Question

Deduction 3rd law from 2nd law of newton

Answer 1

Derivation of Newton’s third law of motion from Newton’s second law of motion

Consider an isolated system of two bodies A & B mutually interacting with each other, provided there is no external force acting on the system.  

Let FAB, be the force exerted on body B by body A and FBA be the force exerted by body B on A.

 

Suppose that due to these forces FAB and FBA, dp1/dt and dp2/dt be the rate of the change of momentum of these bodies respectively.  

Then, FBA =  d p 1 dt     ---------- (i)  

    => FAB =   d p 2 dt     ---------- (ii)  

Adding equations (i) and (ii), we get,  

FBA + FAB =   d p 1 dt +   d p 2 dt  

⇒ FBA + FAB = d( p 1 + p 2 ) dt      

If  no external force acts on the system, then  

d( p 1 + p 2 ) dt      = 0

⇒ FBA + FAB = 0

⇒ FBA = - FAB---------- (iii)  

the above equation (iii) represents the Newton's third law of motion (i.e., for every action there is equal and opposite reaction)...