derive expression for law of conservation vof momentum
Answers
Answer:
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.
Explanation:
suppose object A has mass m1 and its initial velocity is u1. An object B has mass m2 and initial velocity u2.
According to the formula of Momentum, the initial momentum of A is m1 u1 and that of B is m2 u2.
Let the force after the collision of these objects be F1. This force will cause acceleration in A and its velocity will be v1.
Therefore, Momentum of A after collision= m1 v1
According to Newton's third law of motion, A also exerts an equal force on B in opposite direction. This will cause a change in the Momentum of B. If its velocity after collision is v2,
The momentum of B after collision = m2 v2. If F2 is the force that acts on the object B, F2 = -F1
m2 a2 = - m1 a1 ----------since F = ma
m2× (v2-u2)/t = -m1 × (v1-u1)/t -------------since a = (v-u)/t
m2(v2-u2) = -m1(v1-u1)
m2 v2 - m2 u2 = -m1 v1 + m1 u1
(m2 v2 + m1 v1) = (m1 u1 + m2 u2)