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Elastic and Inelastic Collisions

AP Physics 1· difficulty 4/5

A 3.0 kg3.0\,\text{kg} cart moving at 4.0 m/s4.0\,\text{m/s} collides head-on and sticks to a 2.0 kg2.0\,\text{kg} cart at rest. What is the speed of the combined cart and what fraction of the initial kinetic energy is lost?

  • A

    vf=2.4 m/sv_f = 2.4\,\text{m/s}, fraction lost =0.60= 0.60

  • B

    vf=4.0 m/sv_f = 4.0\,\text{m/s}, fraction lost =0= 0

  • C

    vf=2.4 m/sv_f = 2.4\,\text{m/s}, fraction lost =0.40= 0.40

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  • D

    vf=1.6 m/sv_f = 1.6\,\text{m/s}, fraction lost =0.40= 0.40

Explanation

Momentum: 3⋅4=5vf3\cdot 4 = 5 v_f, so vf=2.4 m/sv_f = 2.4\,\text{m/s}. Initial KE =24 J= 24\,\text{J}, final KE =12(5)(2.4)2=14.4 J= \tfrac{1}{2}(5)(2.4)^2 = 14.4\,\text{J}. Fraction lost =(24−14.4)/24=0.40= (24 - 14.4)/24 = 0.40.

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