give derivation of Newton's second law of motion
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Newton's second law of motion :- Newton said " if body changes momentum with respect to time, force must be experienced by body and that force is the rate of change of momentum per unit time."
Let mass of body m is moving with velocity and after t times , velocity of it became .
then, initial momentum =
final momentum =
change in momentum =
according to Newton's law, force =
=
=
we know, from 1st kinematics equation.
so,
hence, is the formula generated with help of 2nd law of motion
Let mass of body m is moving with velocity and after t times , velocity of it became .
then, initial momentum =
final momentum =
change in momentum =
according to Newton's law, force =
=
=
we know, from 1st kinematics equation.
so,
hence, is the formula generated with help of 2nd law of motion
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Newton's 2nd law of motion states that ;
" The rate of change of momentum is directly proportional to the unbalance force in the direction of force "
Consider a body of Mass m having an initial velocity u. The initial momentum of this body will be mu. Suppose a force F acts on this body for time t & causes the final velocity to become v. The final momentum of this body will be mv. Now,the change in momentum of this body is mv - mu & the time taken for this change is t. So, According to Newton's First Law of Motion :
Recall the first equation of motion
v = u + at
Substitute this value in above one
Hence,
But we need to remove the proportionality symbol ,
In order to remove it we need to add an proportionality constant.
So,
k = 1
So,
Derived.
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