Derive Newton's second and third law of motion.
Answers
Hey Mate
The linear momentum of a body is given by:
p = mv
Now According to Newton’s 2nd Law of Motion:
Force is directly proportional to rate of change of momnetum, that is
F α dp/dt
F = k dp/dt
F = k d(mv)/dt
F = k md(v)/dt
F = k ma
Experimentally k =1
F = k ma
Which is the required equation of force.
third law of motion;
Consider an isolated system of 2 bodies A & B. An isolated system means where there is no external force acting.Now let F be the force acting on B by A & F be the force acting on A by B.Now rate of change of momentum of A =dpA/dt and rate of change of momentum of B =dpB/dt
thus FAB=dpB/dt (i)......
FBA=dpA/dt (ii)........
Adding 1 and 2 we get FAB+FBA=dpB/dt+dpA/dt =d(pB+pA)/dt
But if no force is applied momentum will also be 0 because no velocity will be there so rate of change of momentum will also be 0
thus d(pA+pB)/dt=0
therefore FAB+FBA=0
or,FAB=-FBA
(3RD LAW OF MOTION)
hope it helps you
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