Question

derivation of Newton's third law​

Answer 1

Answer:

⏩According to Newton , Every Action has it equal and opposite reaction ⏪

...... i.e action = - reaction .....

Negative shows the opposite direction ..

❤Details about 3rd law of motion❤

The action and the reaction Always act on two different objects...

m1×a1 = m2×a2...

since m1≠m2and a1≠a2

They may not lead the same magnitude of acceleration because the forces act on the different objects that may be have a different mass..

Answer 2

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 = dp1/dt ---------- (i)  

=> FAB = dp2/dt---------- (ii)  

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

FBA + FAB = dp1/dt + dp2/dt

⇒ FBA + FAB = d(p1 + p2)/dt  

If no external force acts on the system, then  

d(p1 + p2)/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).