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Elastic and Inelastic Collisions

AP Physics 1· difficulty 3/5

A 2.0 kg2.0~\text{kg} mass moving at 5.0 m/s5.0~\text{m/s} sticks to a 2.0 kg2.0~\text{kg} mass at rest. What fraction of the initial kinetic energy is lost?

  • A

    1/21/2

    check_circle
  • B

    All of it

  • C

    1/41/4

  • D

    1/31/3

Explanation

After collision (equal masses, one stationary): v′=v/2v' = v/2. So Kf=12(2m)(v/2)2=14mv2K_f = \tfrac{1}{2}(2m)(v/2)^2 = \tfrac{1}{4} m v^2 and Ki=12mv2K_i = \tfrac{1}{2}m v^2; the ratio Kf/Ki=1/2K_f/K_i = 1/2, so half is lost.

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