Question

Derive Law of conversation of linear momentum??​

Answer 1

Derivation of Conservation of Momentum

Consider two colliding particles A and B whose masses are m1 and m2 with initial and final velocities as u1 and v1 of A and u2 and v2 of B. The time of contact between two particles is given as t.

A=m1(v1−u1) (change in momentum of particle A)

B=m2(v2−u2) (change in momentum of particle B)

FBA=−FAB (from third law of motion)

FBA=m2∗a2=m2(v2−u2)t FAB=m1∗a1=m1(v1−u1)t m2(v2−u2)t=−m1(v1−u1)t m1u1+m2u2=m

Hope you understood!

Answer 2

Law of conservation of momentum states that when two objects collide with each other , the sum of their linear momentum always remains same or we can say conserved and is not effected by any action, reaction only in case is no external unbalanced force is applied on the bodies.

DERIVING THE LAW OF CONSERVATION OF MOMENTUM-

Let,

mA = Mass of ball A

mB= Mass of ball B

uA= initial velocity of ball A

uB= initial velocity of ball B

vA= Velocity after collision of ball A

vB= Velocity after collision of ball B

Fab= Force exerted by A on B

Fba= Force exerted by B on A

Now,

Change in momentum of A= momentum of A after collision - momentum of A before collision

= mA vA - mA uA]

Rate of change of momentum A= Change in momentum of A/ time taken

= mA vA - mA uA/t

Force exerted by B on A (Fba)=

Fba= mA vA - mA uA/t. [i]

In the same way,

Rate of change of momentum of B=

mV vB - mB uB/t

Force exerted by A on B (Fab)=

Fab= mB vB - mB uB/t. [ii]

Newton's third law of motion states that every action has an equal and opposite reaction, then,

Fab= -Fba [ ' -- ' sign is used to indicate that 1 object is moving in opposite direction after collision]

Using [i] and [ii] , we have

mB vB - mB uB/t = - (mA vA - mA uA/t)

mB vB - mB uB= - mA vA + mA uA

Finally we get,

mB vB + mA vA = mB uB + mA uA

This is the derivation of conservation of linear momentum.

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Hope it helps...!!!