Question

Deduce+the+law+of+conservation+to+nexton+3+law

Answer 1

Consider two objects A and B of masses m1 and m2 respectively, moving with initial velocity u1 and u2 such that u1>u2. After sometime the objects collide with each other and their velocities change to v1 and v2. Let 't' be the time for which both the objects remain in contact with each other and a1 and a2 be the acceleration produced by them.

According to Newton's 3rd law of motion,

F1➡= ⬅F2

m1 a1= -m2 a2(opp. direction)

m1 (v1-u1/t)=-m2 (v2-u2/t)

[since: acceleration= v-u/t]

m1 (v1-u1) =-m2 (v2-u2)

(t gets cancelled)

m1v1-m1u1= -m2v2 +m2u2

m1v1+ m2v2= m1u1+m2u2

(Total mome (Total mom

-ntum after = -entum bef

collision) ore collisio

-n)

Therefore: This proves that the total momentum of two objects is unchanged or conserved by the collision