Elastic and Inelastic Collisions

AP Physics 1· difficulty 4/5

Cart A (1.0kg1.0\,\text{kg}, 6.0m/s6.0\,\text{m/s}) collides perfectly inelastically with cart B (2.0kg2.0\,\text{kg}, at rest). The combined cart then strikes cart C (3.0kg3.0\,\text{kg}, at rest) elastically. What is the speed of cart C immediately after the second collision?

  • A

    vC=1.0m/sv_C=1.0\,\text{m/s}

  • B

    vC=3.0m/sv_C=3.0\,\text{m/s}

  • C

    vC=6.0m/sv_C=6.0\,\text{m/s}

  • D

    vC=2.0m/sv_C=2.0\,\text{m/s}

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Explanation

After step 1: combined mass 3.0kg3.0\,\text{kg}, speed 163=2.0m/s\dfrac{1\cdot6}{3}=2.0\,\text{m/s}. Elastic with equal masses: target velocity equals incoming, so vC=2.0m/sv_C=2.0\,\text{m/s}.

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