Collision (kinetic Energy Loss)

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Two identical masses stick together after perfectly inelastic head-on collision. Initial speeds 6 m/s and -2 m/s. Fraction of initial total kinetic energy lost?

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1. **Conservation of Momentum**: $m v_1 + m v_2 = (2m) v_f$.
   - $m(6) + m(-2) = 2m(v_f) \implies 4m = 2m(v_f) \implies v_f = 2$ m/s.
2. **Initial Kinetic Energy ($K_i$)**:
   - $K_i = \frac{1}{2} m (6^2) + \frac{1}{2} m (-2^2) = 18m + 2m = 20m$.
3. **Final Kinetic Energy ($K_f$)**:
   - $K_f = \frac{1}{2} (2m) (2^2) = 4m$.
4. **Loss Density**:
   - Energy Lost $= K_i - K_f = 20m - 4m = 16m$.
5. **Fraction Lost**: $\frac{16m}{20m} = 0.8$.
6. **Percentage**: $0.8 	imes 100\% = 80\%$.

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Collision (kinetic Energy Loss)

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