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Wondermath

  • 4 years ago

A cart with mass 0.340 kg moving on a frictionless linear air track at 1.2 m/s strikes a second cart of unknown mass at rest. The collision between the two carts is elastic. After the collision, the first cart continues in its original direction at 0.66 m/s. a) What is the mass of the second cart? b) What is the velocity of the second cart after impact?

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  1. TuringTest
    • 4 years ago
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    Momentum:\[P_{1i}+P_{2i}=P_{1f}+P_{2f}\]\[m_1v_{1i}=m_1v_{1f}+m_2v_2\]And for elastic collisions we have conservation of kinetic energy\[K_{1i}+K_{2i}=K_{1f}+K_{2f}\]\[\frac12m_1v_{1i}^2=\frac12m_1v_{1f}^2+\frac12m_2v_{2f}^2\]So we have a system of equations:\[m_1v_{1i}=m_1v_{1f}+m_2v_2\]\[m_1v_{1i}^2=m_1v_{1f}^2+m_2v_{2f}^2\]Two equations+two unknowns=solvable problem.

  2. Wondermath
    • 4 years ago
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    how come we don't use the two equations for elastic collisions|dw:1327884980480:dw| and the other one?

  3. TuringTest
    • 4 years ago
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    Maybe you can, that equation doesn't ring a bell for me offhand. I was just doing it the way it occurred to me.

  4. Wondermath
    • 4 years ago
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    oh ok thx

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