Irodov Problem 1.144 – Explosion of Stationary Body into Two Parts

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Problem Statement

A body of mass m at rest explodes into two parts of masses m₁ and m₂. The explosion releases energy E. Find the velocities of each part.

$$m_1v_1=m_2v_2,\quad \tfrac{1}{2}m_1v_1^2+\tfrac{1}{2}m_2v_2^2=E$$

Step 1: Momentum: m₁v₁ = m₂v₂ → v₁/v₂ = m₂/m₁.

Step 2: KE: ½m₁v₁² + ½m₂v₂² = E.

Step 3: v₁ = √(2Em₂/[m₁(m₁+m₂)]), v₂ = √(2Em₁/[m₂(m₁+m₂)]).

v₁ = √(2Em₂/[m₁m]) where m = m₁+m₂

$$\boxed{v_1=\sqrt{\frac{2Em_2}{m_1(m_1+m_2)}},\quad v_2=\sqrt{\frac{2Em_1}{m_2(m_1+m_2)}}}$$

The lighter fragment moves faster to conserve momentum. Total KE equals the explosion energy. Heavier fragments carry more momentum but less KE.