Question

Croquet ball A moving at 8.9 m/s makes a head on collision with ball B of equal mass and initially at rest. Immediately after the collision ball B moves forward at 5.0 m/s .

What fraction of the initial kinetic energy is lost in the collision?

Answer 1

mass of ball A (m_A) = m
Mass of ball B (m_B) = m
Initial velocity of ball A (u_A) = 8.9 m/s
Initial velocity of ball B (u_B) = 0 m/s
Now the initial momentum of the system = m_Au_A = 8.9m ------------(1)
Final velocity of the ball A = V_A
Final velocity of the ball B (V_B) = 5 m/s
Final momentum of the system = m_AV_A + m_BV_B = mV_A + 5m ----------(2)
Applying conservation of momentum
mV_A + 5m= 8.9 m
V_A = 3.9 m/s
Now initial kinetic energy(K_i) = (1/2)mu_A² = (1/2)m*8.9²   = 39.605m --------(1)
Final kinetic energy (K_f)= (1/2)mV_A² + (1/2)mV_B² = (1/2)m*(3.9²) +(1/2)*(m*5²) = 20.105m ------------(2)
Now the
K_f /K_i = 20.105/39.605 = 0.51
Therefore lost kinetic energy = 1-0.51 = 0.49
hence 0.49 fraction of initial kinetic energy is lost.