Problem Statement
Two balls undergo a perfectly inelastic collision. Ball 1 (mass m) moves at v₀; ball 2 (mass m) is at rest. Find the fraction of kinetic energy lost.
Given
m₁ = m₂ = m. v₁ = v₀, v₂ = 0. Perfectly inelastic.
Concepts & Formulas
Momentum conserved: mv₀ = 2m·v’ → v’ = v₀/2. KE_initial = ½mv₀². KE_final = ½(2m)(v₀/2)² = mv₀²/4. ΔKE/KE_i = (½mv₀² − mv₀²/4)/(½mv₀²) = ½.
Step-by-Step Solution
Step 1: v’ = v₀/2.
Step 2: KE_i = ½mv₀².
Step 3: KE_f = ¼mv₀².
Step 4: Fraction lost = ½.
Worked Calculation
ΔKE/KE_i = 1/2.
Boxed Answer
Fraction of KE lost = 1/2
Physical Interpretation
Half the initial kinetic energy is converted to heat and deformation in a perfectly inelastic collision between equal masses — the maximum possible loss for this mass ratio.
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