Question

The two blocks of masses M and 2M shown initially travel at the same speed v but in opposite directions. They collide and stick together. How much mechanical energy is lost to other forms of energy during the collision? 

(A) Zero 

(B) 1/2 M v² 

(C) 3/4 M v² 

(D) 4/3 M v² 

(E) 3/2 M v²

Answer 1

Correct option (D) 4/3 Mv²  

Perfect inelastic collision. 

m₁v_1i + m₂v_2i = m_tot(v_f) … Mv + (– 2Mv) = (3M) v_f gives v_f = v/3. 

Then to find the energy loss subtract the total energy before – the total energy after 

[½ Mv² + ½ (2M)v²] – ½ (3M) (v/3)² = 3/6Mv² + 6/6Mv² – 1/6Mv²