A block of mass m1 moving at speed v toward the west on a fr

A block of mass m_1 moving at speed v toward the west on a frictionless surface has an elastic head-on collision with a second, stationary block of mass m_2. Determine expressions for the final velocity of each block.

Solution

for elastic head-on collision:

U1 = v

U2 = 0

V1, V2 are final velocity of each block

for elastic collision:

U1 - U2 = V1 - V2, as e = 1

V2 = V1 + v

momentum conservation:

m1*v+ m2*0 = m1*V1 + m2*V2

m1*v = m1*V1 + m2*(V1+v)

(m1 - m2)*v = (m1 + m2)*V1

V1 = (m1 - m2)*v/(m1 + m2)

V2 = V1 + v = (m1 - m2)*v/(m1 + m2) + v

V2 = 2*m1*v/(m1 + m2)