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5 October, 02:36

Two carts undergo an inelastic collision where they stick together. Cart A has an initial velocity v0, and the second cart B is initially at rest. After the collision, it is observed that the ratio of the final kinetic energy system to its initial kinetic energy is KfK0 = 1/6. Determine the ratio of the carts' masses, mBmA. (Assume the track is frictionless.)

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  1. 5 October, 03:59
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    Initial kinetic energy of the system = 1/2 mA v0²

    If Vf be the final velocity of both the carts

    applying conservation of momentum

    final velocity

    Vf = mAvo / (mA + mB)

    kinetic energy (final) = 1/2 (mA + mB) mA²vo² / (mA + mB) ²

    = mA²vo² / 2 (mA + mB)

    Given 1/2 mA v0² / mA²vo² / 2 (mA + mB) = 6

    mA v0² x (mA + mB) / mA²vo² = 6

    (mA + mB) / mA = 6

    mA + mB = 6 mA

    5 mA = mB

    mB / mA = 5.
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