Physics Bullet question with sum of work

Question

A bullet A of mass m has an initial velocity v0 (vee nought). It strikes a block B (initially at rest on a smooth surface) and completely penetrates the block, emerging from the block with a velocity of 0.2v0 (that is, 20% of its initial velocity).

(a) Determine the velocity of the block after the bullet has emerged, and (b) Determine the total work done on the system by internal forces.

Answer 1

let M = mass of block

Initial momentum of bullet plus block

mV₀ +M*0 = mV₀

Momentum after Collision = m*0.2 V₀ +MV

here V = velocity of block after bullet passes through it

Using conservation of momentum

mV₀ = m*0.2V₀ +MV

Gives V =( mV₀ - 0.2 mV₀ )/M = Velocity of block after bullet emerges from block = 0.8 mV₀ /M

Total work done = Loss in Kinetic Energy = 1/2 mV0² - 1/2 m (0.2V₀)² - 1/2 (0.8mV₀ )²/M