Question

Derive newton's first and third law​

Answer 1

hi frnd

Newton 1st Law of motion

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A body continues to be in its State of rest or uniform motion along line unless it is acted upon by some external force to change the state.

i.e. acceleration , a = 0 => ∑F = 0

it means ∑Fx = 0, ∑Fy = 0, ∑Fz = 0

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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).

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 =  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)...