define the conservation of momentum with derivation
Answers
Answer:
Explanation:
Derivation of Conservation of Momentum
Newton’s third law states that for a force applied by an object A on object B, object B exerts back an equal force in magnitude, but opposite in direction. This idea was used by Newton to derive the law 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=m1v1+m2v2
Therefore, above is the equation of law of conservation of momentum where m1u1 + m2u2 is the representation of total momentum of particles A and B before the collision and m1v1 + m2v2 is the representation of total momentum of particles A and B after the collision.