Fractional Loss of Kinetic Energy in Inelastic Collision – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Collision

Fractional Loss of Kinetic Energy in Inelastic Collision

A block of mass \( m \) moving with a velocity \( v \) collides with another block of mass \( M \) at rest. The two blocks stick together due to the collision. The loss of K.E. expressed as a fraction of total initial kinetic energy is:
\( \frac{M}{m+M} \)
\( \frac{m}{m+M} \)
\( \frac{M^2}{m+M} \)
\( \frac{M-m}{m+M} \)

Solution:

By conservation of momentum, the final velocity after a completely inelastic collision is \( v_f = \frac{mv}{m+M} \). The fractional loss of kinetic energy is \( \frac{K_i - K_f}{K_i} = 1 - \frac{\frac{1}{2}(m+M)v_f^2}{\frac{1}{2}mv^2} = \frac{M}{m+M} \).

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