A 2.0 kg mass moving to the East at a speed of 4.0 m/s collides head-on in an inelastic collision with a stationary 2.0 kg mass. How much kinetic energy is lost during this collision?
A) 8.0 J
B) 16. J
C) 2.0 J
D) zero
E) 4.0 J

Question

Quizplus · Accepted Answer

In an inelastic collision, kinetic energy is not conserved. Initially, the kinetic energy is $ \frac{1}{2} m v^2 = \frac{1}{2} \cdot 2.0 \cdot (4.0)^2 = 16 $ J. After the collision, the two masses stick together and move with a common velocity $ v' $, which can be found using conservation of momentum: $ m_1v_1 + m_2v_2 = (m_1 + m_2)v' $. Substituting the given values, $ 2.0 \cdot 4.0 + 0 = (2.0 + 2.0) v' $, we find $ v' = 2.0 $ m/s. The final kinetic energy is $ \frac{1}{2} (2.0 + 2.0) (2.0)^2 = 8 $ J. The loss in kinetic energy is $ 16 - 8 = 8.0 $ J.

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