moving with initial velocity (u). Let a Force apllied on the body for time (t) so that object acquired velocity (v) after time (t).


Initial Momentum P¡ = mu

Final Momentum Pf = mv

Change in momentum = Pf - P¡

=》mv - mu

=》m( v - u )


Time taken to change this momentum

=》 ( t - 0 ) = t


Rate of Change of Momentum

=》 $\frac{Change\:Of\:Momentum}{Time Taken}$



=》 F $\alpha$$\frac{m( v - u )}{t}$ ...........(1)


=》 a = $\frac{v - u}{t}$


Force can be measured using Second law of Motion

So equation 1 can be written as

F $\alpha$m.a


F = Kma ............. (2)

where K is constant of proportionality

if

F = 1 unit
m = 1 unit
a = 1 unit
1 = K or h = 1


Put this value of K = 1 in the equation (2), we get

F = ma



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Hope this helps . . . . . . .