Problem Statement
A body at rest explodes into two fragments of masses m₁ and m₂. Fragment 1 has kinetic energy T₁. Find the total energy released Q.
Given
Body at rest, breaks into m₁ and m₂. T₁ given.
Concepts & Formulas
Momentum: p₁ = p₂ = p. T₁ = p²/(2m₁). T₂ = p²/(2m₂) = T₁m₁/m₂. Q = T₁ + T₂.
Step-by-Step Solution
Step 1: p₁ = p₂ = p (momentum conservation from rest).
Step 2: T₁ = p²/(2m₁).
Step 3: T₂ = p²/(2m₂) = T₁·m₁/m₂.
Step 4: Q = T₁(1 + m₁/m₂) = T₁(m₁+m₂)/m₂.
Worked Calculation
Q = T₁(m₁+m₂)/m₂.
Boxed Answer
Q = T₁(m₁ + m₂)/m₂
Physical Interpretation
The total released energy is simply T₁ scaled by the mass ratio — the lighter fragment gets more energy, so Q can be found from either fragment’s kinetic energy alone.
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