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Elastic and Inelastic Collisions

AP Physics 1· difficulty 4/5

m, v 2m, 0

A cart of mass mm moving at speed vv collides head-on and sticks to a stationary cart of mass 2m2m. What fraction of the initial kinetic energy is lost in the collision?

  • A

    23\dfrac{2}{3}

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  • B

    14\dfrac{1}{4}

  • C

    13\dfrac{1}{3}

  • D

    12\dfrac{1}{2}

Explanation

Final speed vf=mv3m=v3v_f=\dfrac{mv}{3m}=\dfrac{v}{3}. Ki=12mv2K_i=\tfrac{1}{2}mv^2, Kf=12(3m)(v/3)2=16mv2K_f=\tfrac{1}{2}(3m)(v/3)^2=\tfrac{1}{6}mv^2. Lost fraction =1−13=23=1-\tfrac{1}{3}=\tfrac{2}{3}.

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