Classical Mechanics - Inelastic Collision

In a non relativistic, one-dimensional collision, a particle of mass 2m collides with a particle of mass m at rest. If the particles stick together after the collision, what fraction of the initial kinetic energy is lost in the collision?

A. 0
B. 1/4
C. 1/3
D. 1/2
E. 2/3

(GR0177 #04)

Solution:

Conservation of Momentum (inelastic collision):

m_av_a + m_bv_b = (m_a + m_b)v'

2mv_a + m · 0 = (2m + m)v'

2v_a =  3v'  → v'  = 2v_a / 3

KE_i − KE_f  = ( ½ m_av_a² + ½ m_bv_b² ) − ½ ( m_a + m_b ) (v' )²

= mv_a² − ½ ( 2m + m ) (2v_a / 3)²

= mv_a² − ⅔ mv_a²

= ⅓ mv_a²

  
Answer: C