Answer:
67%
Step-by-step explanation:
In the absence of external forces, the total momentum of the system before the collision is equal to the total momentum after the collision. Since the second ball is initially at rest, the total momentum before the collision is simply m*v.
After the collision, the two balls stick together and move with a common velocity, which can be calculated using conservation of momentum:
m*v + 0 = (m+2m) * v_final
Solving for v_final, we get:
v_final = v/3
The initial kinetic energy of the system is:
K_i = 0.5mv^2
The final kinetic energy of the system is:
K_f = 0.5*(3m)v_final^2 = 0.5(3m)(v^2/9) = 0.5m*v^2/3
The fraction of the initial kinetic energy lost on impact is:
( K_i - K_f ) / K_i = ( 1 - 1/3 ) = 2/3 = 0.67
Therefore, 67% of the initial kinetic energy is lost on impact.