Question

Two bodies of masses m1 andm2 are moving in straight line with velocities U1 and U2 respectively,collide each other.after collision the velocities of the bodies what will happen it? (i) the masses of the bodies are equal. (ii) one of the is at rest. (iii) lighter body is at rest (iv) heavier body is at rest​

Answer 1

Answer:

(i) the masses of the bodies are equal : velocities of bodies get exchanged

(ii) one of the is at rest (if both bodies have same mass) : final velocity of body at rest will be equal to initial velocity of the first body and the first body will come to rest.

(iii) lighter body is at rest : final velocity of the first body will be equal to its initial velocity and final velocity of the body at rest be 2 times the initial velocity of the first body.

(iv) heavier body is at rest​ :  the first body will rebound with the same velocity as came to hit the heavier body at rest and the heavier body at rest will continue to be at rest.

Explanation:

according to conservatiion of momentum

m1u1 + m2u2 = m1v1 +m2v2   - (i)

m1u1 - m1v1 = m2v2 - m2u2

m1(u1 - v1) = m2(v2 - u2)      - (ii)

ke is also conserved

$1/2(m1u1)^{2}$ + $1/2(m2u2)^{2}$ = $1/2(m1v1)^{2}$  +  $1/2(m2v2)^{2}$

(m1u1)^2 - (m1v1)^2 = (m2v2)^2 - (m2u2)^2